# Mathematical Economics, Minimization

by dracolnyte
Tags: economics, mathematical, minimization
 P: 26 1. The problem statement, all variables and given/known data Consider the following general form of a constant elasticity of substitution production function: y = [SLp + (1 - S)Kp]1/p Assume a firm is trying to minimize the cost of producing any given y. Cost are given by C = wL + rK Find the firm's cost minimizing demand function for L. The cost minimizing demand for K is determined simultaneously, so you need both first order conditions. You may assume that nonneggativity constraints on L and K are not binding. 3. The attempt at a solution Is y = [SLp + (1 - S)Kp]1/p expandable?
 Emeritus Sci Advisor PF Gold P: 16,101 Not in any pleasant fashion. Why would you want to expand it?
 P: 26 because my prof said it would be easier if we let a1 = S1/p and a2 = (1-S)1/p and leave our answers in terms of a1 and a2
P: 26

## Mathematical Economics, Minimization

im guessing i can make a1p = S and a2p = (1 - S)
then i would get

y = [a1pLp + a2pKp]1/p

y = [(a1L)p + (a2K)p]1/p
Emeritus