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Unformatted text preview: SD_20102011/8 ISL233M İ KRO İ KT İ SATUYGULAMA DERS İ8 06.12.2010 42. Complete the following table (round each answer to the nearest whole number): Output Total Cost Variable Cost Fixed Cost Marginal Cost Average Cost Avg. Var. Cost Avg. Fixed Cost 0 30 1 35 2 60 3 110 4 200 5 320 6 600 Solution: Output Total Cost Variable Cost Fixed Cost Marginal Cost Average Cost Avg. Var. Cost Avg. Fixed Cost 0 30 0 30 – – – – 1 35 5 30 5 35 5 30 2 60 30 30 25 30 15 15 3 110 80 30 50 37 27 10 4 200 170 30 90 50 43 8 5 320 290 30 120 64 58 6 6 600 570 30 280 100 95 5 43. A firm's total cost function is given by the equation: TC = 4000 + 5Q + 10Q 2 . (1) Write an expression for each of the following cost concepts: a. Total Fixed Cost b. Average Fixed Cost c. Total Variable Cost d. Average Variable Cost e. Average Total Cost f. Marginal Cost (2) Determine the quantity that minimizes average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds. Solution: PART (1) a. TFC 4000 = SD_20102011/8 b. Q 4000 AFC = c. TVC TC TFC TVC Q Q = = + 5 10 2 d. Q 10 5 Q 10Q 5Q Q TVC AVC 2 + = + = = e. ATC TC Q 4000 5Q 10Q Q 2 = = + + f. MC 5 20Q = + SD_20102011/8 PART (2) ATC is minimized where MC is equal to ATC. Equating MC to ATC 4000 5Q 10Q Q 5 20Q 4000 5Q 10 5Q 20Q 4000 10Q Q 400 Q 20 2 2 2 2 2 + + = + + + = + = = = SD_20102011/8 ATC is minimized at 20 units of output. Up to 20, ATC falls, while beyond 20 ATC rises. MC should be less than ATC for any quantity less than 20. For example, let Q = 10: MC = 5 + 20(10) = 205 ( ) ( ) 505 10 10 10 10 5 4000 ATC 2 = + + = MC is indeed less than ATC for quantities smaller than 20. MC should exceed ATC for any quantity greater than 20. For example, let Q = 25: MC = 5 + 20(25) = 505 ( ) ( ) 415 25 25 10 25 5 4000 ATC 2 = + + = MC is indeed greater than ATC for quantities greater than 20. 44. Acme Container Corporation produces egg cartons that are sold to egg distributors. Acme has estimated this production function for its egg carton division: Q = 25L 0.6 K 0.4 , where Q = output measured in one thousand carton lots, L = labor measured in person hours, and K = capital measured in machine hours. Acme currently pays a wage of $10 per hour and considers the relevant rental price for capital to be $25 per hour. Determine the optimal capitallabor ratio that Acme should use in the egg carton division. Solution: ( ) ( ) L K 1.5 MRTS L K L K 1.5 K L 10 L K 15 = MRTS MP MP = MRTS K L 10 K L 25 .4 MP L K 15 K L 25 .6 MP 0.6 0.6 0.4 0.4 0.6 0.6 0.4 0.4 K L 0.6 0.6 0.6 0.6 K 0.4 0.4 0.4 0.4 L = • = = = = = Equate MRTS to w r . 1.5 K L 10 25 1.5 K L 0.4 = = 1.5K = 0.4L; K=0.266L SD_20102011/8 45. Davy Metal Company produces brass fittings. Davy's engineers estimate the production function represented below as relevant for their longrun capitallabor decisions....
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This note was uploaded on 02/01/2012 for the course ECON 101 taught by Professor Meonk during the Spring '11 term at Abu Dhabi University.
 Spring '11
 Meonk
 Economics

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