final exam 2022 - answer key (1)

pdf

School

University of Rochester *

*We aren’t endorsed by this school

Course

401

Subject

Economics

Date

Jan 9, 2024

Type

pdf

Pages

Uploaded by UltraSteel12891

STR401 - Managerial Economics Final Exam - answer key Wednesday, August 24, 2022 Directions: This is a closed-book exam. You will have three hours to complete the exam. Answer all questions as clearly and legibly as possible, using the supplied exam booklets. Do not answer your questions in this exam booklet. In order to get full credit, you need to show your work. The exam has a total of 400 points, and the length of exam is 180 minutes. The number of points are indicated for each question. This exam consists of 9 pages, including this cover sheet. You are expected to work alone. To con°rm this, please complete and submit with your exam this cover sheet to the exam I understand the Simon code of academic integrity and agree that I have completely abided by it will continue to do so. In particular, I have not discussed the contents of this exam with anyone else while completing it, and I will not discuss the contents of this exam with anyone who will take it later. Signed: ________________________________________ Print your name: __________________________________ 1

Basic formulas Optimality: " MB = MC " Elasticity of Q with respect to X : dQ dX X Q inverse elasticity rule: P ° MC P = 1 j E d j competitive market equilibrium: Q d ( p ) = Q s ( p ) pass-through: E S j E d j + E S markets with externalities: SMC ( Q ) = PMC ( Q ) + EMC ( Q ) and SMB ( Q ) = PMB ( Q ) + EMB ( Q ) Two-part tari/s: T = A + pq Nash Equilibrium: "Everybody is playing a best response" Derivative of a quadratic function: If y = a + bx + cx 2 ; then dy dx = b + 2 cx Area of a rectangle: height ° width area of a triangle 1 2 ° height ° width Net Present Value: 1 + ° + ° 2 + ° 3 + ::: = 1 + ° 1 ° ° = 1 1 ° ° 2

PART (A) - SHORT ANSWERS (200 points / 20 each): (a) Brie±y de°ne the concept of cross-price elasticity of demand and discuss how it is useful in both describing relationships across various products and in measuring the competitiveness of markets. Cross-price elasticity of demand measures how sensitive the demand for good X is with respect to the price of good Y, de°ned as dQ x dP y P y Q x (the percentage change in the demand for good X divided by the percentage change in the price of good Y). Positive cross price elasticities indicate that the two products are substitutes, while negative cross price elasticities indicate that the products are complements. The higher cross-price elasticities suggest that the products are more substitutable in the eyes of the consumers and thus making the market more competitive. (b) A market for widgets is currently served by a single °rm (with market power). The current market price of the widgets is $40, and the monthly sales are 1000 units. The government is currently taxing the sales of widgets at the rate of $5 per unit, so that for the sale of each unit, the °rm receives $35 and the government receives $5. The °rm is currently pro°table. An economic advisor comes to you and suggests replacing the $5/unit speci°c tax with a $5,000/month operating fee. Evaluate the e/ects of the proposal on the °rm, the consumers and the overall e¢ ciency of the market. Should you implement the proposal and why? Eliminating the tax would lower the market price while raising the price received by the °rm while expanding sales, so both the consumers and the °rm would be better o/, and the e¢ ciency of the market would be improved. So the proposal makes perfect sense since the government still gets its $5,000. While no °gure was needed for this question, below is an illustration of the solution to highlight the basic e/ects. Figure 1: illustration of solution to q1(b) 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

