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Midterm Exam, Microeconomics

Name………………..

Number………………

Start Time…………..

End Time…………….

April 11, 2022

1. Solve 2 out of the following 3 questions:

(a) Let f (x1 , x2 ) = 2×10.3 x20.3 be a production function. Find the short

run average cost curve for each of x2 = 1, 2, and 3 and for generic

prices w1 , w2 . Find the long run average cost curve for specific

prices of w1 = 2 and w2 = 1. Graph your results for the specific

prices. Be sure to include (and label) in your graph the levels of

output for which the long run average cost curve would coincide

with each of the short run curves above (for the specific prices).

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(b) Assume a Cobb Douglass production function with two inputs and

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exponents inside the production function y = x?1 1 x1??

that are

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less than one. Derive the profit maximizing choices of x1 and y

for arbitrary prices.

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(c) Suppose three firms with the following supply curves: S1 (p) =

p, S2 (p) = p ? 6, S3 (p) = 3p.

i. Find the industry supply curve.

ii. Suppose industry demand equals 5 ? p. What will the equilibrium price and (individual) firm quantities be?

iii. Repeat the last part, but with an industry demand of 10 ? p.

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2. Solve 3 out of the following 4 questions:

(a) Given our notes on the experience with the regulation of advertising for eyeglasses, we can speculate about another similar historical event. In 1977, the Supreme Court ruled that individual states

could not ban lawyers from advertising either their availability or

their prices. Unlike with eyeglasses, all states had previously enacted a ban. What do you think was the effect of this decision on

(long run) legal fees?

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(b) Describe a hypothetical situation in which periods of low inflation

can be used to estimate the effects of eliminating usury laws (a

price ceiling on interest rates) for similar values of real interest

rates without low inflation. Be as specific as possible in terms

of the estimation you would run in terms of the counterfactual

implicit in such an estimation. Explain graphically how such a

comparison is consistent with economic theory. How do mortgage

lenders typically ration credit when price ceilings bind?

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(c) Let AC(y) = 1/y + 2 + 16

y. Find the efficient point of production

for this firm. Suppose every firm in the industry has access to the

technology, find the region of economies of scope, i.e. the amount

of output where production is cheaper if it is concentrated in one

firm as opposed to split evenly between multiple firms. Derive

the long run industry average cost for this function if production

is undertaken by the most cost efficient number of firms for each

level of output.

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(d) Use profit-maximization and revealed choices by firms to show the

law of supply. Be sure to define mathematically (that is use if and

then statements) what is meant by the law of supply.

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Tags:

exponents

production function

arbitrary prices

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