Question

1. Consider a firm with the cost function c(y, w1, w2) = y²(w1 + w2), where wi denotes the price of inputi, i = 1, 2. Let p denote the output price. Derive the output supply function y(p, w1, w2), and the input demand functions xi(p, w1, w2), i = 1, 2

Answer 1

The profit maximizing problem is Taking the first order condition gives Now, we want to find the input demand function. Using the cost function, we know that it takes y2 units of input 1 and y units of input 2 in order to make y units of output in a cost minimizing fashion. The production function that is consistent with such a cost function is Thus, in order to produce ylp, w2) we need y2 units of i and r2 This gives us that