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Can you help me with questions 1, 2, and 3 stating on page 217 Document Preview: Chapter 10: Production and Cost Estimation 205 Learning Objectives After reading Chapter 10 and working the problems for Chapter 10 in the textbook and in this Student Workbook, you should be able to: ? Specify and estimate a short-run production function using a cubic specification of the production function. ? Specify and estimate a short-run cost function using a cubic specification. In order to accomplish these goals, Chapter 10 shows you how to: ? Estimate the parameters of a cubic short-run production function by using the technique of regression through the origin. ? Find the region of diminishing returns. ? Estimate the output level at which AVC reaches its minimum value. ? Estimate the parameters of a cubic short-run total variable cost equation along with the associated average variable cost and marginal cost equations. Essential Concepts 1. The cubic empirical specification for a short-run production function is derived from a long-run cubic production function. The cubic form of the long-run production function is expressed as Q = aK3L3 + bK2L2 2. The properties of a short-run cubic production function (Q = AL3 + BL2 ) are: a. Holding capital constant at K units, the short-run cubic production function is derived as follows: 3 3 2 2 3 2 Q aK L bK L AL BL = + = + where A = aK3and B = bK2 b. The average and marginal products of labor are respectively AP = Q/L = AL2 + BL and MP = ?Q/?L = 3AL2 + 2BL Chapter 10: Production and Cost Estimation 206 c. Marginal product of labor begins to diminish beyond Lm units of labor and average product of labor begins to diminish beyond La units of labor, where and m 3 a 2 L B L B A A = = d. In order to have the necessary properties of a production function, the parameters must satisfy the following restrictions: A 0 3. To estimate a cubic short-run production function using linear regression analysis, you must first transform the cubic equation into linear form: Q = AX + BW where X = L3 andW = L2 . In Attachments: ch-10.pdf; Can you help me with questions 1, 2, and 3 stating on page 217 Document Preview: Chapter 10: Production and Cost Estimation 205 Learning Objectives After reading Chapter 10 and working the problems for Chapter 10 in the textbook and in this Student Workbook, you should be able to: ? Specify and estimate a short-run production function using a cubic specification of the production function. ? Specify and estimate a short-run cost function using a cubic specification. In order to accomplish these goals, Chapter 10 shows you how to: ? Estimate the parameters of a cubic short-run production function by using the technique of regression through the origin. ? Find the region of diminishing returns. ? Estimate the output level at which AVC reaches its minimum value. ? Estimate the parameters of a cubic short-run total variable cost equation along with the associated average variable cost and marginal cost equations. Essential Concepts 1. The cubic empirical specification for a short-run production function is derived from a long-run cubic production function. The cubic form of the long-run production function is expressed as Q = aK3L3 + bK2L2 2. The properties of a short-run cubic production function (Q = AL3 + BL2 ) are: a. Holding capital constant at K units, the short-run cubic production function is derived as follows: 3 3 2 2 3 2 Q aK L bK L AL BL = + = + where A = aK3and B = bK2 b. The average and marginal products of labor are respectively AP = Q/L = AL2 + BL and MP = ?Q/?L = 3AL2 + 2BL Chapter 10: Production and Cost Estimation 206 c. Marginal product of labor begins to diminish beyond Lm units of labor and average product of labor begins to diminish beyond La units of labor, where and m 3 a 2 L B L B A A = = d. In order to have the necessary properties of a production function, the parameters must satisfy the following restrictions: A 0 3. To estimate a cubic short-run production function using linear regression analysis, you must first transform the cubic equation into linear form: Q = AX + BW where X = L3 andW = L2 . In Attachments: ch-10.pdf

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