Building on problem 5.3 in chapter 5, consider the CES utility function written as in (8.2),
(c) Also show that equation (8.9) holds, which we re-write as:
Problem 5.3
Suppose that industry 1 is monopolistically competitive, with a CES sub-utility function as described in problem 5.2. We let the marginal costs be denoted by c1(w,r), and the fixed costs in the industry by αc1(w,r). That is, the fixed costs use labor and capital in the same proportions as the marginal costs. Industry 2 is a competitive industry, and each industry uses labor and capital.
(a) Write down the relationship between the
(b) Write down the full-employment conditions for the two factors. Does the Rybczynski Theorem still apply in some form?
How are your answers to (a) and (b) affected if the fixed costs in industry 1 uses different proportions of labor and capital than the marginal costs?
Problem 5.2
In Krugman’s
Maximize this subject to the budget constraint, p1 c1 + p2 c2 ≤ 1.
(a) Obtain an expression for the relative
(b) The elasticity of substitution is defined as) d ln(c1 / c2 )/ d ln(p2 / p1 . What is the value of the elasticity of substitution for this utility function?
(c) Obtain an expression for the demands c1 and c2 as a function of prices.
(d) What do these expressions imply about the
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