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ECON224 Assignment for Overseas Students.
You have 24 hours to complete and submit this assignment. Work must be uploaded to Moodle by
1pm (GMT) on 11th December 2021.
Choose ONE question
1. With the aid of appropriate diagrams, show how a firm’s supply curves are derived using
an expansion path in: i), the short-run; and ii), the long-run. Explain why the answers to
i) and ii) differ. What are the implications for the firm?
2. Compare and contrast long-run equilibrium in a competitive market with that in a
market characterised by monopoly and their respective implications for consumer and
producer surpluses.
Equilibrium, Consumer & Producer
Surplus, Taxes & Subsidies
Econ 224: Week 4, Lecture, Michaelmas 2021-22
Dr Robert Read
Econ 224: Introduction to Economics for Managers
Equilibrium, Consumer & Producer
Surplus, Taxes & Subsidies
1.
2.
3.
4.
5.
Supply & Demand: Equilibrium
Changes in Equilibrium
Consumer & Producer Surplus
Market Efficiency
Taxes & Subsidies
Part 1: Equilibrium in Supply & Demand
Combining Demand & Supply
Demand and Supply curves can now be shown
together on the same diagram. This diagram has two
important features:
• The equilibrium price (p*).
• The equilibrium quantity (q*)
Equilibrium Price
•
The equilibrium price is the price that balances the
quantity supplied and the quantity demanded.
•
On the diagram, the equilibrium price is p*, where the
Demand and Supply curves intersect.
Equilibrium of Demand & Supply
p
S
p*
E
The equilibrium point E is
where the Demand and
Supply curves intersect –
at equilibrium price p* and
quantity q*.
D
0
q*
q
The ‘Law’ of Demand & Supply
The ‘Law’ of Demand and Supply states that:
• The price of any good will adjust to bring the quantity
supplied and the quantity demanded into balance.
• The price system is a form of communication system
that informs firms, entrepreneurs and consumers of
changing market conditions. This is the concept of
Adam Smith’s Invisible Hand – the automatic
adjustment of the market to equilibrium.
Market Disequilibrium
Markets are not always in equilibrium. In most cases
however, Demand and Supply automatically adjust to
restore equilibrium.
Market Disequilibrium: Excess Demand
When the quantity demanded at any price (p1) is greater
than the supply available ( q2 > q1 ), suppliers will raise
their prices ( p1 -> p* ) since too many buyers are chasing
too few goods – i.e., if q < q* then p < p*. Excess Demand p At price p1, Demand (q2) > Supply (q1). Firms
will raise prices to restore equilibrium E as
consumers will demand less.
S
E
p*
p1
Excess Demand
0
q1
q*
D
q2
q
Market Disequilibrium: Excess Supply
When the quantity demanded at any price (p2), is less
than the supply available ( q3 < q4 ), consumers are reluctant to buy and suppliers will lower their prices. Too few buyers are chasing too many goods (excess supply) – i.e., if q > q* then p > p*.
Excess Supply
p
At price p2, Supply (q4) > Demand (q3). Firms
will lower prices to restore equilibrium E as
consumers will demand more.
Excess Supply
p2
S
E
p*
D
0
q3
q*
q4
q
Part 2: Changes in Equilibrium Supply &
Demand
A New Equilibrium: Increased Demand
Changes in any of the determinants of Demand will
lead to a shift in the Demand curve and therefore
lead to a new equilibrium price/quantity combination.
For example, owing to the very hot weather in the UK
in July, there was an increase in Demand for ice
cream. This (temporary) change in taste led to an
increase in Demand and a rise in both the equilibrium
price and quantity (they move in the same direction).
A New Equilibrium: Increased Demand
p
S
An increase in Demand
(D0 to D1) raises both
the equilibrium price
(p0* to p1*) and quantity
(q0* to q1*).
p1*
p0*
D1
D0
0
q0*
q1*
q
A New Equilibrium: Increased Supply
Changes in any of the determinants of Supply will lead
to a shift of the Supply curve and a new equilibrium
price/quantity combination.
For example, the fall in the price oil in early 2020
reduced input costs for many goods. This change led
to an increase in Supply of these goods, so lowering
their equilibrium price (p and q move in opposite
directions).
A New Equilibrium: Increased Supply
p
S0
S2
An increase in Supply
(S0 to S2) raises the
equilibrium quantity
(q0* to q2*) and lowers
the equilibrium price
(p0* to p2*).
p0*
p2*
D
0
q0*
q2*
q
The Identification Problem
The Identification problem arises when too much
emphasis is placed upon too little information – in other
words, insufficient evidence to be certain. (This often
happens in business games.)
This problem can occur with either or both Supply and
Demand. For example, plotting the prices and sales of
ice cream in Morecambe for four days during the
Summer.
The Identification Problem
p
3
p3
p4
p2
p1
4
2
Observations
1. p1, q1: 31 May.
1
2. p2, q2: 30 June.
3. p3, q3: 31 July.
4. p4, q4: 31 August.
0
q1
q4
q2
q3
q
The Identification Problem
The diagram shows four different combinations of prices
and quantities for ice cream. Does this mean that the
Demand and Supply curves for ice cream have unusual
shapes and therefore behave unexpectedly?
The critical issue is that these points are different market
equilibria. Many of the variables that affect Demand also
affect Supply simultaneously – these are not different
points on the same Demand and Supply curves.
The Identification Problem
p
S3
S4
p*3
p*4
p*2
4
2
S2
D4
D2
1
q*1
1. p*1, q*1: 31 May.
2. p*2, q*2: 30 June.
3. p*3, q*3: 31 July.
D1
0
D3
Observations
S1
p*1
3
4. p*4, q*4: 31 August.
q*4
q*2
q*3
q
The ‘Cobweb’ Problem
The ‘Cobweb’ problem arises when there is a time lag
(delay) between decisions to produce a good and its
sale. In other words, Supply is very inelastic. Producers
choose output based upon their expectations about
future prices (next year, five years time etc. – hence
the use of forward markets).
If producers expect higher (lower) prices in the future,
they will increase (reduce) output. This may lead to
large price fluctuations as Supply and Demand are
never in equilibrium (hence ‘cobweb’). Examples
include mineral extraction (lead times of 5-10 years)
and agricultural crops (months or years).
Part 3: Consumer & Producer Surplus
Consumer Surplus
A market Demand curve for a good or service measures
consumers’ willingness (and ability) to pay. All consumers
would like to pay the lowest price possible since they
would be better off. Most consumers however, have
strong preferences and are therefore willing and able to
pay a higher price.
Consumer Surplus refers to the difference between what
a consumer is willing to pay and how much they actually
pay. It is therefore a good measure of consumer ‘wellbeing’.
Consumer Surplus: Step Diagram
Consumer Surplus can be illustrated by plotting the
willingness to pay and surplus of each consumer.
The Demand Curve therefore becomes a ‘step’ function
which takes into account each individual’s willingness to
pay.
Consumer Surplus: Step Diagram
p
Consumer Surplus: the
amount buyers are
willing to pay minus the
price they pay
Grace’s willingness to
pay – p0
p0
Paul’s willingness to
pay – p1
p1
Marty’s willingness to
pay – p2
p2
Jack’s willingness to
pay – p3
p3
p4
D
0
q1
q2
q3
q4
q
Consumer Surplus: Step Diagram
p
p0
Consumer Surplus: the
amount buyers are
willing to pay minus the
price they pay
Grace’s consumer
surplus at p1
p1
Paul’s consumer
surplus at p2
p2
Marty’s consumer
surplus at p3
p3
Jack’s consumer
surplus at p4
p4
D
0
q1
q2
q3
q4
q
Consumer Surplus: Step Diagram
p
If price is p4, total
Consumer Surplus is the
area below the demand
curve and above p4.
p0
p1
p2
p3
p4
D
0
q1
q2
q3
q4
q
Consumer Surplus
A downward sloping Demand Curve for a good or service
means that; as the price falls, increasing numbers of
consumers are willing to buy at the new lower price. This
increase in Consumer Surplus has two components:
• Those buyers who would have bought the good at a
higher price now pay less than they were actually
willing to do so.
• New buyers are now willing to buy the good at the
lower price, so the quantity demanded rises.
p
Consumer Surplus
As price falls,
Consumer
Surplus rises
Initial Consumer
Surplus
p1
Additional surplus of
existing consumers
Surplus of new
consumers
p2
D
0
q1
q2
q
Consumer Surplus
p
Consumer Surplus is
therefore the area below
the Demand Curve and
above the price line.
Consumer
Surplus
S
E
p*
D
0
q*
q
Producer Surplus
Producer Surplus works in exactly the same way; it
measures the benefit to firms or sellers in terms of the
amount they receive for a good or service (price) and
their costs.
Again, this can be illustrated on a ‘step’ diagram.
Producer Surplus Step Diagram
p
Producer Surplus: the
amount firms receive
(price) minus their costs.
S
p0
p1
p2
p3
p4
0
Lonsdale’s cost.
q1
q2
q3
q4
q
Producer Surplus Step Diagram
p
Producer Surplus: the
amount firms receive
(price) minus their costs.
S
p0
p1
Pendle’s cost.
p2
Fylde’s cost.
p3
Grizedale’s cost.
p4
Lonsdale’s cost.
0
q1
q2
q3
q4
q
Producer Surplus Step Diagram
p
Producer Surplus: the
amount firms receive
(price) minus their costs.
S
p0
Pendle’s producer
surplus at p0.
p1
Fylde’s producer
surplus at p1.
p2
Grizedale’s producer
surplus at p2.
p3
Lonsdale’s producer
surplus at p3.
p4
0
q1
q2
q3
q4
q
Producer Surplus
p
As price rises,
Producer Surplus
increases.
Additional surplus of
existing producers
S
Surplus of new
producers.
p2
p1
Initial Producer
Surplus
0
q1
q2
q
p
Consumer & Producer Surplus:
Competitive Equilibrium
Consumer and
Producer Surplus at
market equilibrium.
Consumer
Surplus
S
E
p*
Producer
Surplus
0
D
q*
q
Part 4: Market Efficiency
Market Efficiency: Competitive Markets
Is the allocation of resources that is determined freely
by competitive markets desirable?
Market Efficiency: Competitive Markets
Competitive markets:
• Allocate supply to those buyers who value it most,
measured by their ‘willingness to pay’.
• Allocate demand to those sellers that can produce at
least cost.
• Produce the quantity that maximises the sum of
consumer and producer surpluses.
Evaluating Market Equilibrium
Where a market is not competitive, the result may be
market power – that is:
• The ability of one or more producers to influence
prices (e.g., monopoly); i.e., raise them above the
efficient level and lower quantity below the efficient
level.
• The ability of one or more consumers to influence
prices (known as monopsony); i.e., lower them
below the efficient level and increase quantity
above the efficient level.
Free Markets vs Government Intervention
Market power therefore generally reduces consumer
surplus and increases producer surplus owing to the
market power of firms. This underlies the laissez faire
argument. Markets should therefore be left alone and
that governments should not intervene:
• Market equilibrium is argued to be the most efficient
– no other outcome generates greater total surplus.
• Governments therefore cannot raise total surplus by
altering the market’s allocation of resources.
Free Markets vs Central Planning
Suppose resources are allocated by a central planner
who cares about society’s well-being rather than by
the market.
To allocate resources efficiently and maximise total
surplus, they would need to know every seller’s cost
and every buyer’s utility function for every good and
service in the entire economy. This is impossible. By
definition, centrally-planned economies can never be
as efficient as a competitive market.
Free Markets vs Intervention:
Market Failure
This argument that competitive markets produce better
outcomes (i.e., they maximise Consumer + Producer
surpluses) depends upon the critical assumption that
they are always efficient. That is, that consumers and
producers have access to all relevant information and
that this informs their decisions.
