A firm has a production function given by Q = 10K0.25L0.25. Suppose that each unit of capital costs R and each unit of labor costs W.
a. Derive the long-run demands for capital and labor.
b. Derive the total cost curve for this firm.
c. Derive the long-run average and marginal cost curves.
d. How do marginal and average costs change with increases in output? Explain.
e. Confirm that the value of the Lagrange multiplier you get from the cost-minimization problem in part (a) is equal to the marginal cost curve you found in part (c).