1. A firm estimates its cubic production function of the following form: Q = AL3 + BL2 and obtains the following results:
|
DEPENDENT VARIABLE
|
Q
|
R-SQUARE
|
F-RATIO
|
P-VALUE ON F
|
|
|
OBSERVATIONS:
|
32
|
0.7547
|
92.31
|
0.0001
|
|
|
VARIABLE
|
|
PARAMETER
ESTIMATE
|
STANDARD
ERROR
|
T-RATIO
|
P-VALUE
|
|
L3
|
|
-0.0016
|
0.0005
|
-3.20
|
0.0032
|
|
L2
|
|
0.4000
|
0.0950
|
4.21
|
0.0002
|
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 $__________.