If this is not the case, then there is Market Failure.
Market prices – and therefore production and
consumption – do not reflect all costs and benefits
(e.g., pollution, climate change).
Free Markets vs Intervention:
Market Failure
Many people who know a little (but not enough)
Economics (e.g., politicians), therefore believe that all
markets are efficient and do not know/understand that
markets may fail (often, ideological blindness).
The critical issue is therefore:
Can intervention improve market efficiency?
Part 5: Taxes & Subsidies
Taxes, Subsidies & Market Efficiency
Taxes and subsidies (and all other types of intervention –
e.g., tariffs) insert a ‘wedge’ between the price paid by
consumers in a market and the price received by sellers.
This means that in any new equilibrium, the market price
and quantity demanded are above or below the previous
‘efficient’ level. In other words, taxes and subsidies ‘distort’
the market in some way and therefore result in a
deadweight loss.
The Impact of a Tax
Imposing a tax on a good or service is equivalent to an
inward shift (to the left) of its Supply Curve i.e., the same
as a rise in the unit cost of production.
A tax therefore raises the equilibrium price and reduces
the equilibrium quantity demanded.
Illustrating the Impact of a Tax
p
St
S
p*t
E
p*
A tax shifts the Supply
Curve to the left (S to St).
This raises the price (p*
to p*t) and reduces the
quantity (q* to q*t).
D
0
q*t
q*
q
The Impact of a Tax
Imposing a tax on a good or service is equivalent to an
inward shift (to the left) of its Supply curve – equivalent
to a rise in the unit cost of production.
A tax therefore raises the equilibrium price and reduces
the equilibrium quantity demanded.
The vertical distance between the two Supply curves is
equal to the magnitude of the tax.
Illustrating the Impact of a Tax
p
St
S
p*t
Rate of
tax
Rate of
tax
E
p*
p’t
Consumers now pay p*t
while producers receive
p’t. The magnitude of the
tax is ( p*t – p’t ).
D
0
q*t
q*
q
Tax Revenue
The revenue raised by a tax is equal to the rate of tax t
multiplied by the post-tax quantity consumed q*t. The
tax rate can be found by identifying the intersections of
the new equilibrium quantity with the pre- and post-tax
supply curves.
Tax revenue
= tax rate t * q*t
= (p*t – p’t) * q*t
Illustrating the Impact of a Tax
p
St
Tax revenue
S
p*t
Rate of
tax
E
p*
p’t
Tax revenue is equal to
the tax rate times the
new equilibrium quantity
(p*t – p’t) * q*t
D
0
q*t
q*
q
Who Pays the Tax? – Consumers
Consumers pay that part of the tax revenue that lies
above the original equilibrium price:
= (p*t – p*) * q*t
Illustrating the Impact of a Tax
p
St
Tax paid by
consumers
S
p*t
Rate of
tax
E
p*
p’t
D
0
q*t
q*
q
Who Pays the Tax? – Producers
Producers pay that part of the tax revenue that lies
below the original equilibrium price:
= (p* – p’t) * q*t
Illustrating the Impact of a Tax
p
St
Tax paid by
producers
S
p*t
Rate of
tax
E
p*
p’t
D
0
q*t
q*
q
The Welfare Effects of a Tax
A tax reduces total surplus (Consumer + Producer
Surplus) because it introduces a distortion that shifts the
market away from its ‘efficient’ equilibrium.
A tax therefore results in a Deadweight Loss.
The Welfare Impact of a Tax
p
Consumer and
producer surplus
before a tax.
Consumer
surplus
S
E
p*
Producer
surplus
D
0
q*
q
Illustrating the Welfare Impact of a Tax
p
St
Consumer
surplus
Tax
revenue
A tax reduces
total surplus and
creates a
Deadweight Loss.
S
Consumer
surplus loss
p*t
Rate of
tax
E
p*
Producer
surplus loss
p’t
Producer
surplus
D
0
q*t
q*
q
The Deadweight Impact of a Tax
p
St
Tax
revenue
S
Consumer
surplus loss
p*t
Rate of
tax
E
p*
Producer
surplus loss
p’t
The deadweight
impact is the
loss of consumer
and producer
surplus (tax
revenue is
redistributed).
D
0
q*t
q*
q
The Welfare Effects of a Tax
The welfare effects of a tax comprise several separate
effects:
• A reduction in consumer surplus.
• A reduction in producer surplus.
• A transfer of tax revenue (from consumers and
producers) to Government.
• A deadweight loss in consumption.
• A deadweight loss in production.
The Deadweight Impact of a Tax
All taxes result in a loss of consumer and producer surplus
and the creation of deadweight loss. The magnitude and
distribution of these negative welfare effects between
consumers and producers however, depend upon the
elasticities of demand and supply.
Of particular interest in terms of economic policy is the
impact of taxes on consumers – and this is determined by
the elasticity of demand.
The Deadweight Impact of a Tax
The Deadweight impact of a tax will be greater the
more elastic is demand and supply:
• The greater will be the decline in quantity consumed
as a consequence of a tax (elastic demand).
• The greater will be the decline in quantity supplied
(elastic supply).
• The greater will be the deadweight loss of the tax
(loss of both consumer and producer surplus).
With each increase in the tax rate, the deadweight loss
rises more than proportionately to the size of the tax.
The Objectives of Taxes On Goods
Discussion of the impact of a tax should focus on its
objectives. There are generally two issues:
• To raise revenue.
• To reduce the quantity consumed.
These two objectives are inter-related; e.g., smoking – a
tax on cigarettes is designed to reduce their
consumption but also raises substantial revenue (which
might pay for extra NHS health care).
Taxation & the Elasticity of Demand
The effect of a tax on consumption is determined by
the Elasticity of Demand.
The lower the price elasticity (i.e., more inelastic), the
greater the impact of a tax on price and the lower its
impact on quantity demanded – and therefore the
greater the likely tax revenue. Consumers bear most of
the tax burden.
If Demand is relatively elastic, producers bear most of
the burden of the tax.
Taxation & Inelastic Demand
So…
Taxes are more likely to be levied on goods with
inelastic Demand since consumers and not producers
will bear most of the tax burden. The more inelastic the
Demand for a good, the greater the impact of a tax on
price and the smaller its impact on quantity demanded
– and the greater the likely tax revenue – maximising (pt
– p’t) * q*t.
Taxation & Inelastic Demand
p
St
Tax paid by
consumers
S
p*t
Rate of
tax
When Demand is
inelastic, the priceraising effect of a tax is
greater than its
quantity-reducing
effect. Consumers pay
most of the tax.
E
p*
p’t
Tax paid by
producers
0
q*t
D
q*
q
Taxation & Inelastic Demand
Taxes targetted at price inelastic goods therefore raise
more revenue. In addition, Demand for many ‘bad’
goods (cigarettes, petrol, alcohol etc.) is inelastic, such
that taxation reduces consumption and raises revenue
at the same time!
Note also that because consumers will bear a
disproportionate share of the tax burden, the tax is on
consumption not production.
Taxation & Elastic Demand
If the demand curve is relatively elastic then the impact
of a tax is to substantially reduce consumption for only a
small increase in price.
Taxes targetted at price elastic goods therefore raise
limited revenue – they are more a tax on production
rather than consumption.
The Deadweight Impact of a Tax
p
When Demand is
elastic, the quantityreducing effect of a
tax is greater than
its price-raising
effect. Producers
pay most of the tax.
St
Tax paid by
consumers
S
p*t
E
p*
Rate of
tax
Tax paid by
producers
p’t
0
q*t
q*
D
q
The Deadweight Loss of Tax Revenue:
the Laffer Curve
In the first instance, imposing a tax raises revenue. As
the tax rate continues to rise, the rate of increase of tax
revenue starts to fall (diminishing marginal tax revenue).
At some (very high) rate of tax, the quantity demanded
becomes so small that tax revenue falls. This relationship
is known as the Laffer Curve.
The Laffer Curve
Tax
revenue
Maximum
revenue
0
Tax rate
100%
The Impact of a Subsidy
Subsidising a good or service has the opposite effect of
imposing a tax. It leads to an outward shift (to the right)
of the Supply curve – equivalent to a fall in the unit cost
of production. The vertical distance between the two
Supply curves is equal to the magnitude of the subsidy.
A subsidy reduces the equilibrium price and increases
the equilibrium quantity demanded. It is either used to
promote production (help an industry or product) or
encourage consumption (e.g., environmental, health
benefits etc.).
What is the welfare effect?
The Impact of a Subsidy
p
A subsidy shifts the Supply
curve to the right (S to Ss).
This lowers the price paid by
consumers (p* to p*s) and
increases the quantity
demanded (q* to q*s).
p’s
Rate of
subsidy
S
Ss
Rate of
subsidy
E
p*
p*s
D
0
q*
q*s
q
The Impact of a Subsidy
p
Gain in Producer
Surplus
S
p’s
Ss
Rate of
subsidy
Rate of
subsidy
p*
Deadweight Loss
E
p*s
D
Gain in consumer
surplus
0
q*
q*s
q
The Impact of a Subsidy
The subsidy increases both consumer and producer
surplus (and therefore aggregate welfare).
• Consumers gain from increased consumption at a
lower price.
• Producers gain from increased output at a higher
price.
There is also a deadweight loss (the cost of the subsidy)
– shown by the usual triangle. This may not actually
represent a loss (Lecture 9).
The Impact of a Subsidy
The impact of a subsidy on production – and therefore
prices and consumption – can be seen to be
determined by the elasticity of Supply. If the objective
of the subsidy is to increase production, there will be a
more than proportionate response if Supply is relatively
elastic.
If Demand is relatively elastic, a price fall will lead to a
disproportionate rise in the equilibrium quantity
consumed. Production subsidies are therefore more
effective when both Supply and Demand are relatively
elastic.
The Impact of a Subsidy
The critical issue (especially for tax payers) is whether
the cost of financing a subsidy is greater or less than the
benefit generated. Normally, it would be argued that
this is not the case but…
The issue of using taxes and subsidies when there is
market failure is tackled in Lecture 9.
Firm Costs, Revenue & Profit
Econ 224: Week 5 Lecture, Michaelmas 2021-22
Dr Robert Read
Econ 224: Introduction to Economics for Managers
Equilibrium, Surplus, Taxes & Subsidies
1. Firms’ Objective – Maximising Profits
2. The Production Function & the
Marginal Product
3. A Firm’s Cost Curves
4. A Firm’s Revenue Curves
5. Profit Maximisation By Firms
6. Solving a Profit Maximisation Problem
Part 1: Firms’ Objective – Maximising
Profits
The Objective of Firms
The optimum production position is the most
efficient point for output, given input costs. But, it
says nothing about Profits.
How is Profit calculated?
Profit (P) = Total Revenue (TR) – Total Costs (TC)
Total Revenue is the amount received by a firm for
its output and Total Cost is the cost of all of its inputs.
Explicit vs Implicit Costs
Explicit Costs
These costs require a financial outlay – buying
machinery, paying for material inputs, wage payments
to workers.
Implicit Costs
These do not involve a financial outlay – e.g., the
opportunity cost of the owner’s time. These are
included in economic but not accounting costs.
Economic vs Accounting Profit
Economics includes all opportunity costs whereas
accountants only include explicit costs. Economic
profit is therefore smaller.
Economic
profits
Accounting
profit
Revenue
Implicit costs
Opportunity costs
Explicit
costs
Revenue
Total
opportunity
costs
Explicit
costs
Part 2: The Production Function & the
Marginal Product
The Production Function
The Production Function shows the relationship
between the quantity of inputs used to produce a
good or service and the quantity of its output. This is
the formalisation of the Isoquant relationship.
q = f (K, L)
Where:
K is Capital (fixed in the short-run).
