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1 Economics 101 Spring 2018 Answers to Homework # 5 Due Thursday, May 3, 2018 Directions: • The homework will be collected in a box before the lecture. • Please place your name, TA name, and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. • Late homework will not be accepted so make plans ahead of time. • Show your work . Good luck! Please realize that you are ess entially creating “your brand” when you submit this homework. Do you want your homework to convey that you are competent, careful, and professional? Or, do you want to convey the image that you are careless, sloppy, and less than professional? For the rest of your life you will be creating your brand: please think about what you are saying about yourself when you submit any work for someone else. Part I: Perfect Competition 1. You have just graduated, and your first job is as a manager at Widget Co., a company that makes widgets. Your engineer gives you the following table of costs, but, for some reason, he has forgotten to fill in most of it. The per unit cost of labor (the wage) is $10, and the per unit cost of capital is $50. Q K L MPL APL FC VC TC AFC AVC ATC MC 0 10 0 - - - - - - 10 1 $1 10 12.5 $20 35 10 3 10 $40 $13.50 10 $550 $10 a) Using your knowledge of producer theory, fill in the missing information from the table. (You may need a calculator for some of the entries.) Remember that: MPL = marginal product of labor = [(change in total product)/(change in total labor)] APL = the average product of labor = [(total product)/(total labor)] AFC = average fixed cost = FC/Q AVC = average variable cost = VC/Q ATC = average total cost = TC/Q MC = marginal cost = [(change in total cost)/(change in output)] Start by filling in the easy entries: Cost of capital is $50 per unit, so fixed costs are $500 all the 2 way down. Now we systematically move down the table one row at a time. In the first row, no labor is used so VC = 0, and TC = FC = $500. Moving down one row, we are now using 1 unit of labor, so VC = $10 and TC = $510. We know that MC = $1 on this line, and that tells us that the (change in total cost)/(change in output) = 1. The change in total cost is 510 – 500 or $10. We can then solve this equation to find the change in output. The change in output must be 10 units. Or, since MC = $1, and we increased total spending by $10, we can infer that Q = 10. Since labor increased by 1 and quantity increased by 10, MPL = 10. Using this, we can derive the various average costs, by dividing by quantity. Moving down again, in the third row we are given AFC = 20. Since AFC = FC/Q, we can solve for Q, finding Q = 25. Since APL = Q/L, we have L = 2. Since labor increased by 1 and quantity increased by 15, we can see MPL = 15. Since we increased spending by another $10 and increased production by 15, we have MC = 10/15 = $0.67. We can then fill in average costs as usual. In the fourth row, we’re given Q = 35 and L = 3. MPL thus is 10 since quantity increased by 10 in response to increasing labor by 1 unit. APL is simply 35/3 = 11.67. Spending increased by $10, and the quantity increased by 10, so MC = $1. The remaining costs can be filled in directly using the standard formulae. In the fifth row, we are given VC = $40, so using the cost of labor, we have L = 4. With these, we can compute all the relevant total costs. Since we now know TC = $530, and ATC = $13.50, we must have Q = 40. From there we can compute the remaining average costs and marginal cost in the usual way. Finally in the last row, total cost is $550, so L = 5. Since MC = $10, and the cost of the last unit of labor was $10, Q must have only increased by 1, so Q = 41. With that the remaining columns can be filled from the usual formulae. Q K L MPL APL FC VC TC AFC AVC ATC MC 0 10 0 - - $500 $0 $500 - - - - 10 10 1 10 10 $500 $10 $510 $50 $1 $51 $1 25 10 2 15 12.5 $500 $20 $520 $20 $0.80 $20.80 $0.67 35 10 3 10 11.67 $500 $30 $530 $14.29 $0.86 $15.14 $1 40 10 4 5 10 $500 $40 $540 $12.50 $1 $13.50 $2 41 10 5 1 8.20 $500 $50 $550 $12.19 $1.21 $13.41 $10 b) Suppose the market price of widgets is $1. Using your answers to the previous part, what level of production would you recommend in the short run? Rigorously justify your answer. You know that at an optimum, you should set price equal to marginal cost. Notice from the table, there are 2 production levels that have a marginal cost of $1. Let’s consider the first option of Q = 10 first. Suppose you produce Q = 10. Notice that marginal cost is falling at that quantity, so if you were to increase production, the marginal units would cost less than $1, and can be sold at market price for $1. So it would be profitable to produce more. Thus the optimal level of

ECON | 101 | INTRODUCTORY MICROECONOMICS | homework | 1 Economics 101 Spring 2018 An