(c) Suppose there are two goods, X and Y, the markets for which can be characterized as perfectly competitive (and the goods are independent, so there are no cross-price e/ects, and there are also no externalities). The supply of both goods is in°nitely elastic, while the own-price elasticity of demand for good X is ± 2 : 3 and the own-price elasticity of demand for good Y is ± 4 : 1 . If the government wants to raise a °xed amount $A dollars in tax revenue from the two markets while minimizing the deadweight loss associated with the tax, which market should the government tax relatively more and why? Recall that the deadweight loss caused by a tax is ampli°ed by the elasticity, so the optimal strategy is to tax the less elastic market relatively more. Thus, the market for good X should be taxed relatively more than the market for good Y. (d) Suppose your (inverse) demand curve is given by P ( Q ) = 15 ± 1 4 Q while your total cost of production is given by TC ( Q ) = 10+ Q + 1 4 Q 2 . Solve for your pro°t-maximizing price and whether you want to continue operating in the business. Marginal cost of production is MC ( Q ) = 1+0 : 5 Q; while the total revenue is (15 ± 1 4 Q ) Q , giving marginal revenue of 15 ± 0 : 5 Q: Thus, the optimal output level is given by 1 + 0 : 5 Q = 15 ± 0 : 5 Q ! Q = 14 and so the price is P = 15 ± 0 : 25 ° 14 = 11 : 5 . Your pro°ts are (15 ± 0 : 25 ° 14) ° 14 ± 10 ± 14 ± 0 : 25 ° 14 2 = $88 > 0 so it is worthwhile to stay in business. (e) Suppose that the price of gasoline is currently P = $4 : 54 . Concerned over the impact of such high gasoline prices on consumer welfare, the government imposes a price ceiling of P = $4 on the gasoline market. Use the supply-and-demand framework to graphically and verbally illustrate the e/ects of such regulation on the gasoline market. Who gains, who loses and what is the overall impact on market e¢ ciency? The solution is illustrated in the below °gure ²At ceiling of $4, the ceiling is binding and relative to the market equilibrium, shrinks supply while creating excess demand. Given the quantity traded shrinks, that creates a deadweight loss for the units that would be valuable to trade but no longer get traded since suppliers are unwilling to supply them at price of $4. The producers are strictly worse o/, producing less and receiving a lower price. Consumers may be worse o/ or better o/ ² the lower price generates a surplus transfer (CS(2) area) from producers to consumers, but at the same time the consumers also lose their share of the deadweight loss triangle. And recall that this is the minimum ine¢ ciency, where we are still assuming that the good is getting allocated to those who actually value it the most. (f) Ann and Bob are working on a joint project and choosing how many hours to contribute towards the project. The payo/ matrix is given by the table below. Solve for the Nash equilibrium of the game where Ann and Bob choose their contributions simultaneously (and only once). Brie±y describe the process how you got to your answer. 4

Figure 2: Graph for question 1(e) We follow the logic of best responses ²with the best responses bolded in the table below. Then, the Nash equilibrium is given by the cell where the two best responses meet so that neither player wants to change what they are doing, giving the equilibrium as Ann contributing 1 hour and Bob contributing 0 hours. Bob 0 1 2 Ann 0 2, 2 4 ,1 7 ,1 1 4 , 3 3,2 5,1 2 3,5 2, 7 6,6 (g) You operate a Hampton Inn, franchised from Hilton. You have just completed an extensive market research project to identify your demand curve and adjusted your pricing accordingly to maximize your pro°ts. Right after this, however, Hilton informed you that the annual franchise fee that you need to pay has increased from $100,000 to $125,000 per year. Your CFO comes and says, "given the increase in the franchise fee, we should increase the price of our rooms to recoup the increased cost." How would you respond? The franchise fee is a °xed cost, and as a result should have no e/ect on the pricing decision. Given that the pricing strategy is currently optimal, then changing prices would only decrease your pro°ts further. (h) Brie±y explain the impact of product di/erentiation (vertical or horizontal) on the intensity of price competition and the pro°tability of the °rms involved. The purpose of product di/erentiation is to decrease the intensity of price competition and thus increase pro°tability, whether that di/erentiation is vertical or horizontal. In both cases, having your loyal customers decreases your incentives to go after other customers. 5