L is Labour (variable in the short-run).
The Production Function:
Marginal Product
Recall: the Marginal Product of any input is the increase
in output Q arising from an additional unit of that input.
MPL = dq /dL
MPK = dq / dK
For example; whether to hire an additional worker.
Output q will rise by the worker’s Marginal Product while
the Marginal Cost is the worker’s wage. Is it worthwhile
employing them?
The Production Function &
the Marginal Product of Labour
Q
Production
function
dq/dL
q5
In the short-run,
Capital (K) is fixed.
Output (q) increases
only if additional
workers (L) are
employed. Note that
the rate of increase of
q is declining.
q4
q3
q2
q1
0
L1
L2
L3
L4
L5
L
Diminishing Marginal Product
The diagram shows that the Marginal Product of
Labour (MPL) is diminishing. This is measured by the
slope of the Production Function – the rate of
increase in output (dq/dL) is declining. Each
additional worker is less productive than the previous
one because there is less Capital per worker (K is
fixed) – remember the short-run Expansion Path.
More generally, the Marginal Product of a factor (MPL
here) diminishes as its use increases, regardless of the
fixed input (Capital, K, here).
Part 3: A Firm’s Cost Curves
The Total Cost Curve
The Total Cost (TC) curve shows the relationship
between the quantity (q) a firm can produce and its
costs. This is important in determining a firm’s pricing
decisions.
The Total Cost curve increases with output (q); but
the precise relationship depends upon the shape of
the Production Function (i.e., technology and the
relationship between Capital and Labour).
Capital (K) is fixed in the short-run; so the cost of
output varies according to the input of Labour (L).
The Total Cost Curve
In the short-run,
Capital (K) is fixed.
Output (q) and costs
(C) rise together as
additional workers (L)
are employed.
Cost
Total Cost curve:
pK*K + pL*L
c5
Note that the TC
Curve gets steeper
because of the
diminishing MPL.
c4
c3
c2
c1
0
q1
q2
q3
q4
q5
q
Fixed & Variable Costs
The Total Cost of production can be divided into two:
• Total Fixed Cost (TFC); those costs that do not vary
with output (e.g., Capital in the short-run).
• Total Variable Cost (TVC); those costs that vary with
output (e.g., materials as well as Labour in the
short-run).
TC = TFC + TVC = pK*K + ( pL*L + materials)
In the short run:
=> TFC = pK*K
=> TVC = pL*L + materials
Fixed & Variable Cost Curves
Cost
Total Variable Cost
curve: pL*L
In the short-run,
TFC (pk*K) is
constant while TVC
(pL*L) rises with
output q.
c5
c4
c3
c2
c1
TFC
0
q1
q2
q3
q4
q5
q
Implications of the Relative Magnitudes
of Fixed & Variable Costs
The shares of Fixed and Variable Costs in Total Costs
are directly related to the factor intensity of
production.
TC = TFC + TVC
TFC/TVC is approximately equivalent to K/L – the
Capital/Labour ratio.
Implications of the Relative Magnitudes
of Fixed & Variable Costs
If Total Costs are dominated by Fixed Costs, it indicates
that Capital (i.e., technology) has a greater role in
output – i.e., capital-intensity ( K/L ) is high. This also
means greater potential for economies of scale (high
Fixed Costs being spread over substantial output).
If Variable Costs dominate, output is relatively Labourintensive ( K/L is low) and there are few potential gains
from scale economies.
Average Cost
Average Cost (AC) is calculated by dividing a firm’s
Total Cost (TC) by output (q).
• Average Total Cost (ATC):
ATC = TC / q
• Average Fixed Costs (AFC):
AFC = TFC / q
• Average Variable Cost (AVC): AVC = TVC / q
=>
ATC = AFC + AVC
Average Cost Curves
Cost
AFC declines with Q while
AVC rises with Q. ATC
therefore has an inverted ‘U’
shape.
ATC
AVC
AFC

0
q
The Shape of the Average Cost Curve
The Average (Total) Cost (AC) curve is ‘U’-shaped for
several reasons:
•
•
•
•
The AC is high at low levels of output .
Fixed Costs are spread over increasing output.
The AC declines as output increases.
The AC starts to rise as the rise in AVC offsets the fall
in AFC.
Marginal Cost
Marginal Cost (MC) is the change in Total Cost (dTC)
from producing one additional unit of output:
MC = Total Cost (q+1) – Total Cost(q)
MC = ( TCq+1 – TCq )
This can therefore be written as:
MC = dTC / dq
The Marginal Cost Curve
Cost
Marginal Cost
curve:
dTC / dq
MC
The MC curve
increases with output
q and is inversely
related to the MPL.
0
q
Average & Marginal Cost Curves
Cost
Note: that the MC curve
always cuts the ATC curve
at its lowest point.
MC
ATC
AVC
AFC
0
q
The Average & Marginal Cost Curves
There is an important relationship between the Average
Cost (AC) and the Marginal Cost (MC) Curves.
• When the AC curve is falling, Marginal Cost must be
less than Average Cost (MC < AC). • When the AC curve is rising, Marginal Cost must be greater than Average Cost (MC > AC).
The MC curve must therefore cross the AC curve at its
minimum point (i.e., where MC = AC).
The Average & Marginal Cost Curves
Cost
The MC curve always cuts
the AC curve at its lowest
point.
MC
AC
0
q
The Average Variable & Marginal Cost
Curves
There is a similar relationship between the Average
Variable Cost (AVC) and the Marginal Cost (MC)
Curves.
• When the AVC curve is falling, Marginal Cost is less
than Average Variable Cost (MC < AVC). • When the AVC curve is rising, Marginal Cost is greater than Average Variable Cost (MC > AVC).
• The MC curve also crosses the AVC curve at its
minimum point (i.e., where MC = AVC).
Cost
The Average Variable & Marginal Cost
Curves
The MC curve always cuts
both the AVC and ATC
curves at their lowest
points.
MC
ATC
AVC
0
q
The Total Cost Curve
Cost
TC = pK*K + pL*L
TC
K is fixed in the short-run.
pK, pL are assumed to be
constant.
0
q
Costs in the Short- & Long-Run
The distinction between Fixed and Variable Costs
therefore depends upon the time horizon.
• Some costs are fixed in the short-run (factories,
machinery, land).
• Fixed Costs become variable in the long-run –
Capital (K) is no longer fixed (firms can invest in new
plant, factories etc.).
Recall: Short-Run Expansion Path
K
The short-run expansion
path is constrained by
inelastic capital (fixed at K0).
Output rises only if inputs of
L increase.
K0
Q0
0
L0
L1
L2
Q1
Q2
L
Costs in the Short- & Long-Run
In the long-run, the ATC of any output q is the cost per
unit using the most efficient mix of inputs. This means
that:
• Factory size is determined by the lowest ATC.
• The mix of inputs (K, L) is optimised according to
cost/productivity (i.e., Isoquants).
A firm’s long-run cost curves will therefore differ to
those in the short-run – since the mix of all inputs can
be optimised.
The Choice of Plant/Factory Size
Any plant or factory will have its own short-run ATC.
The firm can change the size of its factory in the longrun – and therefore shift to the associated long-run
ATC.
The Choice of Plant/Factory Size
Cost
Long-run AC with
feasible plant sizes.
LRAC
0
q
The Choice of Plant/Factory Size
Any plant or factory will have its own short-run ATC.
The firm can change the size of its factory in the longrun – and therefore shift to the associated long-run
ATC.
• To produce less than qA, the firm will choose a small
factory in the long-run.
The Choice of Plant/Factory Size
Cost
LRATC
Short-run ATC with
small factory.
0
qA
q
The Choice of Plant/Factory Size
Any plant or factory size will have its own short-run
ATC. The firm can change the size of its factory in the
long-run – and therefore shift to the associated longrun ATC.
• To produce less than qA, the firm will choose a small
factory in the long-run.
• To produce between qA and qB, it will chose a
medium factory in the long-run.
The Choice of Plant/Factory Size
Cost
LRATC
Short-run ATC with
small factory.
Short-run ATC with
medium factory.
0
qA
qB
q
The Choice of Plant/Factory Size
Any plant or factory size will have its own short-run
ATC. The firm can change the size of its factory in the
long-run – and therefore shift to the associated longrun ATC.
• To produce less than qA, the firm will choose a small
factory in the long-run.
• To produce between qA and qB, it will chose a
medium factory in the long-run.
• To produce more than qB, it will choose a large
factory in the long-run.
The Choice of Plant/Factory Size
Cost
Short-run ATC with
small factory.
LRATC
Short-run ATC with
large factory.
Short-run ATC with
medium factory.
0
qA
qB
q
A Typical Long-Run Average Total Cost
Curve
Cost
A more realistic long-run
ATC curve might look
something like this.
0
LRATC
q
Economies & Diseconomies of Scale
The assumption so far is that there are Constant
Returns to Scale in output – that is, the shape of the
long-run ATC curve remains unchanged regardless of
the volume of output.
This is not always the case:
Economies of Scale
Economies of scale occur when long-run Average
Total Cost falls as output q increases. This is often the
result of technology and increasing specialisation in
production – efficiency improves as individual workers
focus on specific tasks. The benefits of scale
economies may be more evident at low levels of
output.
Economies of Scale
Cost
A downward sloping long-run ATC curve
means that the unit cost of output falls (c1 to
c2) as production increases (q1 to q2).
c1
c2
ATC
0
q1
q2
q
Diseconomies of Scale
Diseconomies of scale occur when long-run Average
Total Cost rises as output q increases. These often arise
because of insufficient technology and problems of
co-ordination and management in organisations. The
problem of diseconomies of scale may be more
evident at high levels of output.
Diseconomies of Scale
Cost
An upward sloping long-run
ATC curve means that the
unit cost of output starts to
rise (c1 to c2) as production
increases (q1 to q2).
ATC
c2
c1
0
q1
q2
q
Economies & Diseconomies of Scale
Cost
q = f (K, L); q = f (lK, lL)
Where: l is the scale factor.
l > 1, economies of scale
ATC
l < 1, diseconomies of scale. l = 1, constant returns to scale. 0 q Part 4: A Firm’s Revenue Curves Total Revenue How do we calculate Total Revenue? Total Revenue = Price * Quantity sold This can be written as: TR = p * q Average Revenue Total revenue is proportionate to output, so we can calculate revenue per unit: Average Revenue = Total Revenue/Sales = Price This can be written as: AR = ( TR / q ) = p Marginal Revenue Marginal Revenue is the change in total revenue (dTR) from the sale of one additional unit: MR = TR(q+1) – TR(q) This can be written as: MR = ( TRq+1 – TRq ) MR = ( dTR / dq ) The Marginal Revenue of a Competitive Firm In a competitive market, a firm can keep increasing its output q without affecting the market price, p. Each unit increase in q increases revenue by the same amount (p is constant). Thus, in a competitive market: MR = p and therefore also: AR = p Part 5: Profit Maximisation By Firms Profit Maximisation The profit of a firm is the difference between its Total Revenue from sales (TR) minus the Total Cost of production (TC): Profit (P) = Total Revenue (TR) – Total Costs (TC) The objective of a firm is therefore to maximise the difference between Total Revenue and Total Cost. Pmax (TR – TC) Profit Maximisation: Marginal Revenue & Marginal Cost It is useful to think about profit maximisation in terms of the relationship between the change in revenue (dTR) and costs (dTC) for each unit of output; i.e., Marginal Revenue (MR) and Marginal Cost (MC). Profit Maximisation: Marginal Revenue & Marginal Cost If the Marginal Revenue earned from selling an additional unit of output is greater than the extra cost of producing it (Marginal Cost) – MR > MC –
then the firm makes a profit on the marginal unit. It
should therefore produce more and continue to
increase output so long as this is the case:
If:
MR > MC
=>
dP > 0
A firm should therefore continue to expand output so
long as each additional unit produced increases its
total profit.
