Question

Suppose one firm has production function f(K, L) =√K+√L, and another firm has the production function f(K, L) = (√K+√L)^(.3). Will these firms have the same supply functions?

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Answer 1

The supply curves are obtained from the long run cost functions of the firms. The upward sloping part of the marginal cost functions will be the supply functions of the firms. Now in this case the second production function is a monotonic transformation of the first firms production function and hence the points of equilibrium will essentially be the same. Thus the supply curves of the two firms will also be the same as follows as shown by the same total cost functions below.