econ101_ps6_sol - 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 (With Answers) 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 100 102 106 112 120 130 142 156 172 190 TFC 100 100 100 100 100 100 100 100 100 100 TVC 0 2 6 12 20 30 42 56 72 90 AFC - 100 50 100/3 25 20 50/3 100/7 25/2 100/9 AVC 0 2 3 4 5 6 7 8 9 10 ATC - 102 53 112/3 30 26 71/3 156/7 43/2 190/9 MC=2Q+1 (using function) - 3 5 7 9 11 13 15 17 19 MC b/w (change in TC between quantities) 102- 100= 2 106- 102= 4 112- 106= 6 120- 112 =8 130- 120= 10 142- 130= 12 156- 142= 14 172- 156= 16 190- 172= 18 b. What is the farmer's fixed cost? Give some examples of what costs might be fixed for a wheat farmer. Fixed cost is the component of total cost that does not change when quantity produced changes. Looking at the equation for total cost, we see that any component of TC without a Q in it is a fixed cost. Thus fixed cost is just the vertical intercept of TC. So, FC = 100. c. Write the equation giving the farmer's variable cost as a function of quantity. Variable cost is the component of total cost that changes as quantity changes. Looking at the equation for total cost, we see that any component of TC with a Q (or function of Q; e.g. Q 2 , etc.) in it is a variable cost. Here, then, we have TVC = Q+ Q 2 . Notice that TC = TFC + TVC. d. Write the equations for the farmer's average total cost (ATC) and average variable cost (AVC), both as functions of Q.
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2 ATC = TC/Q = (100 +Q+ Q 2 )/Q AVC =T VC/ Q = (Q+ Q 2 )/Q = 1+Q AFC = TFC/ Q = 100/Q Note that ATC = AFC + AVC. This is not surprising, since TC = TFC + TVC. Dividing both sides by Q shows that ATC = AFC +AVC. This is another identity helpful to have on hand. 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. AFC is decreasing in Quantity as AFC=100/Q. Also, you can check this fact in the graph. In fact, AFC is always downward-sloping because that is defined as fixed amount of money divided by the quantity. Thus, if you increase quantity, the fixed cost spreads over increasing quantity to get less AFC. 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 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.
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3 Q 0 1 2 3 4 5 6 7 8 9 10 TVC 0 45 85 120 155 195 240 290 345 405 470 AVC - 45 42.5 40 38.75 39 40 41.43 43.13 45 47 MC - 45 40 35 35 40 45 50 55 60 65 b. Do the curves have the shapes that you might expect? Explain.
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This note was uploaded on 01/05/2012 for the course ECON 101 taught by Professor Gulipektunc during the Spring '11 term at Middle East Technical University.

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econ101_ps6_sol - METU Department of Economics Econ 101:...

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