Profit Maximisation:
Marginal Revenue & Marginal Cost
If however, the Marginal Revenue from selling an
additional unit of output is less than the extra cost of
producing it (MC) – MR < MC – then the firm is making a loss on the marginal unit. It should therefore reduce output. A firm should continue to cut its output so long as this is the case: If: MR < MC =>
dP < O A firm will increase its profit by reducing output so long as each additional unit produced makes a loss. Profit Maximisation Profit maximisation must therefore be where any increase or reduction in production results in a reduction in profit; i.e.: P Max =>
MR = MC
This must be where the MR and MC curves intersect
(i.e., are equal).
This critical relationship is an important insight of
economic analysis of firm behaviour; it always holds
true, regardless of the nature of competition.
Firm Profit Maximisation Diagram
Profit maximisation can therefore be shown on the
cost curve diagram.
The Marginal Cost (MC) curve is upward sloping, while
the Average Total Cost (ATC) curve is ‘U’ shaped.
Firm Profit Maximisation Diagram
Cost/
Revenue
MC
ATC
AVC
0
q
Firm Profit Maximisation Diagram
Profit maximisation can therefore be shown on the
cost curve diagram.
The Marginal Cost (MC) curve is upward sloping, while
the Average Total Cost (ATC) curve is ‘U’ shaped.
We also know that in a competitive market:
MR = AR = p
Remember: the MC curve always crosses the ATC
curve at its lowest point.
Firm Profit Maximisation Diagram
Cost/
Revenue
At output q1,
MR > MC, therefore
increased output
would raise profit.
MC
ATC
p=AR=MR
p
AVC
MC1
0
q1
q
Firm Profit Maximisation Diagram
Cost/
Revenue
If the firm decides to
produce at output q2, MR < MC, reducing output would increase profit. MC MC2 ATC p=AR=MR p 0 AVC q2 q Firm Profit Maximisation Diagram Cost/ Revenue The profit-maximising level of output is where MR = MC at q*. MC ATC p = MC* ATC* p=AR=MR Maximum Profit AVC ATC at q*. 0 q* q Part 6: Solving a Profit Maximisation Problem Solving a Profit Maximisation Problem Profit-maximisation can be solved algebraically: We know: P = TR – TC TR = p * q for Pmax, MR = MC MR = dTR / dq MC = dTC / dq and, in a competitive market: MR = p Solving a Profit Maximisation Problem Information is also needed about price and production costs. For example: let the market price, p, be 70 and the firm‘s cost function (q is output): TC = 80 - 20q + 3q2 What is the profit-maximising level of output and the firm’s profit? Solving a Profit Maximisation Problem What is the profit-maximising level of output and the firm’s profit? MC = dTC / dQ TC = 80 - 20q + 3q2 MC = dTC = -20 + 6q MR = 70 MR = MC => -20 + 6q = 70
=> q = 15
Solving a Profit Maximisation Problem
TR = p * q
TR = 70 * 15 = 1,050
P = TR – TC
P = 1,050 – TC
TC = 80 – 20q + 3q2; q = 15
TC = 80 – 300 + 3 * 225 = 455
P = 1,050 – 455 = 595
The firm’s profit-maximising level of output is q = 15 and
its profit P is 595.
Supply & the Theory of the Firm
Econ 224: Week 3 Lecture, Michaelmas 2021-221
Dr Robert Read
Econ 224: Introduction to Economics for Managers
Supply & the Theory of the Firm
1. The Efficient Output of a Firm
2. Firm Efficiency – Minimising Production
Costs
3. Optimising Production
4. The Supply Curve
5. The Elasticity of Supply
Part 1: The Efficient Output of a Firm
Supply
This is the quantity supplied of any good or service that
sellers are willing and able to sell.
The ‘Law’ of Supply
The quantity supplied of a good rises when its price rises,
ceteris paribus.
The analysis of Supply has many similarities with that of
Demand – except that the terminology differs.
The Firm: Constrained Optimisation
The output of a firm is determined by combining the
two factors of production:
Capital – K, and Labour – L.
The Production Function shows all of the possible
combinations of Capital (K) and Labour (L) in output, Q
– i.e., some combination of K and L:
Q = f (K, L)
This can be represented graphically using isoquants –
lines of equal output (like Indifference Curves).
A Firm’s Production: Isoquants
K
Q0 is an isoquant; a line of equal
output using different combinations
of K and L: (K1, L1) give a firm
exactly the same output as (K2, L2).
K1
K2
Q0
0
L1
L2
L
Isoquant Maps
Each firm has a set of Isoquants – an Isoquant Map.
These Isoquants have several important properties.
• They are downward sloping – they show how much
of a factor (K or L) can be substituted for the other
while keeping output constant.
• They are convex (bowed) to the origin – the
gradient of an isoquant diminishes along the x.
Isoquant Maps
Each firm has a set of Isoquants – an Isoquant Map.
These Isoquants have several important properties.
• Firms want to maximise their efficiency by locating
on the highest possible isoquant for the least input of
Capital and Labour.
An Isoquant Map
K
Every combination of K, L on isoquant
Q1 produces greater output than any
combination of K, L on isoquant Q0.
K1
K2
Q1
Q0
0
L1
L2
L
Isoquant Maps
Each firm has a set of Isoquants – an Isoquant Map.
These Isoquants have several important properties.
• Firms want to maximise efficiency by locating on the
highest possible isoquant for the least input of
Capital and Labour.
• Isoquants cannot cross (transitivity).
Isoquants Cannot Cross
K
A firm produces the same output at A
& B and also at B & C. A & C cannot
produce the same output – a logical
impossibility.
C
B
A
Q0
Q1
0
L
The Slope of the Isoquant
The slope of the isoquant is determined by the ability of
a firm to substitute Capital (K) for Labour (L) and vice
versa yet maintain output Q constant.
This is the Marginal Rate of Technical Substitution
between K and L.
Slope
= MRTSKL
Isoquants
K
The slope of the isoquant is the
MRTSKL – the maximum rate at which
technology enables a firm to substitute
more K for less of L (or vice versa) to
produce the same output Q0.
dQ = 0
0
Q0
L
Marginal Productivity
Recall that production is:
Q = f (K, L)
The Marginal Productivity is the rate of change of output
as the inputs change. How much does output rise when
the input of K or L increases?
dQK = dQ / dK = fK = MPK
dQL = dQ / dL = fL = MPL
These are the Marginal Products of Capital (K) and
Labour (L) respectively.
Marginal Productivity
For any isoquant : dQ = 0
Such that:
dQ = ( fK dK + fL dL ) = 0
=>
fK dK = – fL dL
=>
The slope of the isoquant is therefore:
dK / dL = fK / fL
dK / dL = MPK / MPL
– the change in output (Marginal Product) of K wrt L.
Diminishing Marginal Productivity
The slope of an isoquant is convex to the origin because
of Diminishing Marginal Productivity. Moving down the
isoquant to the right involves substituting more Labour
(L) for the Capital (K) foregone (and vice versa) yet
leaving total output constant.
dK / dL = MPK / MPL = MRTSKL
= – dQL / dQK
Part 2: Firm Efficiency – Minimising
Production Costs
The Costs of a Firm
Most firms want to minimise their costs for any given
level of output (i.e., maximise their efficiency):
• It is therefore not possible to increase the use of one
factor of production without reducing the use of the
other.
• Total output is therefore limited by a firm’s available
resources (the firm’s budget constraint).
This challenge applies to many every-day decisions
that individuals, firms and governments have to make.
The Firm’s Cost Constraint
Firms face a cost constraint which limits their use of factors
of production (Capital, Labour) and purchase of inputs,
as in the case of budget constraints of consumers. The
greater a firm’s resources, the greater will be the output of
its goods and services.
A firm’s cost constraint can be analysed on the basis of
the costs of Capital and Labour, where output depends
upon some combination of K and L (Input costs are
assumed to be constant).
This can be represented buy an Isocost Curve.
An Isocost Curve
K
The slope of the isocost curve is
the relative price of the two factors
of production, K, L.
K1
Slope = -pL1 / pK1
0
L1
L
Changes in a Firm’s Resources
An increase in a firm’s available resources (or a fall in
input costs) will shift its isocost curve outwards parallel
to the origin (and vice versa). There will be no change
to the slope of the isocost curve since the relative
prices of Capital (K) and Labour (L) have not changed.
An Isocost Map
K
The slope of the isocost curve is
the relative price of the two factors
of production, K, L.
K1
Slope = -pL1 / pK1
0
L1
L
Changes in the Prices of Factors of
Production
Any change in the prices of the factors of production
(Capital and Labour) will alter the slope of the isocost
curve.
The use of any factor of production whose price has
fallen relatively can be expected to increase while
that of the other can be expected to fall. A firm can
therefore substitute between factors in the production
process (depending upon the nature of the
technology – i.e., is the K/L ratio fixed?).
Changes in the Prices of Factors of
Production
K
A fall in the cost of Labour alters the
slope of the firm’s isocost curve – more
Labour is used relative to Capital
K1
Original slope = -pL1 / pK1
New slope = -pL2 / pK1
0
L1
L2
L
Part 3: Optimising Production
Optimal Production
The analysis is completed by combining the firm’s isocost
curve together with its isoquants. Optimal production will
be where the ratio of the relative prices of Capital and
Labour (-pL/pK) is equal to the Marginal Rate of
Technical Substitution (MRTS) between K and L (dK / dL):
-pL / pK = MRTSKL = dK / dL
i.e., where the isoquant is tangential to the firm’s isocost
curve, such that Q0 is produced using inputs of K0 and L0.
Optimal Production
K
Optimal production is where the
slope of the isocost curve pL / pK is
equal to the slope of the isoquant
MRTSKL.
K0
Q0
0
L0
L
Optimal Production
If the firm’s resources increase (decline), then the isocost
curve will shift outwards (inwards) and will be tangential
to a new isoquant, Q1. This isoquant is in the same ‘family’
of isoquants as Q0, so that the use of both K and L will
increase (fall).
An increase in a firm’s resources therefore increases its
output by enabling the production of more Q using more
K and L. A reduction in firm resources will have the
opposite effect.
Optimal Production
K
As the isocost curve Q0 shifts
outwards, it is then tangential
to a higher isocost curve, Q1.
K1
K0
Q1
Q0
0
L0
L1
L
The Expansion Path of Firm Output
Given a set of isocost curves and isoquants, an
Expansion Path of firm output can be derived.
That is, how the efficient output Q* of a firm changes as
its resources change, for a given price relationship
between Capital (K) and Labour (L).
The Expansion Path of Firm Output
K
K3
K2
The Expansion Path shows how
output increases as a firm’s
resources increase. Output passes
through a succession of optimal
points for a given set of Isocost
curves (pL / pK, is constant).
K1
Q3
Q2
Q1
0
L1
L2
L3 L
Part 4: The Supply Curve
The Expansion Path of Firm Output:
the Supply Curve
The Expansion Path of firm output shows all of the
efficient combinations of output as inputs of Capital
and Labour change for a given factor price ratio (pL /
pK). This is the Supply Curve for a firm.
Note: The Supply Curve says nothing about:
• The price of the good or service produced.
• The structure of competition in the industry.
• The profitability of the firm.