(i) Brie±y explain the concepts of learning curves and economies of scale and how they di/er from each other. Economies of scale refers to the situation where your average costs are falling as you expand the scope of your operations (say, output per month). The basic idea is that some scale is always good to lower your average costs, whether it is due to specialization, ability to spread °xed costs over a bigger number of units or maybe improved bargaining power with your suppliers. Learning curves, in turn, also deal with decreasing average costs but deals with the idea of learning, i.e. getting better at doing things over time. So the idea of learning curves is that it becomes cheaper for you to produce any level of output the more experience you have, which we can measure by the cumulative output you have produced up to today. That is, because you have already produced 100,000 cars over time, your average costs are lower for any output level than when you had only produced 1,000 cars. (j) A vertical merger, where two companies in a supply chain merge together, is di/erent from a horizontal merger, where two competitors in the same market merge, because it does not have a direct e/ect on the market by simply reducing the number of competitors. Such vertical mergers, however, are still evaluated by the Department of Justice or the Federal Trade Commission for their potential anti-competitive e/ects. Brie±y describe some of the ways how such a merger may either help or hurt the °nal consumer and thus be either pro- or anti-competitive. On the bene°t side, one of the main components is the elimination of double marginalization, where the upstream supplier uses its market power to extract surplus from the downstream poducer, which then increases prices to the °nal consumers and, as a result, lowers overall pro°ts for the supply chain as a whole. Then, a merger can actually lower prices to the consumers by making the merged °rm worry about pro°ts in the whole supply chain. One of the main concerns, on the other hand, is the risk of what we call market foreclosure. The merged entity may have an incentive to prevent its competitors from having access to the upstream supply (e.g. AT&T could be tempted to block other cable companies from having access to Time Warner content), thus gaining a competitive advantage in the marketplace and being able to charge higher prices due to the reduced competition (increased product di/erentation in the case of content, for example, since only you can now sell the content), or simply skewing the competitive environment by charging the competitors much higher prices for the input, thus weakening competition by increasing the production costs of your competitors. 6

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

PART (B) - LONG ANSWERS Question 2 (50 points): This question consists of two parts. The °rst part examines your decision to go to the movies, while the second part examines some of the aspects on the theater³s side: Part (A) Clive is facing a dilemma. He was planning on going to the movies to see Top Gun 2. He places an expected value of $40 on seeing the movie, and the tickets cost $15. In addition, if he goes to the movies, he has the option of buying candy, pocorn and soda. If he goes, candy gives him $5 of extra value and costs $7, popcorn gives him an extra $10 of value while costing $7 and soda gives him an extra $7 of value and costs $5. But his friend just called him up and asked him to go and play pool instead. (i) [5 points] If Clive chooses to go to the movies, which items (if any) will he purchase - candy, popcorn and/or soda? Buying candy would give negative consumer surplus while buying soda and popcorn gives positive consumer surplus so Clive would buy popcorn and soda while passing on candy. (ii) [10 points] Suppose that Clive has already bought the ticket (non-refundable) but has not made any other commitments. Given your answer to (i), what is the minimum value $X that Clive needs to place on seeing his friend and playing pool so that he chooses that instead of going to see Top Gun 2. If Clive goes to the movies, he will get $40 value from the movie and $3 net value from popcorn and $2 from soda, so the net value is $45. The ticket is a sunk cost at this point. As a result, Clive needs to place at least $45 value on seeing his friend. (Alternatively in the math you can include -$15 for the price of ticket to both options, which gives you the same answer) (iii) [10 points] Suppose that instead of having bought just the ticket, Clive has bought a luxury package which includes soda, popcorn, candy and the ticket, for a total price of $30 (non- refundable). What is the minimum value $X that Clive needs to place on seeing his friend and playing pool so that he now chooses that instead of going to see Top Gun 2. Brie±y explain how and why your answer di/ers from (ii). Now, all the consumption is bundled together to the luxury package, which then gives a total value of $40+$5+$10+$7=$62. The price you paid is now sunk, so you would need to value the time with your friend at least at $62. (or you could again include the -$30 for the price of the package to both options, leaving the answer unchanged). The reason for the di/erence is that a bigger part of the costs associated with going to the movies are now sunk (unavoidable), so that going to the movies is now relatively more attractive and thus the value of your friend needs to be higher to compensate for that. 7

