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T4 – ECON 303
1. Robert washes his white clothes using the production function qR = 6.5B0.55G0.45
where B is the number of cups of Clorox bleach and G is the number of cups of
OxiClean. Marie, his wife, on the other hand washes her white clothes using the
production function, qM = 6.5B0.36G0.64. R and M in the superscripts are used to
denote the production functions for Robert and Marie, respectively.
a) What is Robert’s marginal productivity from using Clorox bleach for his
white clothes? What is Marie’s marginal productivity from using Clorox
bleach for his white clothes?
b) What is Robert’s MRTS between using the two types of whiteners (Clorox
and OxiClean) for his clothes? What is the same for Marie?
c) Is it possible that both Robert and Marie have the different marginal
products for the bleaching agents, yet have the same MRTS? Explain your
reasons as succinctly as possible.
2. A paper company dumps nondegradable waste into a river that flows by the firm’s
plant. The firm estimates its production function to be:
Q = 6KP,
where Q = annual paper production measured in pounds, K = machine hours of
capital, and P = gallons of polluted water dumped into the river per year. The firm
currently faces no environmental regulation in dumping waste into the river.
Without regulation, it costs the firm $7.50 per gallon dumped. The firm estimates
a $30 per hour rental rate on capital. The firm produces 600 million pounds of
paper per year. For this problem, consider the long-run production of output.
a. Determine the firm’s optimal ratio of wastewater to capital.
b. Given the firm’s output of 600 million lbs., how much capital and
wastewater should the firm employ?
c. How much will it cost the firm to produce the 600 million lbs. of paper?
d. The state environmental protection agency plans to impose a $7.50 fee for
each gallon that is dumped (this is in addition to the current cost of $7.50).
Assuming that the firm intends to maintain its same output level, how
much capital and wastewater should the firm employ?
e. How much will the firm pay in fees? What happens to the firm’s cost as a
result of the fee?

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