ECO 406 University at Buffalo Cobb Douglass Production Function Economics Questions

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only Q1(b) &Q2(b)&(c)

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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
2
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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