Part (B) Now consider the pricing on the movie theater side. Suppose that the theater sells only popcorn and soda. The theater has four potential customers, Ann, Bob, Chrissy and Dave. Their valuation for popcorn and soda are given by the following table. The marginal cost of both popcorn and soda is zero. (hint: for parts (i)-(iii), since you have only four distinct customers with unit demands, you will e/ectively need to experiment with di/erent pricing options to °nd which one is the best) Ann Bob Chrissy Dave popcorn $8 $6 $9 $2 soda $5 $7 $1 $9 (i) [5 points] Suppose that you can only have a price for popcorn and a price for soda. What prices would you set to maximize your pro°ts (here: revenue since MC=0). This question requires just some trial and error ²for popcorn, pricing at 9 sells to Chrissy and gives $9, pricing at 8 sells to Ann and Chrissy for a total of $16 revenue and pricing at $6 sells to Ann, Bob and Chrissy, for a total of $18. Going all the way to $2 to sell to Dave as well would only bring in $8 and so the optimal popcorn price is $6, and following the same logic the optimal soda price is $5, for a total revenue of $18+$15=$33. (ii) [5 points] Suppose you decide to sell only a popcorn and soda combo for $X (no individual prices). What price would you set for the combo? To price the bundle, we need the total valuations for both goods, which are $13, $13, $10 and $11 for Ann, Bob, Chrissy and Dave, respectively. Pricing at $13 then gives $26, pricing at $11 gives $33 and pricing at $10 gives $40, so the optimal bundle price is $10, all individuals buy the bundle and the revenue created is $40. (iii) [5 points] Solve for the optimal mixed bundle, that is, the price for the soda/popcorn combo and the individual prices set for soda and popcorn if bought individually. Here we need to follow similar exploration ² from above we already know that if we set the price of the bundle at $40, then everyone is happy buying the bundle, and there³s no need for individual prices, since they would just pull people away from the bundle. But can we do better? So let us raise °rst the price of the bundle to $11. Now, everyone but Chrissy buys the bundle, for total of $33, while we can price popcorn at $9, which is just attractive to Chris (while bundle gives negative value) ²and total revenue is $42. Note that we don³t want to introduce separate soda price. Finally, suppose we raise the price of the bundle to $13. Now, ann and bob are happy to buy the bundle but chrissy and dave don³t buy anything. But if we price popcorn at $9, Chrissy becomes just willing to buy that, and pricing soda at $9 makes Dave just willing to buy that. And importantly, note that at these prices, neither Ann or Bob wants to switch away from the bundle, 8

so we get total revenue of $26 (bundle to Ann and Bob) plus $18 (popcorn for Chrissy and soda for Dave), for a total of $44. This is the best you can do. (iv) [10 points] in addition to movie theaters, the prices at concession stands in concerts, sporting events, etc., are notoriously high. Can you explain why a hot dog (or any other drink/snack of your choice) should be so much more expensive at the event than, say, your corner hot dog stand (or local bar). This is about the elasticity of demand and how that re±ects the availability (or the absence of) substitutes. Outside of a venue, you have many options where to grab your hotdog (or beer), and, as a result, you are relatively price sensitive and thus °rms optimally charge lower prices. Once you are in a venue, you are fundamentally a captive market. The only options you have are either paying for the beer and hot dogs at the venue³s concession stand, or you will need to go completely without. And given this lack of substitutes and the resulting inelastic demand, the concession stands optimally charge higher prices. 9