Deriving a Supply Curve
p
S
p3
The output of a good (q1,
q2, q3) can be plotted
against price and
therefore its feasible cost
of production (c1, c2, c3).
p2
p1
0
q1
q2
q3
q
The Supply Schedule
The Supply schedule shows the relationship between the
price and quantity of a good or service that is supplied
by plotting all of the possible combinations.
The Supply Curve is upward sloping to the right such that
price and quantity are positively related – as in the ‘Law’
of Supply.
The Market Supply Curve
The Market Supply curve can be derived from summing
the quantities supplied by every firm at each price.
Generally, the Supply curves of each firm can be
added horizontally to obtain the Market Supply curve.
The Market Supply Curve
Generally, individual firm supply curves are added
horizontally to make the Market Supply Curve.
Firm 1
Price
Firm 2
Price
Price
p
p
p
q1
Market = Firm 1 + Firm 2
Quantity
q2
Quantity
q1+q2 Quantity
A Shift in the Supply Curve:
The Number of Firms
An increase in the number of firms in an industry will
increase total supply, such that the market Supply Curve
will shift outwards to the right (and vice versa). will
therefore be supplied at each and every price.
Note that, as new firms are added to the Supply curve,
the market Supply curve becomes flatter (i.e., more
elastic).
The Impact of New Firm Entry
p
As firms enter an industry,
the Supply Curve shifts
right and becomes flatter
(more elastic); more is
supplied at each price.
S
S’
p
0
Q0
Q1
Q
Changes to the Supply Curve
There are two ways in which the Supply curve may
change:
•
A change in the price of the product. This leads to a
movement along the Supply curve.
•
A change in one or more other determinants (e.g.,
input prices), leading to a shift of the supply curve
(including a possible change in its slope).
Effect of a Price Change On Supply
p
S0
B
£2.00
£1.50
0
Recall that on a hot day,
ice cream sellers may raise
their prices (from £1.50 to
£2.00). This increases the
quantity they are willing to
supply from 200 to 350.
A
200
350
q
The Supply Curve:
Non-Price Determinants
The derivation of the Supply Curve is based upon several
critical assumptions (hence, ceteris paribus):
•
•
•
•
The number of firms is constant.
Technology is constant.
The prices of all inputs (including K, L) are constant.
Expectations are consistent and stable.
Qsx = f (px, pK, pL, pI ,Tech., Exp, etc…)
Changes in the Supply Curve:
Non-Price Determinants
The supply curve will shift outwards to the right if:
•
•
•
•
There is an increase in the number of firms.
There is a technological improvement.
The price of one or more inputs falls.
Expectations improve.
An Outward Shift of the Supply Curve
p
S0
B
S1
B’
£2.00
£1.50
0
A
qA
A shift of the Supply Curve
outwards (S0 to S1) means
that more of a good is
supplied at any price.
A’
qA’ qB
qB’
q
Changes in the Supply Curve:
Non-Price Determinants
The supply curve will shift inwards to the left if:
• There is a fall in the number of firms.
• The price of one or more inputs rises.
• Expectations deteriorate.
An Inward Shift of the Supply Curve
p
S2
B’’
S0
B
£2.00
£1.50
0
A’’
qA’’
A shift of the Supply Curve
inwards (S0 to S2) means
that less of a good is
supplied at each and every
price.
A
qA qB’’
qB
q
A Shift in the Supply Curve:
Technological Change
Technology determines the extent to which Capital and
Labour can be substituted for each other in the
production process – hence the slope of the isoquant is
the MRTSKL.
Technological change generally means a cost-saving
improvement in productive efficiency; the same effect
as a fall in the price of inputs. It therefore shifts the Supply
Curve outwards since a firm (or industry) is willing to
supply more than before at each and every price.
(‘clean’ technologies however, might move the Supply
Curve inwards.)
A Shift in the Supply Curve:
Input Prices
A fall in any input price – e.g., the cost of Capital (K),
wages (Labour – L), raw materials and intermediate
inputs – will mean that production is more profitable at
each and every price (and vice versa). This means that
a firm will be willing to supply more than before, so that
the Supply Curve will shift outwards to the right.
A Shift in the Supply Curve:
Expectations
In general, firms adjust supply according to their
expectations of future prices.
For example; many oil firms adjust output according to
price expectations. If it is expected to rise, they may
withhold some output to sell at a higher price later on.
In contrast, bananas are highly perishable and have
only 21 days to be sold after harvesting – very difficult
to vary supply in the short-run. This may give rise to the
‘Cobweb’ problem (discussed later).
Part 5: The Elasticity of Supply
What is Supply Elasticity?
The discussion of the price elasticity of supply is broadly
similar to that of demand price elasticity.
• It measures by how much the quantity of a good or
service responds to a change in its price – i.e., the
sensitivity of supply to price changes.
• It is therefore the proportionate change in quantity
for a given change in price.
The Price Elasticity of Supply
The percentage change in the quantity supplied for a
given percentage change in price is:
ES
=
% change in qS
% change in p
=
(dq/q) / (dp/p)
=
(dq/dp) * (p/q)
Note: the Mid-Point Method should also be used to
calculate the Price Elasticity of Supply.
The Elasticity of Supply:
Perfectly Price Inelastic
If the price elasticity is zero, Supply remains constant
regardless of the price – i.e., price changes have no
effect. Firms are unable to change their output decision
in the short-run.
A Perfectly Inelastic Supply Curve
p
S0
If Supply is perfectly inelastic in
the short-run, a change in price
from p1 to p2 has no effect on the
quantity supplied, which remains
fixed at q0.
p1
p2
0
q0
q
The Elasticity of Supply:
Perfectly Price Elastic
When Supply is perfectly price elastic, the price
elasticity is infinity. At p*, firms will supply any quantity.
For any price p > p*, supply is infinite and for any p < p* supply is zero. All firms are able to adjust their output perfectly (immediately) in response to changes in Demand or prices. A Perfectly Elastic Supply Curve p At price > p*, supply will be infinite.
At price = p*, supply will be infinite.
At price < p*, supply is zero. Firms are able to respond immediately to changes in the quantity demanded S0 p* 0 q0 q1 q The Elasticity of Supply: Unit Price Elasticity When Supply is unit elastic, the price elasticity is one, such that any percentage change in price leads to an identical percentage change in the quantity supplied. A Unit Elastic Supply Curve p S0 p1 The percentage change in price leads to an identical percentage change in the quantity supplied. p0 0 q0 q1 q Determinants of Supply Elasticity The Price Elasticity of Supply refers to the capacity of producers to vary the quantity of the good or service that they supply. This, in turn, depends upon: • Firms’ ability to hold stocks/carry inventory. • The elasticity of supply of factors of production. • The elasticity of supply of other inputs – raw materials and intermediate inputs. Determinants of Supply Elasticity The Elasticity of Supply of a good or service however, is not constant over time. In the short-run, Supply may be relatively inelastic while in the long-run it is generally elastic. Consider how firms can increase their output: • Encourage overtime. • Introduce new shifts (employ more workers). • Install more machines – takes time. • Expand the existing plant or build a new one – takes time. Supply is Inelastic in the Short-Run In the short-run, firms cannot buy/install new machinery or expand their plant operations. This is because in the short-run, the supply of Capital (K – not money but technology, machinery etc.) is inelastic – investment decisions take time to fulfil. This is not the same as capacity. The supply elasticity of Labour however, is relatively elastic, even in the short-run. This has important implications Expansion Path of firms. for the short-run Short-Run Expansion Path of Output A firm’s short-run Expansion Path is constrained by the inelastic Supply of Capital (fixed at K0). Increased output (Q1, Q2) is only possible through increased inputs of Labour (L1, L2 etc.). K K0 Q0 0 L0 L1 L2 Q1 Q2 L Supply Elasticity & Total Revenue The total amount of revenue received by a firm is equal to price times quantity (p * q). This can be shown simply as the box around the Supply curve. The Supply Curve & Total Revenue p S0 A firm’s Total Revenue is equal to the area p * q. p0 0 q0 q Supply Elasticity & Total Revenue There are two separate elasticity effects: • A higher price means increased revenue for every unit sold. • A higher price means more units supplied. For Supply, price and quantity are positively related, so that a rise in p raises revenue while a fall in p reduces revenue. The relative magnitude of the changes in p and q depend upon the Supply Price Elasticity. Supply Elasticity & Total Revenue If Supply is relatively inelastic: ES < 1 The % change in p (dp) > % change in q (dq)
The revenue impact of any price change outweighs the
impact of the change in quantity – total revenue rises.
