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CH4 Solutions - 306-310 ENGINEERING ECONOMY SOLUTIONS TO...

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1 3 0 6 - 3 1 0 E N G I N E E R I N G E C O N O M Y SOLUTIONS TO PROBLEM SET #4 – PRODUCTION AND COST ANALYSES 1. i) The total cost function consists of two linear segments intersecting at a rate of 500 units per week. Let L represent the number of person-hours of labour employed per week. The mar- ginal cost function is: For L 500: MC = 20 (also vc because of the linear cost function) For L 500: MC = 30 At the current production rate, the total production costs are: 400 (50) = 20 000 Therefore, the fixed cost is: 20 000 - 400 (20) = 12 000 The total production cost function is: For L 500: TC = 12 000 + 20 (L) For L 500: TC = 12 000 + 20 (500) + 30 (L - 500) = 7000 + 30 L Therefore, the average cost function is: For L 500: AC = 12 000 / L + 20 For L 500: AC = 7000 / L + 30 The marginal and average cost curves are shown in the diagram below. 0 20 40 60 80 100 120 140 160 180 200 0 100 200 300 400 500 600 700 800 900 1000 PRODUCTION RATE (units/week) UNIT COSTS ($) Average Cost Marginal Cost
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