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 3 (50 points) : Consider the titanium dioxide industry. Currently, the demand for titanium dioxide is given by Q d ( P ) = 30 ± 5 P and the industry is characterized by a large number of small producers (do that the market can be characterized as perfectly competitive), with the total supply given by Q s ( P ) = 3 P ± 6 . (i) [10 points] Solve for the equilibrium in the titanium dioxide market: the equilibrium price, quantity traded and the consumer and producer surpluses associated with that equilibrium. The inverse demand curve is P = 6 ± 1 5 Q and the inverse supply curve is P = 2 + 1 3 Q . Thus, the market equilibrium quantity solves 6 ± 1 5 Q = 2 + 1 3 Q . ! 4 ± 8 15 Q = 4 ! Q = 7 : 5 and so the market price is P = 4 : 5 : The consumer surplus is then 1 2 ( P max ± P ) Q = 1 2 (6 ± 4 : 5) ° 7 : 5 = 5 : 625 while the producer surplus is 1 2 ° P ± P min ± Q = 1 2 (4 : 5 ± 2) ° 7 : 5 = 9 : 375 (ii) [10 points] In addition to the standard costs of production, the production of titanium dioxide pollutes the environment, with the external marginal cost estimated to be EMC ( Q ) = 1+ 1 6 Q . Solve for the e¢ cient level of titanium dioxide production and the deadweight loss associated with the solution to part (i) To construct the social marginal cost of production, we need to combine the external marginal cost with the inverse supply curve, giving 2 + 1 3 Q + 1 + 1 6 Q = 3 + 1 2 Q . Thus, the e¢ cient quantity solves 6 ± 1 5 Q = 3 + 1 2 Q ! 7 10 Q = 3 ! Q = 4 : 286 : Then, the deadweight loss is given by 1 2 ° Q comp ± Q efficient ± ° EMC ( Q comp ) = 1 2 (7 : 5 ± 4 : 286) ° (1 + 1 6 ° 7 : 5) = 3 : 62 ²so the deadweight loss associated with the competitive equilibrium is $3.62. (all areas are illustrated in the °gure below) (iii) [5 points] What tax on titanium dioxide would restore e¢ ciency in the market? The e¢ ciency is always restored by introducing a tax that matches the size of the externality at the e¢ cient output level. Thus, if we levied a tax T= ° 1 + 1 6 ° 4 : 286 ± = $1 : 71 per unit produced, we can restore e¢ ciency in the market. (iv) [15 points] suppose that there is industry consolidation so that the small producers merge into a single, large °rm. Compute the equilibrium price and quantity traded in the market, and the deadweight loss associated with the equilibrium (the externality is still present and there is no corrective tax in place). Compare and explain the di/erence in the deadweight losses between this consolidated market and the competitive market in part (ii). If the industry is consolidated, then the °rm will have market power and price accordingly. Recall that the supply curve in a perfectly competitive industry is the marginal cost curve, which 10

in this case is MC ( Q ) = 2 + 1 3 Q . To construct the marginal revenue curve, note that the total revenue now is TR ( Q ) = 6 Q ± 1 5 Q 2 and so the marginal revenue curve is MR ( Q ) = 6 ± 2 5 Q: Optimal output level is then 2 + 1 3 Q = 6 ± 2 5 Q ! Q = 5 : 45 ; and so the resulting deadweight loss is (reading from the graph) 1 2 ° Q monopoly ± Q efficient ± ° ( SMC ( Q monopoly ) ± PMB ( Q monopoly )) = 1 2 (5 : 45 ± 4 : 286) ° ( ° 3 + 1 2 ° 5 : 45 ± ± ° 6 ± 1 5 ° 5 : 45 ± ) = 0 : 47 . Thus, the dead- weight loss now is only $0.47. In other words, the deadweight loss under market power is now smaller than the loss under perfect competition. The reason is that in the presence of negative externalities, perfectly competitive markets over-supply the product, and so market power, which leads °rms to cut back their production, actually works to the bene°t of the society. We still didn³t °x the whole problem, but we did get considerably closer. Figure 3: Illustration of the solution to q3 (v) [10 points] When regulating pollution, it is sometimes argued that, instead of taxes, it would be better and more e¢ cient to impose a uniform standard on all polluting entities because that way everyone has to pay their fair share for the emission reductions. Brie±y discuss whether you agree or disagree with this statement and why. The pitfall of the argument is that when facing a uniform standard, the cost of meeting that standard may be highly di/erent across °rms and so some °rms may face considerably higher costs to meet that standard than others. While it may make sense that °rms that pollute a lot, should then bear a much higher cost, the point is that often it doesn³t matter which exact °rm pollutes but how much pollution overall there is. Then, it makes sense that the °rms that °nd it easier to 11

cut back on emissions should do more of that, while the °rms that °nd it extremely costly, should do less of that. Using an emissions tax (or abatement subsidy) would allocate such costs more e¢ cienctly across the °rms. 12

