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1. A firm estimates its cubic production function of the following form: Q = AL^

ID: 1240414 • Letter: 1

Question

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

Q = AL^3 + BL^2

and obtains the following results: (See chart in attached image)


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 $__________.


Explanation / Answer

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 $__________.