Question

Suppose a firm has production function f(x1, x2) = x1 + x2. How much output should the firm produce in the long run?

Answer 1

There seems to be a perfect substitutability between the two inputs, X1 and X2. If assume that their prices are P1 and P2, then we have a long run equilibrium condition where MRTS = P1P2. In this case the marginal rate of technical substitution is 1 which indicates that the long run equilibrium condition has P2 = P1. Now if we observe that in the long run, P2>P1, it means using X2 is expensive and therefore the output is Q = X1.

Similarly, if we observe that in the long run, P2<P1, it means using X1 is expensive and therefore the output is Q = X2. This analysis indicates that the long run production depends upon the price level of two inputs.