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Question 4 (50 points): Consider the following game between Spirit Airlines and Delta. Each company can choose one of three prices, high, medium and low, with the resulting pro°ts captured by the following payo/ table: Delta P = high P = medium P = low Spirit P = high 30,50 10, 55 5,40 P = medium 40 ,45 20, 50 10,35 P = low 30,25 25 , 30 15 ,25 (i) [10 points] Suppose that the two companies choose their prices simultaneously and only once. What are the equilibrium prices chosen by the two °rms? With best responses bolded above, the Nash equilibrium is for Spirit to charge a low price and for Delta to charge a medium price. (ii) [10 points] Suppose that Delta could commit to its price °rst, which is seen by Spirit who then chooses its price. What are the prices chosen by the two °rms now? Brie±y explain how and why your answer di/ers from part (i). If, following the choice by Spirit, Delta could change its price, would it want to do so and why or why not? What does this suggest about the sustainability of the equilibrium you found over time? While we could draw the game tree to be sure, we can use the above directly to deduce the answer. In particular, since Spirit sees the price chosen by Delta, then Delta knows if it chooses high, spirit will respond with medium for pro°t of 45, while if it chooses medium or low, spirit will respond with low, for pro°ts of 30 and 25, respectively. So of the three possible outcomes, Delta prefers to choose a high price, followed by spirit³s medium price, for a pro°t of 45. The logic is that by committing to a price °rst, Delta is able to avoid the temptation to undercut Spirit, and thus both parties are able to sustain higher prices in this case. However, for the latter part of the question, once Spirit chooses the medium price, Delta would like to change its choice to Medium as well because it can make more pro°ts that way (after which spirit would go low), suggesting that over time Delta would need some commitment power not to change its price or the equilibrium of Spirit choosing medium price and Delta choosing high price will not be sustainable. (iii) [15 points] Suppose now that the game is in°nitely repeated, each °rm discounts the future at rate ° (that is, receiving a dollar next period is worth ° today) and the pricing choices are simultaneous. For what discount factors ° does the following strategy combination constitute an equilibrium: "Spirit charges a medium price and Delta charges a high price, and they continue to do so as long as neither °rm has deviated. If somebody has done something di/erent, then Spirit will choose a low price and Delta will choose a medium price" Note that Spirit is already playing its best response in this suggested equilibrium, so that Spirit could be completely myopic and still be happy to choose a medium price in response to Delta³s 13

high price. For Delta, sticking with the strategy gives a NPV of pro°ts of 45 + 45 ° 1 ° ° while the optimal deviation gives 50 today while dropping future per-period pro°ts to 30, with the resulting NPV of 50 + 30 ° 1 ° ° : Thus, delta is willing to play according to the proposed strategy as long as 45 + 45 ° 1 ° ° ² 50 + 30 ° 1 ° ° ! 3 ° 1 ° ° ² 1 ! ° ² 1 = 4 : Thus, a dollar next period needs to be worth at least 25 cents today. If Delta is even more impatient, then the strategy is not sustainable. (iv) [15 points] Suppose that Spirit is considering going "upmarket," improving the quality of its airplanes and service. Brie±y discuss both benefts and costs/risks of such strategy. The natural bene°t of improving the quality of your service is the fact that consumers will be willing to pay more for a better service, other things constant. However, there are two downsides. First, of course, quality improvements generally cost money and so you need to weigh the bene°ts gained to the cost of provision. Second, other things are unlikely to be constant. In particular, improving the quality of the service will make the product more similar to Delta, you become more of a competitive threat to which the optimal response by Delta is to lower their prices, which will limit your ability to actually extract the value of your improved service. Indeed, even if quality improvements were free, you may not want to make that improvement because the competitive pressure increases so much that you actually make less money with a better product on the market. 14

