Homework 1, Managerial Economics: Eco 685 Due: Thursday, August 30, 2018

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1 Question 1 Homework 1, Managerial Economics: Eco 685 Due: Thursday, August 30, 2018 One of the easiest ways to think about opportunity costs is to compute your wage per hour. The idea is that the next best alternative is working (ignore for the purposes of this question that people who work fixed hours may find it difficult to work one more/one less hour). Suppose Ralph has a salary of $100,000. a. Compute the hourly wage assuming a 40 hour work week and 50 weeks worked per year. b. Suppose Ralph decides to see his favorite band The National in Atlanta. He buys two plane tickets at $300 each. How many hours does Ralph need to work to pay for the plane tickets? c. Suppose Ralph spends $40 to purchase the video game Fortnight and plays the game for two hours. What is the minimum dollar value of entertainment(revenue) that Ralph gets? Assume the next best alternative is working. d. Suppose Ralph decides NOT to take a night class which costs $2,000 and takes up 10 hours per week of his time for 8 weeks. What is the maximum dollar value of the class to Ralph? Assume the next best alternative is working. Question 2 A recent article described how the manager of a customer service call center introduced a new policy: employees would be given additional pay based on the number of service calls they answer. In one week the number of calls answered per day doubled. Although not necessary, it is easiest to think of the call center as being part of firm selling the product (the call center is not outsourced). a. Explain why this form of compensation will not cause employees to maximize profits. (How did the employees increase the number of calls so much?) b. Give a type of incentive pay that is likely to work better. c. Give one possible problem with the type of compensation you gave in (b). Question 3 Classify each of the following as marginal product, marginal revenue product, or marginal expenditure. a. Senior loan officers at a bank can process 8 loan applications per week. 1

2 b. Angelina Jolie was paid $33 million for starring in the film Maleficent. c. A UPS P70 box delivery truck gets 10.2 miles per gallon. d. The average for Starbucks is $1500 revenue per day/15 hours open per day/4 workers = $25 revenue per worker per hour. e. A professor teaches a class in Managerial Economics to 40 students who each pay $2,000 per credit times 2 credits for a total of $160,000. Question 4 SupposethecityofMiamiisconsidering buildingasoccerstadium. Thecostofthestadiumis $200 million. The city estimates that the stadium will generate $250 million in tax revenues. Assume a planning horizon of 1 year and an interest rateof zero. The city wants to maximize profits which are tax revenues less costs. There are 3 options. Build the stadium in Overtown. The city believes it can acquire the land for $60 million. Build the stadium on a waterfront park the city already owns. Assume the value of the waterfront park is $80 million. I computed this based on the value of nearby land with condos. Do not build a stadium. a. Calculate the economic profits of each option. b. Calculate the accounting profits of each option. c. What is the correct decision? d. Evaluate the following statement by a city official: We should build on the water. We can use the land for free and generate enough taxes to cover the construction costs. Question 5 Assume the marginal revenue is not one so that marginal product and marginal revenue product are not equal. Answer true for MRP, true for MP, true for both, or true for neither. a. Profits are maximized when equal to zero. b. Production is maximized when equal to zero. c. Profits are maximized when equal to the cost of the input. d. If positive, an extra input always adds to profits. 2

3 e. Is the slope of the production function. Question 6 Cool Candle Co. (CCC) produces candles (Q) from pounds of wax (W) according to: Q = W 1 2 W2 (1) The candles sell for $7 and the wax costs $49 per pound. a. How much wax should CCC use to maximize profits? b. Compute the maximum profit at CCC. c. Compute the marginal revenue product of the tenth pound of wax. Explain why it is or is not profit maximizing to use the tenth pound of wax. d. How much wax should be used to maximize production? e. Explain why it is or is not profit maximizing to use the quantity of wax you found in part (d). Question 7 Workers at a hospital file insurance claims for a certain procedure. Let L be the number of hours worked by the workers and Q output (claims filed). Assume all claims have the same value/price. Input (L) Claims Filed (Q) Marginal product Marginal Revenue Product 2 NA NA $ $ Table 1: Insurance claim production. a. Complete Table 1 (may be done in Excel). b. If workers make $20 per hour, how many hours of labor should the hospital firm choose to maximize profits? Question 8 (REQUIRES TUESDAY S NOTES) A goal of many sustainability programs is to reduce fuel/energy consumption. At first glance, one would think reducing energy use always reduces costs. However, in most cases one has 3

4 to compensate by using more of other inputs. For example, more frequent tune-ups and other maintenance activities improve fuel economy but also require more labor in the form of maintenance worker hours. Jet engines are most aerodynamic when their moving parts are clean. Soot residue builds up in airplane engines over time from fuel burning. Engine washing thus improves fuel efficiency, but of course is costly. An engine wash can be accomplished via a specialized vehicle that comes out to the plane. Consider the following data gleaned from Southwest Airlines Sustainability Reporting (all data from 2009): Cost of jet fuel: $1.56 per gallon. To align units, note that the cost is 1.56 billion dollars per billion gallons. Cost of an engine wash $5000. This corresponds to 0.05 billion dollars per 10K washes. 10K Washes/year (W) Table 2: Production (Q), in billions of airline seat miles per year. Fuel is in billions of gallons per year and engine washes has units of 10K washes per year. a. Fill in the following tables (easiest if done on Excel). Note: Please use all digits in table 2 and report all answers to the nearest hundredth. 4

5 Washes (W) 1.41 NA NA NA NA NA Table 3: Marginal product of fuel. Washes (W) 1.41 NA 1.43 NA 1.45 NA 1.47 NA 1.49 NA 1.51 NA 1.53 NA 1.55 NA 1.57 NA 1.59 NA Table 4: Marginal product of engine washes. 5

6 Washes (W) 1.41 NA NA NA NA NA 1.43 NA 1.45 NA 1.47 NA 1.49 NA 1.51 NA 1.53 NA 1.55 NA 1.57 NA 1.59 NA Table 5: Marginal rate of technical substitution. b. Suppose Southwest has a sustainability goal of using no more than 1.43 billion gallons of fuel and in 2009 flew 98.1 billion airline seat miles. About how many engine washes does Southwest need to use? c. Using the table, does the marginal product of fuel diminish, increase, or remain constant? d. Using the table, does the marginal product of engine washes diminish, increase, or remain constant? e. What combination of fuel and engine washes is closest to optimal? f. Calculate the airline seat miles per gallon at the optimal combination of fuel and labor. (Hint: what are the units for the marginal products?) g. Southwest advertises the fuel savings achieved from engine washing to promote their reputation as a sustainable company. Calculate the gallons of fuel savings from engine washing at the optimal combination of fuel and engine washing. To do this, multiply the total engine washes at the optimum by the billions of gallons of fuel saved per 10K washes. For the latter number, think about the units of the MRTS. 6