Supply Elasticity & Total Revenue
If Supply is relatively elastic:
ES > 1
The % change in p (dp) < % change in q (dq) The revenue impact of any price change is outweighed by the impact of the change in quantity – total revenue still rises. Supply Elasticity & Total Revenue If Supply is unit elastic: ES = 1 The % change in p (dp) = % change in q (dq) The revenue impact of any price change is equal to the impact of the change in quantity – total revenue still rises. Econ 224: Introduction to Economics for Managers Course Delivery The lecture programme is face-to-face until further notice. Those students not yet arrived in Lancaster have access to a recording posted on Moodle. Lectures are supported by a weekly face-to-face seminar per (Weeks 2 - 9). Those students who have not yet arrived in Lancaster have a designated online seminar (see your timetable). Supporting Lecture slides will also be available on Moodle (in advance) as will seminar worksheets and suggested solutions. Course Lecturer Weeks 1-10: Dr Robert Read, LUMS B13 (r.read@lancaster.ac.uk). Econ 224: Introduction to Economics for Managers Course Textbook G. Mankiw, M. Taylor & A. Ashwin, Business Economics or Microeconomics. Note that the first text also includes Macroeconomics at not much greater cost and may support (not guaranteed) Econ 225 in Lent Term. There is also one called Economics as well just to confuse. Older editions are ok but beware changes in the order of content, different page numbers and questions. The course text is also supported by the customised on-line MindTap resource from the publishers (can be purchased at the same time as the text from the University Bookshop). This includes additional material, self-assessment tools, quizzes etc. Econ 224: Introduction to Economics for Managers – Seminars These are designed to: • Explore selected issues from the lectures in greater depth. • Work through set problems from question papers on Moodle (see the course paper – also on Moodle). • Deal with questions and issues relating to the course material. Reminder: Seminars are compulsory. Poor attendance/not doing the worksheets is highly correlated with poor course performance (i.e., don’t make plans for August!). Econ 224: Introduction to Economics for Managers – Student Questions If you have problems with the Econ 224 material: • Ask questions in the seminars or afterwards. • e-mail your Tutor. • e-mail me – r.read@lancaster.ac.uk. • Arrange an appointment with your Tutor (there may be specified Office Hours). It is our objective is to do what we can to ensure that you all gain a good pass in this course – even if you don’t come to love Economics or start with no desire to love it! Econ 224: Introduction to Economics for Managers Prior courses in Economics Some students may have taken a prior course in Economics – e.g., ‘A’ level, Baccalaureate, etc. This is not necessarily an advantage! This course follows its own curriculum: the Economic concepts are always the same but the approach, method, depth and means of analysis may differ to previous experience. Please do not assume that you know it all... Choice & Resource Allocation Under Scarcity Econ 224: Lecture 1, Michaelmas 2021-2022 Dr Robert Read Econ 224: Economics for Managers Choice & Resource Allocation Under Scarcity 1. Constrained Optimisation. 2. The Budget Constraint. 3. Opportunity Cost & Indifference Curves. 4. Optimising Consumption. 5. Normal & Inferior Goods. 6. The Income & Substitution Effects. Part 1. Constrained Optimisation What is Economics? Constrained Optimisation The objective of the course is to provide students following business-related degrees to gain a good understanding of the behaviour of consumers and firms along with policies introduced by government. It examines how consumers, firms, markets and governments engage in optimising behaviour (i.e., how do they make decisions?). What is Economics? Constrained Optimisation • • • • Consumers want to maximise their satisfaction or happiness (‘utility’). Firms want to maximise their profits and minimise their costs (be efficient). Markets determine the level of competition between firms and therefore outputs and prices. Governments might want to maximise social benefit (‘welfare’) or taxation while minimising waste and damage to the environment (well, many do). Constrained Optimisation Economics is really about analysing issues of constrained optimisation – i.e., choice. If money, resources etc. are limited, how do individuals, firms and governments choose between different options? Constrained Optimisation For example, maximising consumer utility subject to a key constraint – i.e., income, a notable challenge for students. • • These constraints are normally fixed (i.e., you have a budget), so the focus of analysis is to optimise your behaviour given this constraint. The constraints can then be relaxed to see how behaviour changes. If you can learn how to think like an Economist (!), you should be able to apply relevant analytical tools to understand, tackle and solve everyday problems in consumption, production and business – i.e., ‘real life’. Constrained Optimisation: Problems Optimisation is not always easy however... ...too little information. ...neglected information. In addition, beliefs are not unbiased. Microeconomic theory needs to be used... as a starting point for more realistic models. Is Economics a perfect representation of reality? No way! but it certainly helps to understand how people, firms, markets and governments behave. Part 2. The Budget Constraint (Money or the lack of it) Consumer Choice: the Budget Constraint Most consumers have limited money – especially students. This gives rise to issues of choice under scarcity: • It is not possible to increase consumption of one good without reducing the consumption of at least one other (beer vs pizza, textbook vs night out etc.). • Total consumption is limited by the resources available – income (the budget constraint). This challenge applies to many every-day decisions that individuals, firms and governments have to make. The Budget Constraint The budget constraint simply indicates what any consumer can afford to spend; the greater the budget, the greater will be the expected consumption of most goods and services. How can we analyse the budget constraint? The Budget Constraint This can be done by analysing the choice between two goods or services (e.g., x and y), where x is the one that we are interested in and y can be just another good or service, several or all others. For this part of the analysis, x and y are just two different goods. An individual’s consumption therefore comprises some combination of x and y: c = f (x, y) The Budget Constraint Suppose that the consumption choice is a simply one between just two goods: pizza and baked beans. The cost of (frozen) pizza is £2.00 and a pack of 4 cans of baked beans £1.00. The weekly food budget is £20. Given this budget constraint for food, if all the money is spent on pizza, a student can buy a maximum of 10 pizzas per week while if it is all spent baked beans, then they can buy a maximum of 80 tins of baked beans. The Budget Constraint A diet of just pizza or just baked beans is probably not a good thing or likely until near the end of term. The likelihood is that a student would actually want to buy some combination of pizza and baked beans (and other things). To have more of pizza, a student would have to give up consumption of some baked beans. Given the price relationship; this would be one pizza for two packs of baked beans. This relationship can be expressed as the slope of the Budget Constraint. The Budget Constraint Once we know this price relationship – one pizza equals two packs of baked beans - It is possible to construct a Budget Line. This shows all of the possible combinations of pizza and cans of baked beans in terms of either price p or quantity q. Price: -px / py =>
-ppizza / 0.5baked beans
=>
-2qbaked beans / qpizza
or Quantity:
-qy / qx
The Budget Constraint
Baked
Beans (y)
The slope of the budget line is the
relative price of the two goods – one
pizza per two packs of baked beans.
30 @
£1.00
Slope (p) = -p / 0.5bb
Slope (q) = -2qbb / qp
0
15 @
£2.00
Pizzas (x)
The Budget Constraint
How do we decide what combination of pizza and
baked beans to consume?
That depends upon our preferences…
Some people like pizza more than baked beans and
others baked beans more than pizza – so individuals will
choose different combinations – to be discussed shortly.
Changes to the Budget Constraint:
A Change in Income
What happens if the budget constraint changes – that is,
we have more or less money to spend?
A change in Income shifts the budget line outwards (a rise
in Income) or inwards (a fall in Income) parallel to the
origin. There is no change in its slope since prices have not
changed.
Individuals can therefore afford to consume more baked
beans and pizza if income rises and consume less if
income falls.
The Budget Constraint
Baked
Beans (y)
A rise in income to £36 shifts the
budget line upwards and increases the
maximum possible consumption of
both baked beans and pizza.
36
30
Slope (p) = -p / 0.5bb
Slope (q) = -2qbb / qp
0
15
18
Pizzas (x)
The Budget Constraint
Baked
Beans (y)
A fall in income to £20 shifts the budget
line downwards and reduces the
maximum possible consumption of
both baked beans and pizza.
30
Slope (p) = -p / 0.5bb
Slope (q) = -2qbb / qp
20
0
10
15
Pizzas (x)
Changes to the Budget Constraint:
A Change in Price
A change in the price of either good however, alters the
slope of the budget line since the relative price of baked
beans and pizza has changed.
If the price of a pizza falls to £1.50p, it is now possible to
buy a maximum of 20 with the same budget (£30).
The slope of the budget line changes to:
-p / 0.66bb
-1.5bb / p
or:
The Budget Constraint
Baked
Beans (y)
If the price of a pizza falls to £1.50, the
Budget Line will pivot outwards from
the y-axis since the maximum possible
consumption of pizza has increased
from 15 to 20.
30
New slope = -0.66bb / p
or -1.5bb / p
0
15
20
Pizzas (x)
Changes to the Budget Constraint:
A Change in Price
For any new price relationship, consumption is expected
to increase for the good which had a relative price fall.
Consumption however, will fall for the other good (its price
remains unchanged but has increased relative to the
other good).
This is the Substitution Effect – the change in consumption
of y when the price of x good changes.
By how much will consumption of each good therefore
change? That is determined by consumers’ preferences.
Part 3. Opportunity Cost & Indifference
Curves
Preferences: Utility & Indifference Curves
The budget constraint tells us absolutely nothing about
consumer preferences. Students (consumers) generally
have similar incomes but that does not mean that they
necessarily consume the same combinations of goods
and services (e.g., pizza and baked beans).
This depends upon their tastes.
Preferences: Utility & Indifference Curves
Consumers usually want to maximise their own satisfaction
or happiness – (‘utility’ in economics-speak).
To do this, they will consume goods and services, e.g.,
baked beans and pizza or x and y, in their own personal
preferred combination. This can be expressed as:
U = f (x, y)
Where utility, U, is some function of x and y.
Preferences: Utility & Indifference Curves
The personal preferences of consumers can be analysed
with reference to Utility using Indifference Curves.
An Indifference Curve shows all combinations of x and y
for which a consumer’s has exactly the same utility; i.e., it
is constant. This means that, at any point along the same
Indifference Curve, a consumer is equally happy/satisfied.
For the purposes of this analysis, x can be a specific good,
e.g., chocolate, y can represent all other possible goods.
Choice & Opportunity Cost
The concept of Opportunity Cost is extremely important in
the economic analysis of choice. Opportunity Cost is the
cost of choosing one activity or expenditure relative to
another, when choice is constrained. When choosing
what to consume, consumers must sacrifice one good in
order to consume another (e.g., pizza versus baked
beans). The Opportunity Cost of choosing pizza is not
consuming baked beans.
The Opportunity Cost is therefore the benefit foregone by
not choosing the alternative. The objective of individuals,
firms etc. is therefore try to minimise the total Opportunity
Cost of their choices.
Utility & Indifference Curves
Focusing on individual preferences, we know that
consumers have different tastes. This means that each
consumer has their own valuation of Opportunity Cost for
any given choice.
It is possible to represent the preferences of any individual
consumer and their Opportunity Cost valuations using
Indifference Curves. These illustrate the trade-off that any
consumer is willing to make in choosing between two
goods x and y – i.e., their respective Opportunity Cost.
For some combinations of x and y, utility (and therefore
Opportunity Cost) must be constant – and can be
represented by an Indifference Curve.
An Indifference Curve
y
An Indifference Curve is a locus of
points of equal utility gained by
consuming different combinations of
x and y.
I
0
x
Utility & Indifference Curves
Indifference Curves have several important properties:
• They are downward sloping – some of good y must be
sacrificed to consume more of good x.
• They are convex (bowed) to the origin – the
relationship is generally non-linear; the amount of good
y that must be sacrificed to consume more of good x is
not constant.
The Indifference Curve
I0 is a line of equal indifference:
combinations, x1, y1 give a consumer
exactly the same utility as x2, y2.
y
y1
y2
I0
0
x1
x2
x
Utility & Indifference Curves
Indifference Curves have several important properties:
• They are downward sloping – some of good y must be
sacrificed to consume more of good x.
• They are convex (bowed) to the origin – the
relationship is generally non-linear; the amount of good
y that must be sacrificed to consume more of good x is
not constant.
• Consumers want to be on the highest possible
Indifference Curve since it represents the greatest utility
or satisfaction; I1 is preferable to I0 : U [ I1 ] > U [ I0 ]
An Indifference Map
Every combination of x and y on I1
gives greater utility than any
combination of x and y on I0.
y
y1
y2
I1
I0
0
x1
x2
x
Utility & Indifference Curves
Each consumer has their own set of Indifference Maps.
Indifference Curves have several important properties:
• They are downward sloping – some of good y must be
sacrificed to consume more of good x.
• They are convex (bowed) to the origin – the
relationship is generally non-linear; the amount of good
y that must be sacrificed to consume more of good x is
not constant.
• Consumers want to be on the highest possible
Indifference Curve since it represents the greatest utility
or satisfaction; I1 is preferable to I0 : U [ I1 ] > U [ I0 ]
• Indifference Curves cannot cross (transitivity).
A Logically Impossible Indifference Map
A consumer is indifferent between A and
B and also between points B and C.
But, A and C have different levels of
utility – a logical impossibility.
y
C
A
B
I0
I1
0
x
The Slope of the Indifference Curve
The slope of the Indifference Curve is determined by the
willingness (i.e., the Opportunity Cost) of a consumer to
give up units of x so as to be able to consume more y and
vice versa.
This is referred to as the Marginal Rate of Substitution
between x and y, MRSxy.
This is the rate at which a consumer is willing to sacrifice
consumption of one good for the other.
The Slope of the Indifference Curve
A consumer is willing to give up
(y1 -> y2) so as to gain (x1 -> x2).
y
y1
y2
I0
0
x1
x2
x
The Slope of the Indifference Curve
Note that the Marginal Rate of Substitution between x
and y changes along the Indifference Curve.
Each additional unit of y sacrificed requires compensation
in terms of more units gained of x. The opposite is also
true. The Opportunity Cost of sacrificing y for x therefore
also changes.
Diminishing Marginal Utility
The change in the willingness to trade x for y and y for x is
know as Diminishing Marginal Utility. Increased
consumption of good x increases the Opportunity Cost of
not consuming good y and vice versa.
For example; however much you like chocolate relative
to water, at some point if you keep eating more
chocolate, you will start to value a drink of water more
than eating an additional chocolate!
The Slope of the Indifference Curve
A consumer is willing to give up
(y1 – y2) so as to gain (x1 – x2).
y
y1
y2
I0
0
x1
x2
x
The Slope of the Indifference Curve
To gain (x2 – x3 ) however, they
would only be willing to give up
(y2 – y3).
y
y1
y2
I0
y3
0
x1
x2
x3
x
Marginal Utility
Recall, utility is:
U = f (x, y)
Marginal utility is the rate of change of utility as the
consumption of a good changes. How much does utility
rise when consumption of x or y increases ?
