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   = _______