A firm estimates its cubic production function of the form
Q = AL3 + BL2
and obtains the following estimation results:
a. What are the estimated total, average, and marginal product functions?
b. Are the parameters of the correct sign, and are they significant at the 1 percent level?
c. At what level of labor usage is average product at its maximum?
Now recall the following formulas derived in Chapter 8: AP = Q/L, AVC = w/AP, and SMC = w/MP. Assume that the wage rate for labor (w) is $200.
d. What is the output when average product is at its maximum?
e. At the level for part d, what average variable cost and marginal cost?
f. When the rate of labor usage is 120, what is output? What are AVC and SMC at that output?
g. Conceptually, how could you derive the relevant cost curves from this estimates of the production functions?