Unformatted text preview: University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 17 Solutions Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 Suppose the Ontario government levies a fine on tobacco companies for misleading smokers about the dangers of smoking (a similar measure was passed in the US a few years ago). If the fine is collected as a lump sum tax, should tobacco companies raise the price of cigarettes to compensate for the fine? Hint: what is the rule for profit maximization? Answer: The fine is collected as a lump sum tax which will show up on the books as an increase in TFC. From MR = MC, we know that only current demand and cost conditions should be taken into account when choosing optimal output and price. An increase in TFC does not, and should not, impact optimal output and therefore price. Question 2 Ajax Cable Company (ACC) provides internet access to subscribers in downtown Toronto. ACC leases network capacity from Rogers by paying Rogers $2m a month plus $10 per subscriber per month. ACC's other expenses are $2m a month. ACC's marketing department estimates demand for its internet services to be: Q = 4 P/5 where Q is number of subscribers in millions and P is the monthly price in dollars. (a) Calculate ACCs revenue maximizing price and subscribers? Show all steps clearly. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: To maximize revenues we need the MR equation. The demand equation is: Q = 4 P/5 You cannot use the short cut for MR unless the demand curve is linear with P on the left hand side and Q on the right hand side: P = 20 5Q MR = 20 10Q Set MR = 0 20 10Q = 0 Q = 2 P = 20 5(2) = $10 (b) What is the price elasticity for your answer in part (a)? Answer: It is E = 1 if the firm maximizes revenues with no capacity constraints. That's all you need to say. You can also show this by actually computing E: E = (dQ/dP)(P/Q) = (1/5)(10/2) = 1. (c) What is ACC's cost equation? What is the fixed cost? What is the MC? Show all steps clearly. Answer: The fixed costs are $2m for Rogers and $2m for other expenses, which is a fixed cost of $4m. Each subscriber costs ACC $10. Thus: C(Q) = 4 + 10Q TFC = $4m MC = $10. 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (d) Calculate ACC's profit maximizing price and subscribers. Show all steps clearly. Answer: Set MR = MC From part (a) we know MR = 20 10Q. Thus: MR = MC 20 10Q = 10 Q = 1 Note how ACC has fewer subscribers when maximizing profits than when maximizing revenues. The price is: P = 20 5(1) = $15 (e) ACC introduces "popup" advertising on its website, which is raises MR by $10. Calculate ACC's profit maximizing price and subscribers. Answer: If popup advertising raises MR by $10 (intuitively each additional subscriber generates an extra $10 in revenues) then setting "MR = MC" where the MR is $10 higher than before yields: MR + 10 = 10 20 10Q + 10 = 10 30 10Q = 10 10Q = 20 Q = 2 P = 30 5(2) = $20 ACC expands the subscriber base by reducing price. 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (f) Rogers and ACC renegotiate their contract. Under the terms of the new contract, Rogers will provide network capacity for 1.5m subscribers a month and charge ACC $3m a month. Calculate ACCs optimal price and subscribers. Show all steps clearly. Answer: Note how under the terms of the new contract, MC = 0. Thus, ACC will set price to maximize revenues, the answer to which is already known from part (a). But there Q = 2 which is greater than the capacity of 1.5. Hence the answer is: Q = 1.5 from which: P = 20 5(1.5) = $12.5 Question 3 (Summer 2008 Test 3 Question) In this question, the decision variable is "time". After graduating from UT's Commerce program, you fulfill your lifelong dream to produce a movie. You've just finished work on "The Dark Monopolist" based on the life of a nefarious criminal SadDamn Hussain. The movie cost $50m to produce. Assume the MC of "printing" movies on films is negligible. If the movie is released into theaters the revenues as a function of the number of weeks in theaters is: R(w) = 10w 0.25w2, where R is millions of dollars and w is the number of weeks the movie is shown in theaters. What is the optimal number of weeks the movie should be shown in theaters? Show all steps clearly. Answer: The decision variable in this problem is weeks w. Since MC is $0, you want to maximize revenues. Set MR = 0, where MR means the additional revenue from showing the movie for another week in theaters: R(w) = 10w 0.25w2 dR(w)/dw = MR = 10 0.5w MR = 0 10 0.5w = 0 w = 20 4 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain To maximize revenues, the movie should be shown for 20 weeks in theaters. Question 4 In this question you will use the concept of opportunity cost to solve a 3rd degree price discrimination problem and "yield management". Yield management is a technique used by airlines to price seats. In some airlines, such as PIA, aircrafts have a first, business and economy classes but the fares within each class are uniform. In other airlines, there is price heterogeneity within classes. That is, even within the economy class seats can be sold at different prices (here's a very funny article