MUx = dU / dx = fx
MUy = dU / dy = fy
Marginal Utility
For any Indifference Curve:
dU = 0
Such that:
dU = fx dx + fy dy = 0
=>
=>
fy dy = – fx dx
dy / dx = fx / fy
The slope of the Indifference curve is: dy / dx
The change in utility (Marginal Utility) of y wrt x.
Diminishing Marginal Utility
The slope of the Indifference Curve is therefore convex to
the origin because of Diminishing Marginal Utility. The
more that you have of good y, the more of y that you are
willing to give up to gain more of good x while leaving
total utility unchanged.
dy / dx = MRSxy =
– MUx / MUy
Diminishing Marginal Utility
Diminishing Marginal Utility has broader implications than
just affecting the slope of Indifference Curves. It is an
important characteristic of consumption generally.
The more units of a good consumed, the lower the
marginal utility derived from it by a consumer. The greater
the quantity of x relative to y, the lower the value of each
additional unit of x relative to y.
Indifference Curves: Perfect Substitutes
Not all Indifference Curves have curved slopes.
Perfect substitutes are always traded like-for-like so that
the utility from one is always equal to that of the other;
e.g., 50p pieces and £1 coins. The Indifference Curves
must be straight lines because the rate of exchange
remains constant.
Indifference Curves: Perfect Substitutes
If x and y are perfect substitutes, then they
will be traded ‘like-for-like’ – hence straight
line Indifference Curves.
y
300
200
100
I0
0
100
I1
200
I2
300
x
Indifference Curves:
Perfect Complements
These are consumed in proportion to each other so that
additional units of one good without the other do not
increase consumer utility; e.g., left and right shoes (for
those with two feet – not both left ones). The Indifference
Curves must be rectangular since the two goods are
consumed in proportion.
Indifference Curves:
Perfect Complements
If x and y are perfect complements,
then they will be need to be consumed
in strict proportion – hence rectangular
Indifference Curves.
y
3a
I2
2a
I1
a
I0
0
b
2b
3b
x
Part 4. Optimising Consumption
Optimising Consumption
It is now possible to complete the analysis of consumption
by putting the Budget Line and Indifference Curve
analyses together.
This requires the ratio of relative prices of x, y to be equal
to the Marginal Rate of Substitution between them:
px / py = MRSxy
This must be where the furthest Indifference Curve from
the origin is just tangential to the budget line, such that x0,
y0 is the optimal quantity and combination consumed.
Optimal Consumption
Optimal consumption is where the
slope of the budget line px / py is
equal (i.e., tangential) to the slope
of the Indifference Curve MRSxy.
y
y0
I0
0
x0
x
Optimal Consumption
If a consumer’s income rises, their budget line shifts
outwards and will be tangential to a new Indifference
Curve, I1. This curve is in the same ‘family’ of Indifference
Curves as I0 – i.e., the MRS is constant – so that
consumption of both x and y will increase.
Optimal Consumption
As the budget line shifts outwards, it
is tangential to a higher Indifference
Curve, I1.
y
y1
y0
I1
I0
0
x0
x1
x
Optimal Consumption
If a consumer’s income rises, their budget line shifts
outwards and will be tangential to a new Indifference
Curve, I1. This curve is in the same ‘family’ of Indifference
Curves as I0 – i.e., the MRS is constant – so that
consumption of both x and y will increase.
A rise in income therefore increases consumer utility by
enabling the consumption of more of both goods x and y
(x1, y1).
Part 5. Normal & Inferior Goods
Normal Goods
So far, a rise in a consumer’s income has increased the
consumption of all goods and a fall in income has led to
reduced consumption of all goods. This is the ‘Income
Effect’, which is positively related to the consumption of all
goods x and y.
This is true for Normal goods; more of them are consumed
at higher levels of income and fewer at lower levels of
income. Most goods and services are ‘normal’.
It is possible to plot the consumption of a good (x) against
different levels of income (Y) to show how its consumption
varies with income – an Engel Curve.
The Engel Curve for a Normal Good
Income,
Y,
As Income, Y, rises, consumption of x
rises – x must be a Normal good.
Y3
Y2
Y1
0
x1
x2
x3
x
Inferior Goods
For some goods however, an increase in Income actually
leads to lower consumption – these are Inferior goods.
These are usually staples – as in student diets – bread,
pasta, potatoes, rice, baked beans etc…
People on lower incomes are therefore likely to consume
more Inferior goods. As their Income rises – e.g., students
getting jobs – their consumption of Inferior goods will fall.
The Engel Curve for an Inferior Good
Income,
Y,
As Income, Y, rises, consumption of x
falls – x is an Inferior good.
Y3
Y2
Y1
0
x3
x2
x1
x
The Engel Curve of an Inferior Good
Income,
Y,
In some cases of an Inferior
good, as Income, Y, rises,
consumption of x first rises then
falls. So, at very low incomes,
the good appears Normal but
later becomes Inferior!
Y3
Y2
Y1
0
x3
x1
x2
x
‘Giffen’ Goods
Giffen Goods are an extreme case of Inferior Goods for
which few if any substitutes exist.
They can be defined as goods for which the Income
Effect of a price rise is greater than the Substitution Effect.
If the price of an Inferior Good rises, the Substitution Effect
will be negative – buy less – but the Income Effect is
positive – buy more. In the case of a Giffen Good, the
latter effect is greater than the former so that
consumption actually increases!
Conspicuous Consumption:
Veblen Goods
More than a century ago, the economist Thorstein Veblen
coined the term conspicuous consumption to refer to
goods which are viewed by consumers as high quality,
luxury and exclusive. Diamonds, Rolls-Royce cars, Rolex
watches, some champagne brands (Cristal) and designer
brands (e.g., the Hermès Birkin handbag).
These are not Giffen Goods but their ‘snob’ appeal
means that their prices are inversely related to
consumption – the higher the price, the greater the desire
to consume. If too many people buy a Veblen good, it
loses its exclusivity and its demand falls!
Part 6. Income & Substitution Effects
The Income Effect
The Income Effect has already been discussed with
regard to changes in the Budget Line, where there is a
change in absolute or relative Income.
The Budget Line moves outwards or inwards in parallel
since relative prices remain constant, leading to a shift to
a different (higher or lower) Indifference Curve.
The Substitution Effect
The Substitution Effect occurs when the price of a good, x,
changes such that the slope of the Budget Line also
changes. This was shown briefly earlier.
Any change in absolute or relative prices between two
goods, x and y, means that the optimum position on the
MRSxy must also change. This is because there has been a
shift along an Indifference Curve since the Opportunity
Cost has changed.
Showing the Income & Substitution Effects
It is possible to illustrate and quantify the Income and
Substitution Effects in a single diagram.
The ‘simplest’ way to do this is to demonstrate what
happens when the price of a single good, x, falls while the
prices of all other goods, y, remain constant.
This requires a little graphical manipulation and leads to
possibly slightly different results depending upon how it is
drawn.
The Income & Substitution Effects
The Budget Line is now tangential to
a higher Indifference Curve, I1.
y
I0
y0
I1
I0
0
x0
x
The Income & Substitution Effects
Consumption of both x and y has
increased (to x1, y1).
y
y1
y0
I1
I0
0
x0
x1
x
The Income & Substitution Effects
A change in the price of a Normal good (a fall or rise) has
two effects:
The Income Effect
A fall (rise) in the price of a good increases (reduces)
relative income so that a consumer can afford to buy
more (less) of both goods.
The Substitution Effect
A fall (rise) in the price of one good makes it relatively
cheaper (expensive). A consumer will therefore buy more
(less) of the cheaper (expensive) good and less (more) of
the more expensive (cheaper) one.
The Magnitudes of the Income &
Substitution Effects
However, the overall effect of a price change of one
good on all goods is not known.
In all cases, the impact on the good with the price
change (x) is known – if its price falls, consumption
increases, if its price rises, consumption falls. This is not the
case with the other good whose price has not changed
(y). In the example shown, the fall in the price of x
increases the consumption of both x and y.
It is therefore important to disaggregate the overall effect
into the specific Income and Substitution Effects.
The Magnitude of the Substitution Effect
I1
The Substitution Effect is shown by
drawing the new Budget Line parallel
to the original Indifference Curve. It is
seen in the move along I0.
y
I0
y0
I1
I0
0
x0
x
The Magnitude of the Substitution Effect
To measure the Substitution Effect of a price change, the
new Budget Line is drawn parallel with the original
Indifference Curve at the new combination of x and y
(the MRS is different). This shows the shift along the
Indifference Curve and so separates this from the Income
Effect. The change in consumption of x (x0 to x’) and y (y0
to y’) is the Substitution Effect.
For Normal Goods, consumption of the good whose price
has fallen (x) will rise and consumption of the good whose
relative price has risen (y) will fall.
The Magnitude of the Substitution Effect
I1
The Substitution Effect is shown by
the parallel shift of the new budget
line tangential to the original
Indifference Curve. It is seen in the
move along I0. Consumption of x
rises (x0 to x’) while y falls (y0 to y’).
y
I0
y0
y’
I1
I0
0
x0 x’
x
The Magnitude of the Income Effect
The Income Effect of a price change is shown by
comparing the difference in consumption between the
two tangential points for the Substitution Effect and the
combined Substitution and Income Effects (the residual
must be the Income Effect). This is the shift between
Indifference Curves.
The Income Effect is therefore the change in consumption
of x from x’ to x1 and y from y’ to y1. For Normal Goods, a
rise in (relative) income leads to a rise in consumption of
both goods.
The Magnitude of the Income Effect
I1
The Income Effect is shown by the shift
from the new tangency on the original
Budget Line on I0 (x’, y’ – Substitution
Effect) to the same tangency on the
new Budget Line I1.
y
I0
y’
I1
I0
0
x’
x
The Magnitude of the Income Effect
I1
In this case, consumption of x rose (x’
to x1) and y rose (y’ to y1). The Income
Effect here is therefore positive in both
cases
y
I0
.
y1
y’
I1
I0
0
x’
x1
x
The Magnitudes of the Income &
Substitution Effects
The impact of the fall in price of x on the consumption of x
and y is as expected for Normal Goods:
Good x:
Income Effect
Substitution Effect
Overall effect
+ve (x’ to x1)
+ve (x0 to x’)
+ve (x0 to x1)
Good y:
Income Effect
Substitution Effect
Overall effect
+ve (y’ to y1)
-ve (y0 to y’)
?
(y0 to y1)
Determinants of Demand &
Demand Elasticities
Econ 224: Week 2 Lecture, Michaelmas 2021-22
Dr Robert Read
Econ 224: Introduction to Economics for Managers
Determinants of Demand &
Demand Elasticities
1.
2.
3.
4.
The Determinants of Demand
The (Own) Price Elasticity of Demand
The Income Elasticity of Demand
Cross-Price Elasticity of Demand
Part 1: The Determinants of Demand
What is Demand?
The Quantity Demanded
The amount of a good or service that consumers are
willing to purchase.
The ‘Law’ of Demand
That the quantity demanded of a good or service will fall
when its price rises and rise when its price falls – ceteris
paribus – other things being equal. Exceptions include
Veblen Goods (luxuries) and Giffen Goods (very inferior
goods).
Deriving a Demand Curve
The tools introduced in Lecture 1 can be used to derive
a Demand curve for a consumer.
Using the Budget Line and Indifference Curves, it is
possible to plot a consumer’s preference for good x at
each and every price – keeping the price of y (i.e., all
other goods and services) constant.
Deriving a Demand Curve
y
As the price of x falls, so the budget line
rotates to give a new higher level of
maximum consumption of x. This is
tangential to a new Indifference Curve I1.
