Mathematics3 - A firm's total cost function is given by the...

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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 PART (1) a. TFC = 4000 b. AFC = Q 4000 c. TVC = TC - TFC TVC = 5Q + 10Q 2 d. AVC = Q TVC = Q 10Q 5Q 2 = 5 + 10Q e. ATC = Q TC = Q 10Q 5Q 4000 2 f. MC = 5 + 20Q (2) Determine the quantity that minimizes average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds. PART (2) ATC is minimized where MC is equal to ATC. Equating MC to ATC
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Q 10Q 5Q 4000 2 = 5 + 20Q 4000 +5Q + 10 2 = 5Q + 20Q 2 4000 = 10Q 2 Q 2 = 400 Q = 20 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:
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This note was uploaded on 06/04/2011 for the course ECONOMICS 435 taught by Professor Mcin during the Spring '10 term at Central Lancashire.

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Mathematics3 - A firm's total cost function is given by the...

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