Economics 101 Spring 2005 Homework #4 Due 3/30/05 1. Suppose that you have the information shown in the table about a firm’s costs. Quantity TC($) AFC($) AVC($) ATC($) 0 120 MC($) 1 180 2 200 3 210 4 225 5 260 6 330 (Note) TC: Total cost AFC: Average fixed cost ATC: Average total cost MC: Marginal cost. a. What is the firm’s total fixed cost? b. Complete the missing data in the table. What is the firm’s minimum-cost output? c. On one diagram, draw the firm’s average total cost (ATC), average variable cost (AVC), and marginal cost (MC) curves. 1 2. The graph below shows three average total cost (ATC) curves associated with alternative scales of plant that a firm can build. The LRATC curve shows the firm's long- run average total cost curve. a. Indicate at what point on its LRATC curve the firm is operating the optimum scale of plant at its optimum rate of output. b. Choose the correct answer: 1) If the firm expected to produce 100-thousand units of the good in the long run, the firm should build a plant associated with ATC 1 / ATC 2 / ATC 3 . 2) If the firm currently was producing at point C on the ATC 2 in the accompanying figure, but anticipates increasing output to 225-thousand units in the long run, the firm will build a smaller / larger plant and experience economies of scale / diseconomies of scale . 3. The total short-run cost function of a firm is given by the equation C=190+53Q, where C is the total cost and Q is the total quantity of output. a. What is the firm’s fixed cost? b. If the firm produces 100 units, what is its average cost and average variable cost? c. What is its marginal cost per unit produced if the firm is currently producing 100 units and decides to produce an additional unit? d. Suppose that the firm’s fixed cost rises by $50, but its marginal cost falls to $45 per unit. Write the new cost equation. 2

ECON | 101 | INTRODUCTORY MICROECONOMICS | homework | Economics 101 Spring 2005 Home

ECON | 101 | Principles of Economics | 

Economics 101 Homework #1 Answer Key Fall 2007 1. a. 0 10 20 30 40 50 0 5 10 15 20 25 30 Line B Line A b. Line A: y = (-1/6)x + 15 Line B: y = 3x – 5 c. x = 120/19 = 6.32 y = 265/19 = 13.95 2. a. Normative b. Positive c. Positive d. Normative 3. a. Jack has the absolute advantage in the production of wheat. b. Jack has the absolute advantage in the production of shirts. c. Jack: 1 shir

homework1answersfall2007.doc-Economics 101 Homework #1 Answer Key

5 i. What is the acceptable range of trading prices in terms of brownies for 5 pies? Illustrate this using the number line approach presented in class. Make sure to include the arrows and labels that indicate Joe’s perspective and Susie’s perspective. Answer: a. b. B = 20 – 2P Pies produced by Susie Brownies produced by Susie 2 16 8 4 8 4 6.5 7 9 2 c. d. B = 40 – (4/3)P Combination of (Brownies, Pies) * Location of combination relative to Joe’s PPF 6 (36, 3) Lies on the PPF (33, 6) Lies beyond the PPF: when Pies = 6, then Brownies = 32 using the equation for the PPF (22, 12) Lies inside the PPF: when Pies = 12, then Brownies = 24 using the equation for the PPF (24, 15) Lies beyond the PPF: when Pies = 15, then Brownies = 20 using the equation for the PPF ( 2, 27) Lies inside the PPF: when Pies = 27, then Brownies = 4 using the equation for the PPF *Note: the table purposefully alter the order of the coordinate points from (Pies, Brownies) which is what you graphed in (a) and (c) and instead listed the coordinate points as (Brownies, Pies) to make sure you knew to enter the values in the “right” places in the equation you found in (d). e. Joe has the absolute advantage in the production of brownies since he can absolutely produce more brownies than Susie (40 brownies versus 20 brownies). f. Susie has the comparative advantage in the production of brownies since she has a lower opportunity cost for producing brownies than does Joe. Susie’s opportunity cost of producing a brownie is equal to ½ pie, while Joe’s opportunity cost of producing a brownie is equal to ¾ pie. g. Start by finding the intercepts. Clearly if Susie and Joe produced no pies they could make 40 + 20 = 60 brownies together. Similarly they could make 40 pies if they produced no brownies. To determine the rest of the graph, pretend Susie and Joe were initially thinking about producing only brownies but then decided to make one pie. Who should make this pie? We know that Susie has the comparative advantage in brownies, which means Joe must have the comparative advantage in pies. Hence Joe should make the first pie, and every pie after that until he can make no pies, i.e. until we reach the kink point where Joe makes 30 pies and Susie makes 20 brownies. With the kink point and the intercepts you can find the equations of the two line segments using methods as in 1 (a). h. 7 i. 4. Jacob and Marley produce windows and doors using only their labor. The following table provides you with information about the amount of labor that Jacob and Marley must use in order to produce these doors and windows. Assume that Jacob and Marley both have the same amount of labor and that their PPFs are linear. Amount of Labor Needed to Produce One Window Amount of Labor Needed to Produce One Door Jacob 2 hours of labor 4 hours of labor Marley 6 hours of labor 3 hours of labor a. Given the above information, who has the absolute advantage in the production of windows? Explain your answer. b. Given the above information, who has the absolute advantage in the production of doors? Explain your answer. c. Given the above information, what is Jacob’s opportunity cost of producing one window? Explain your answer. d. Given the above information, what is Marley’s opportunity cost of producing three doors? Explain your answer.

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