on airline pricing). You may have experienced this yourself when booking a flight: the fare changes over time as the airline tweaks prices on current demand conditions. Let's see how yield management works. Suppose an airline operates a 180 seat aircraft between Toronto and Boston. The aircraft has a single "class". However as is typical in airlines there are different types of travelers: say "early bookers" (E) and "late bookers" (L). Their demand equations are: QE = 250 PE QL = 330 PL Let's suppose the MC of all passengers is 0 (think of it this way: the flight always operates and passengers are not served any drinks or meals). (a) Suppose this airline was like PIA and charged the same price for all passengers. What is the common price for early and late bookers? Hint: The airline is not segmenting the market and is aggregating across segments. You may want to derive the aggregate demand curve. Answer: The airline is treating all bookers as one: that is, it is aggregating passengers into a single market. Denote the common price by P (i.e. P = PE = PL). To aggregate the market we should add the early and late bookers demands: Q = QE + QL Q = 250 PE + 330 PL Q = 580 2P To maximize profits we set MR = MC. Since MC = 0, we have, after rearranging the demand 5 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain curve to P = 290 0.5Q: 290 Q = 0 Q = 290 However, this answer is not feasible since aircraft capacity is 180 seats. Thus, the airline will sell 180 seats requiring a price of: P = 290 0.5(180) = $200 Of course, given that it is optimal to sell 290 seats, the airline would in the long run expand capacity. Until then, it must content itself with selling 180 seats. Revenue will be: R = PQ = ($200)(180) = $36,000. (b) Suppose you are in charge of pricing "early bookers" seats. If your salary is a percentage of revenues from early bookers what price will you choose? Answer: This is a bit like the franchise problem. Your salary is a function only of revenues from early bookers. Hence you will want to maximize RE. You will therefore set: MRE = 0. We had: QE = 250 PE PE = 250 QE MRE = 250 2QE MRE = 0 250 2QE = 0 QE = 125 Therefore you will sell 125 seats to early bookers (and therefore 180 125 late bookers). But wait: what about the late bookers? If this airline pays the late bookers manager a percentage of late bookers revenue then she will be setting MRL = 0 which yields QL = 330/2 = 165 (and therefore 180 165 early bookers). So we have a problem: if the airline goes with your decision then aircrafts will carry 125 early bookers. If the airline goes with the late booker manager's decision which it will (why?) aircrafts will carry 165 late bookers. 6 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Put simply, by compensating managers on their "division" revenues will create problems (just as maligned interests created problems in the franchise problem). The solution? Align the interests of the two divisions by basing their salaries on the airlines total revenues 1 . (c) Suppose you are in charge of pricing "early bookers" seats. If your salary is a percentage of total revenues what price will you choose? Use the concept of opportunity cost. Answer: Now that your salary is a percentage of total revenues, each time you sell a seat to early bookers you'd worry about its opportunity cost, the profits lost from not selling to the next best opportunity the "late bookers". Thus your choice is: MRE = MC + M Opportunity Cost The MC is 0. What is the M opportunity cost? It is the profits foregone from not selling the seat to late bookers. In turn this is: MRL MCL = MRL 0 = MRL. Hence: MRE = MC + M Opportunity Cost MRE = MRL This says, the optimal revenues involves setting MR of early bookers equal to late bookers. Note: This is exactly the same result you'd have gotten setting marginal profit of each activity equal to each other. This yields: 250 2QE = 330 2QL 2QL 2QE = 330 250 QL QE = 40 You need another equation (since there are two unknowns). You know: QL + QE = 180 This implies that: QL = 110 and hence QE = 70. Hence from: 1 In the 1990s, the investment bank HSalomon BrothersH was confronted with the same problem: each division, compensated on the basis of its performance, was taking decisions contrary to the interests of the bank was a whole. Accordingly, the bank sought to compensate on the bank's performance. Many banks, including HCiti BankH, followed suit. 7 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain QE = 250 PE QL = 330 PL We have: PE = 250 QE = 250 70 = $180 PL = 330 QL = 330 110 = $220. The airline will initially sell 70 seats at a price of $180 and then, closer to the departure date, sell 110 seats at a higher price of $220. In real life, instead of early and late bookers there is a continuum of bookers, where the WTP increases closer to the departure date. Thus, you will observe a steady increase in prices as the departure date approaches (Farecast.com and Sidestep.com show the trajectory of prices for most routes). 8 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto.
 Fall '08
 HUSSEIN
 Economics, Microeconomics

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