I1
I0
0
x
Deriving a Demand Curve
y
As the price of x continues to fall, so the
budget line rotates to give new higher levels
of maximum consumption of x. This is
tangential to new Indifference Curves I1, I2.
I2
I1
I0
0
x
Deriving a Demand Curve
y
For example:
px0 = 40, qx0 = 24
px1 = 30, qx1 = 50
px2 = 20, qx2 = 70
I2
I1
I0
0
x0 = 24
x1 = 50
x2 = 70
x
Deriving a Demand Curve
All of these different price-quantity combinations of x can
then be transposed into (px, qx) space by plotting price
(px) against its quantity (qx). This gives the Demand Curve
for x.
Remember: the prices of all other goods (y) must remain
constant.
Deriving a Demand Curve
p
This is the Demand Curve
derived from the earlier
Indifference Curve analysis.
40
30
20
D
0
24
50
70
q
The Demand Curve
The Demand Curve shows the relationship between the
price and quantity of a good or service and plots all of
the possible combinations of p and q.
The Demand Curve is generally downward sloping to the
right, such that price and quantity are inversely related –
as in the ‘Law’ of Demand.
The Market Demand Curve
From the individual Demand Curve that has been
derived, it is possible to produce a Market Demand
Curve. This is obtained by adding the quantity
demanded by every consumer for each price – in other
words, it represents the sum of all of the individual
Demand Curves.
More generally, the Demand Curves of every individual
can be summed horizontally to obtain the Market
Demand Curve (i.e., Sqx * n, where n is the population).
The Market Demand Curve
Individual Demand curves are summed horizontally to
derive the Market Demand curve.
Consumer 1
Price
Consumer 2
Price
x1
Quantity
Market = Consumers 1+2
Price
x2
Quantity
x1+x2
Quantity
Changes to the Demand Curve
A Demand Curve may change in two important ways:
• A change in the price of the product x. This leads to a
movement along the Demand Curve for x.
• A change in one or more other determinants. This
leads to a shift of the Demand Curve for x (including a
possible change in its slope).
Effect of a Price Change On Demand
p
£2.00
On hot days, ice cream sellers
may raise their prices (from
£1.50 to £2.00). This results in
a shift along the Demand
Curve (from A to B) and a fall
in Demand from 250 to 200.
B
A
£1.50
D
0
200
250
q
The Demand Curve: Non-Price
Determinants
The derivation of the Demand Curve is based upon
several critical assumptions (hence, ceteris paribus –
everything remains constant):
•
•
•
•
•
The number of consumers is constant.
Incomes are constant.
The prices of all other goods are constant.
Tastes are constant.
Expectations are consistent and stable.
Qdx = f (px, Y, psubstitutes,, pcomplements, T, Exp, etc.)
Changes in the Demand Curve:
Non-Price Determinants
The Demand Curve will therefore shift outwards to the
right if:
• There is an increase in the number of consumers.
• At least one person has an increase in Income.
• The prices of one or more other goods change (rise in
price of a substitute or fall in price of a complement).
• There is increased taste for the good (e.g., made
popular by Instagram influencers).
• Expectations improve.
An Outward Shift of the Demand Curve
p
But: On a hot day, more people
visit Morecambe (more
consumers) and more want an
ice cream (change in tastes).
The Demand Curve shifts
outwards (D0 to D1) so that more
of a good is consumed at each
and every price.
B’
B
£2.00
A
£1.50
D0
0
200
250
300
D1
q
Changes in the Demand Curve:
Non-Price Determinants
The Demand Curve will shift inwards to the left if:
• There is a fall in the number of consumers.
• There is a fall in Incomes.
• The prices of one or more other goods change (fall in
price of a substitute or rise in price of a complement).
• There is decline in taste for the good.
• Expectations deteriorate.
These factors are the opposite of those that led to a shift
to the right.
An Inward Shift of the Demand Curve
p
On a cold day in October, the
Demand Curve can be
expected to shift inwards (D0
to D2). Fewer ice creams are
consumed at each and every
price.
B
£2.00
A
£1.50
D2
0
125 200 220 250
D0
q
A Shift in the Demand Curve:
Normal & Inferior Goods
Normal Goods
Remember: the demand for a Normal Good is positively
related to Income. A rise in Income therefore increases
the quantity demanded at each and every price.
Inferior Goods
Remember: the demand for an Inferior Good is negatively
related to Income. A rise in Income therefore reduces the
quantity demanded at each and every price.
A Shift in the Demand Curve:
Complements & Substitutes
Complementary Goods
Remember: the demand for complementary goods is
positively related to the demand for x. A fall in the price
of a complement therefore increases the demand for x,
shifting its Demand Curve to the right – and vice versa.
Substitute Goods
Remember: the demand for substitute goods is inversely
related to the demand for x. A fall in the price of a
substitute reduces the demand for x shifting its Demand
Curve to the left – and vice versa.
Part 2. The Price Elasticity of Demand
What is the Elasticity of Demand?
An example to think about:
You take over running a shop that has not being doing
particularly well. You want to increase its business and,
hopefully, its profitability.
Do you raise prices, lower them (or keep them the same)?
What is the Elasticity of Demand?
• If you raise prices: Will you increase your business or
will people buy even less from you?
• If you lower prices: Will more people buy more from
you or not – and, if so, how much?
What is the Elasticity of Demand?
Business owners in this situation often raise prices! Why?
The answer is not straight forward – it depends upon the
Elasticity of Demand. That is:
• How do consumers react to a change in price?
• What is the impact of this change on the revenue
(and profits) of the business?
The (Own) Price Elasticity of Demand
The (Own) Price Elasticity of Demand measures the
impact of a change in the price of a good or service on
its consumption.
In other words, it measures the extent to which Demand
is sensitive to a change in price.
The (Own) Price Elasticity of Demand
More formally, it is the proportionate change in the
quantity demanded for a given proportionate change in
price:
ED
=
% change in qD
% change in p
=
(dq/q) / (dp/p)
=
(dq/dp) * (p/q)
The (Own) Price Elasticity of Demand
You may have noticed that there is something wrong
with the equation! – for Normal Goods, p and q do not
tend to move in the same direction.
The correct equation is actually:
ED
= (-1) *
% change in qD
% change in p
The short-cut treats Demand Elasticity as if it is positive
even though it usually isn’t (BEWARE!).
Price Elasticity & Total Revenue
Returning to the question of the shop and its prices, we
are now in a better position to understand what will
happen to the shop’s revenue if it raises or lowers its
prices and therefore decide an appropriate strategy.
Revenue = p * q
Price Elasticity & Total Revenue
Changing prices has two separate effects:
• Price effect: selling at a higher price means increased
revenue from every unit sold (p is greater) while selling
at a lower price reduces the revenue per unit sold.
• Volume effect: a higher price means fewer units sold
(q is smaller) while a lower price means more units are
sold.
Since Price and Quantity are inversely related; a rise in p
raises revenue and a fall in q reduces it. Their relative
magnitudes depend upon the Price Elasticity of Demand.
Price Elasticity & Total Revenue
If Demand is relatively elastic:
ED > 1 => (dq) > (dp)
The change in volume q (dq) is greater than the change in
price p (dp).
A rise in price p therefore leads to increased revenue per
unit that is outweighed by the fall in revenue from the
lower q sold. So (p * q) falls. A reduction in price will
therefore increase revenue.
Therefore, if the Elasticity of Demand for the shop’s goods
is greater than unity, then it should lower its prices.
Price Elasticity & Total Revenue
p
If p = £2.50, q = 800
Revenue = £2,000
£2.50
If p = £2.00, q = 1,200
Revenue = £2,400
£2.00
When D is elastic,
a price reduction increases
revenue.
D
0
800
1,200
q
Calculating Price Elasticity
The demand elasticity can be calculated for the
example:
ED
= (dq/q) / (dp/p) =
(dq/dp) * (p/q)
= (400/-0.50) * (2.50/800) = -800 *0.003125
ED
= 2.5
ED
2.5 > 1; Demand is therefore elastic.
Determinants of Price Elasticity
Demand tends to be more elastic when:
• There is a large number of close substitutes (less
differentiation).
• A good is a luxury rather than a necessity.
• A good is defined more narrowly – e.g., the demand for
a specific brand.
• The time horizon is longer – elasticity is greater in the
long-run (tastes may change).
Determinants of Price Elasticity
Demand tends to be more elastic when:
• Buyers are aware of prices and features of rival
products (e.g., using comparison websites – Go
Compare, Compare the Market etc.).
• Goods and services are bought infrequently and take
a large share of spending (houses, cars, white goods).
Calculating Price Elasticity
However:
If this action is reversed and, instead, the price changes
back to £2.50 from £2.00, quantity falls from 1,200 to 800:
ED
= (-400/0.50) * (2.00/1200)
= -800 * 0.0017
ED
= 1.33 !!!
The elasticity is different – it is still elastic but less so…
Calculating Price Elasticity:
the Mid-Point Method
The reason for this is that the denominator has changed
– it is greater for a price reduction than for a price rise.
The Mid-Point Method uses the same denominator to
ensure that the answer is the same, regardless of the
direction of change, by averaging the start and end
prices and quantities.
Calculating Price Elasticity:
the Mid-Point Method
ED
= (dq/dp) * [(( p1+p2 )/2) /(( q1 + q2 ) / 2)]
= (-400/0.50) * [((2.50+2.00)/2)
/ ((800+1200)/2)]
= -800 * (2.25/1000)
ED = 1.80
The correct elasticity actually lies in between…
The Mid-Point Method is always used to calculate all
elasticities
Price Elasticity & Total Revenue
If Demand is relatively inelastic:
ED < 1 => (dq) < (dp) The change in volume q (dq) is less than the change in price p (dp). A rise in price will lead to increased revenue per unit sold that outweighs the fall in revenue from lower sales. So (p * q) rises. A rise in price therefore increases revenue while a fall in price will reduce revenue. Therefore, if the Elasticity of Demand for the shop’s goods is less than unity, then it should raise its prices. Price Elasticity & Total Revenue p If p = £2.50, q = 1,000 Revenue = £2,500 £2.50 If p = £2.00, q = 1,200 Revenue = £2,400 £2.00 When D is inelastic, a price reduction reduces revenue D 0 1,0001,200 q Calculating Price Elasticity: the Mid-Point Method The elasticity of Demand can be calculated for this second case, again using the Mid-Point Method: ED = (dq/dp) * [(( p1+p2 )/2) /(( q1 + q2 ) / 2)] = (200/-0.50) * [((2.50+2.00)/2) / ((1000+1200)/2)] = -400 * (2.25/1100) ED = 0.81 < 1; ED = 0.81 Demand is inelastic. Determinants of Price Elasticity Demand tends to be less elastic when: • There is a lack of available close substitutes. • A good is a necessity. • The market is more widely-defined (mobile phones versus i-phones). • The time horizon is short (no time for tastes to change). Determinants of Price Elasticity Demand tends to be less elastic when: • Product comparisons are difficult (product complexity). • There are high switching costs (familiarity versus learning new programmes/upgrades). • There is a need for specialised training • A product is used in conjunction with another. Price Elasticity & Total Revenue If Demand is unit elastic: ED = 1 => (dq) = (dp)
The change in volume q (dq) is the same as the change in
price p (dp).
The revenue impact of any price change is equal to the
impact of the change in quantity. So (p * q) is constant.
In this case, there is no point in the shop changing its
prices.
Effects of Improvements to Big Data
•
On-line sales promotions and real time supermarket
checkout data help businesses to estimate current price
elasticities (and changes).
•
Promotions (e.g., three for two or 20% off next purchase)
enable the demand response to be measured …
Purchase answer to see full
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