Firms and Production
Short-Run Production: One Variable and One Fixed Input
1. In the short run, a firm cannot vary its capital, K=2, but it can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short run if its production function is q=10L+K. (mathematical problem).
2. If the Cobb-Douglas production function is q=L^0.75K^0.25, and K=16, what is the elasticity of output with respect to labor? (mathematical problem).
Long-Run Production: Two Variable Inputs
3. What is the MRTS of the CES production function q=(aLρ+bK^ ρ)^d/p (mathematical problem)
Returns to Scale
4. A production function is said to be homogeneous of degree γ if f(xL, xK)=x^ γf(L, K), where x is a positive constant. That is, the production function has the same returns to scale for every combination of inputs. For such a production function, show that the marginal product of labor and marginal product of capital functions are homogeneous of degree γ-1. (mathematical problem).
Challenge
5. If a firm lay’s off workers during a recession, how will the firm’s marginal product of labor change?