Suppose there is a fixed amount of capital K¯ = 20.
a) Find the short run cost function CFK(q) when the wage is 6 and the rental rate of capital is 3 for a firm whose production function is F(K, L)=3K3/5L2/5.
b) What is the elasticity of substitution for this production function?
c) What does this say about the marginal return to labor as you increase the amount of labor used?
d) How does your answer in a) changes if the firm can freely use K and L?