econ101_ps6_001 - METU Department of Economics Econ 101:...

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1 METU Department of Economics Econ 101: Introduction to Economics I Sections 01-02-03 Fall 2010 PROBLEM SET 6 Q.1. A wheat farmer has total production costs given by the equation TC=100+Q+Q 2 , where Q is output, measured in bushels of wheat. a. Fill out the table with columns for quantity TC, TFC, TVC, AFC, AVC, ATC and MC. Q 0 1 2 3 4 5 6 7 8 9 TC TFC TVC AFC AVC ATC MC b. What is the farmer's fixed cost? Give some examples of what costs might be fixed for a wheat farmer. c. Write the equation giving the farmer's variable cost as a function of quantity. d. Write the equations for the farmer's average total cost (ATC) and average variable cost (AVC), both as functions of Q. e. Show the ATC, AVC, AFC and MC on one graph. f. Explain what is happening to average fixed costs as Q increases, and explain how this relates to what you see in your graph. Q.2. The following table gives capital and labor requirements for 10 different levels of production of X-USB memory stick. Q 0 1 2 3 4 5 6 7 8 9 10 K 0 2 4 6 8 10 12 14 16 18 20 L 0 5 9 12 15 19 24 30 37 45 54
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a. Assume that the price of labor is $5 and the price of capital is $10 per unit. Compute and graph the total variable cost curve, the marginal cost curve, and the average variable cost curve for the firm. b. Do the curves have the shapes that you might expect? Explain. c. Using the numbers in this example, explain the relationship between marginal cost and variable cost. d. Using the numbers in this example, explain the meaning of “marginal cost” in terms of additional inputs needed to produce a marginal unit of output. e. If output price was $ 57, how many units of output would the firm produce? Explain. Q.3. Factory A’s short-run cost function is TC A = 124 + 18Q, while factory B’s is TC B = 18 + 124Q. Answer the following questions: a. You are told that both of the factories had the same total cost in this period. What was output in factory A? In factory B? b. What are fixed costs for factory A? For factory B? c. What are marginal costs for Factory A? For factory B? d. Suppose you want to produce only 0.5 units (Q=0.5). You want to pay as little as possible but must pay the cost of production. Which factory would you choose? e. Repeat part (d) assuming you want to produce 2 and 3 units, separately. f. What is a rule for production about choosing where to produce? (i.e. produce in factory A if _____, factory B if ______) Q.4. The following equations represent the TFC and the TVC of the firms, X-Logistics Inc. and Y-Logistics Inc. costs X-Logistics Inc. Y-Logistics Inc. TFC 30 50 TVC 20Q + 0.2Q 2 2Q 3 +3Q 2 +8Q a. What is the TFC for the firms when output equals 2 and when output equals 5, respectively?
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econ101_ps6_001 - METU Department of Economics Econ 101:...

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