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Unformatted text preview: ECON W3211.002 Intermediate Microeconomics Problem Set 6 Due Wednesday, November 10, 2010 1. Perloff, Chapter 7: 28, 29, 31, 32 28. The production function is decreasing returns to scale; therefore the long-run cost func- tion will increase at an increasing rate. This means the long-run average cost will rise and marginal cost will be above average cost. Mathematical Derivation: The cost-minimization problem is min K,L wL + rK such that Q = AL K Notice that the firms decision variable is K and L , where wL + rK is the objective function and Q = AL K is a constraint. Since Q = AL K , K = Q A L- 1 Substituting this into the objective function, we get min L wL + r Q A L- 1 We can now differentiate with respect to L and set resulting derivative equal to zero. That is, w + r Q A 1 - L- - 1 = 0 The above equation can be solved to get L as a function of w , r , and Q ....
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This note was uploaded on 10/03/2011 for the course ECON W3211 taught by Professor Elmes during the Fall '09 term at Columbia.
- Fall '09