ECO 405 Lecture Notes - Lecture 10: Production Function, Partial Derivative, Envelope Theorem
Document Summary
Suppose q=min(k,2l) (need worker and 1 crane to produce 1 x-ray machine or 2 cranes and 1 worker will produce 2 x-ray machine. Cost per machine is + = . this is just the mc and atc of producing one x-ray machine. Cost for 50 machines = 50* = ,500. Substitute into the production function and solve for l, then for k v l b l. 1/ q a b b a a b a b b a b a a a b w a v a b b w a b v b a b. Where b is a constant that involves only the parameters and . Cost functions are all homogeneous of degree one in the input prices. A doubling of all input prices will not change the levels of inputs purchased. Inflation will shift the cost curves up: non-decreasing in q, v, and w. Cost functions are derived from a cost-minimization process.
