A firm estimates its cubic production function of the following form: Q = AL3 +

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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 $__________. Chapter 10: Production and Cost Estimation 218 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: DEPENDENT VARIABLE: AVC R?SQUARE F?RATIO P?VALUE ON F OBSERVATIONS: 45 0.6145 33.47 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T?RATIO P?VALUE INTERCEPT 175.0 25.00 7.00 0.0001 Q ?3.20 0.80 ?4.00 0.0003 Q2 0.08 0.01 8.00 0.0001 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

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