The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L,C) = co LC: C2 where co, C1, and c2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. a. In this example, assume co - 6, c1 = 0.75, and c2 - 0.25. Assume each unit of labor costs $25 and each unit of capital costs $75. With $85,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. If your answer is zero enter "0". Маx s.t. L, C b. Find the optimal solution to the model you formulated in part (a). Hint: Put bound constraints on the variables based on the budget constraint. Use L s 3000 and Cs 1000 and use the Multistart option as described in Appendix 8.1. Round your answer for optimal solution to one decimal place, if needed. and C - for an optimal objective function value of

The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L,C) = co LC: C2 where co, C1, and c2 are constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. a. In this example, assume co - 6, c1 = 0.75, and c2 - 0.25. Assume each unit of labor costs $25 and each unit of capital costs $75. With $85,000 available in the budget, develop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. If your answer is zero enter "0". Маx s.t. L, C b. Find the optimal solution to the model you formulated in part (a). Hint: Put bound constraints on the variables based on the budget constraint. Use L s 3000 and Cs 1000 and use the Multistart option as described in Appendix 8.1. Round your answer for optimal solution to one decimal place, if needed. and C - for an optimal objective function value of

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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. Various measures of cost Douglas Fur is a small manufacturer of fake-fur boots in Chicago. The following table shows the company’s total cost of production at various production quantities. Fill in the remaining cells of the following table. Quantity Total Cost Marginal Cost Fixed Cost Variable Cost Average Variable Cost Average Total Cost (Pairs) (Dollars) (Dollars) (Dollars) (Dollars) (Dollars per pair) (Dollars per pair) 0 120 — — 1 200 2 240 3 285 4 340 5 425 6 540 On the following graph, plot Douglas Fur’s average total cost (ATC) curve using the green points (triangle symbol). Next, plot its average variable cost (AVC) curve using the purple points (diamond symbol). Finally, plot its marginal cost (MC) curve using the orange points (square symbol). (Hint: For ATC and…
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es Output 6 1 2 3 4 5 S 6 17 8 9 Total Cost $ 2,500 3,416 4,040 4.480 4,900 5,220 5,540 6,310 7,328 9,718 2500 Total Variable Cost b. What is the value of total fixed cost? 6 units $ 0 units 910 1540 1980 2400 2720 3040 3810 4820 7210 Marginal Cost c. What is the most productive level of output? $ 910 630 440 420 320 320 770 1010 2390 Average Total Cost $ d. At what output is economic capacity? Output: e. If TFC doubled, what is the marginal cost of the 7th unit? 3410 2020 1493.33 1225 1044 923.33 901.42 915 1078.89 Average Variable Cost $ 910 770 660 600 544 506.67 544 29 6025 801.11 Average Fixed Cost 2500 1250 833.33 625 500 416.67 35713 312.5 27778
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Fill in the space (d) in the table below associated with the firm William Perry, Inc., that delivers refrigerators in the Chicago area, using the two inputs of labor and trucks. Number of Amount of Trucks Labor 2 2 2 2 2 2 2 0 1 2 3456 Total Output 0 75 (c) 380 (f) Average Product of Labor (a) (b) 100 (d) (e) 75 Marginal Product of Labor 100 50 (g) 0
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ips Under decreasing returns to scale, average cost cost curve. as the quantity produced increases. Over this range of output, the marginal cost curve is Grade It Now the average Save & Continue
a. Calculate marginal cost using the formula given in the chapter: ATotal cost/AQuantity. Quantity Variable cost ($) Total cost ($) Marginal cost ($) 0 0 100 1 60 160 2 110 210 100 3 180 280 100 4 270 370 100 5 400 500 100 b. Calculate AVariable cost/AQuantity. Quantity Variable cost ($) AVariable cost Total cost ($) ($)/ AQuantity 0 0 100 1 60 160 100 2 110 210 100 3 180 280 100 4 270 370 100 5 400 500 100
c. How does fixed cost affect marginal cost? Why is this relationship important?
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