1. A firm estimates its cubic production function of the following form:

Q = AL^{3} + BL^{2}

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 + cQ^{2}

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 = _______

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