1. A firm estimates its cubic production function of the following form:
Q = AL3 + BL2
and obtains the following results:
a. The equations for total product, average product, and marginal product are:
TP = ___________________________
AP = ___________________________
MP = ___________________________
b. The estimated values of A and B are statistically significant at the (exact) levels, ________ and _________, respectively.
c. At _______ units of labor usage, marginal product of labor begins to diminish.
When the wage rate is $300, answer the following questions. (Remember that AP = Q/L; AVC = w/AP; and SMC = w/MP.)
d. Average product of labor reaches its maximum value at ________ units of labor.
e. At the output for part d, average variable cost is $______________ and marginal cost is $____________.
f. When the rate of labor usage is 100 units of labor, output is _______ units.
Average variable cost is $_________ and marginal cost is $__________.
2. Suppose Heritage Corporation believes that its total variable costs follow a cubic specification and so it estimates its average variable costs using the following specification:
AVC = a + bQ + cQ2
The regression analysis produces the following computer output:
a. Do the estimated coefficients have the required signs to yield a -shaped AVC curve? Discuss the significance using the p-values.
b. Heritage Corporation's marginal cost function is
SMC = ___________________________________.
c. At what level of output does AVC reach a minimum? What is the value of AVC at its minimum?
Qmin = ___________ AVC min = _______________________
d. Compute AVC and SMC when Heritage produces 8 units.
AVCQ=8 = _______
SMCQ =8 = _______