Question 5 (50 points): You are Apple and designing your product portfolio for next year. You have identi°ed that you have two di/erent types of customers, Apple loyalists and casual users. You want to introduce to introduce a phone targeted for each of the two market segments. Apple loyalists are willing to pay TB H ( Q ) = 30 Q ± 1 2 Q 2 for a phone of quality Q (with marginal bene°t of incremental quality improvements as MB H ( Q ) = 30 ± Q ), while the casual users are willing to pay TB L ( Q ) = 15 Q ± 1 2 Q 2 for a phone of quality Q (with marginal bene°t of incremental quality improvements as MB L ( Q ) = 15 ± Q ). Your cost of producing a phone of quality Q is 10 + 5 Q . Assume that the two segments have the same number of customers each. (i) [10 points] Suppose you decide to introduce phones of quality Q L = 10 and Q H = 25 . What prices T L ; T H should you set so that the casual users choose to buy the low-end phone while the Apple loyalists will buy the high-end phone? To get the casual consumers to buy the low-end phone the price can at most equal their valuation of the phone, so we get T L = TB L (10) = 15 ° 10 ± 0 : 5 ° 10 2 = 150 ± 50 = $100 : So the low-end phone will retail for $100 (or $99 if you want to be generous). To get the Apple loyalists to buy the high-end phone, they need to get more CS from the high-end phone than the low-end phone, so it needs to be that TB H (25) ± T H ² TB H (10) ± T L 30 ° 25 ± 0 : 5 ° 25 2 ± T H ² 30 ° 10 ± 0 : 5 ° 10 2 ± T L 437 : 5 ± T H ² 250 ± 100 T H = $287 : 5 so you can retail your low-end phone at $100 and the high-end phone at $287.5. Given the production costs (not asked here but for concreteness), your pro°ts from the low-end phone are now $100-10-50=$40, while the high-end phone nets you 287.5-10-125=$152.5 per phone sold. (ii) [15 points] Suppose instead that you decide to introduce phones of quality Q L = 5 and Q H = 25 . What prices T L ; T H should you set now so that the casual users choose to buy the low-end phone while the Apple loyalists will buy the high-end phone? Brie±y explain how and why your answer is di/erent from (i) Following the same logic from above, with the exception that the low-end phone is now of lower quality. The price for the low-end phone now needs to be T L = TB L (5) = 15 ° 5 ± 0 : 5 ° 5 2 = $62 : 5 while the price for the high-end phone can be T H = TB H (25) ± ( TB H (5) ± T L ) = $437 : 5 ± (137 : 5 ± 62 : 5) = $362 : 5 : The price of the low-end phone is thus lower simply because we are selling a worse phone, but the price of the high-end phone is higher because the Apple loyalist now gets less consumer surplus 15

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

from buying the low-end option and, as a result, it is possible for Apple to raise the price of that phone, even if it has exactly the same quality, by nearly $100 dollars. The new pro°ts per phone are now $27.5 for the low-end model and $227.5 for the high-end model. (iii) [15 points] Suppose that you decide to not produce the low-end phone at all and only cater to Apple loyalists. What quality phone would you produce and how much could you charge for it (now you can produce any quality phone, not only one of the options presented above, so part of the solution is to solve for the optimal quality)? Is this a better strategy in this case than either (i) or (ii)? Brie±y explain your reasoning. If I target the phone only towards Apple loyalists, that is equivalent to perfect price discrim- ination ² only one type of product o/ered to one particular type of customer, with the goal of extracting all surplus. Following the logic of price/quality packages, the solution involves providing the e¢ cient quality and then charging the total value of that quality from the consumer. So from above, MB H ( Q ) = 30 ± Q while the marginal cost of providing quality is 5, and equating the two gives Q=25. So a phone of quality 25 is the optimal phone to sell to the Apple loyalists. Then the price you can charge is the full valuation, which was TB H (25) = $437 : 5 and so your pro°t margin is $302.5 for each phone sold after taking away the production costs. Given the equal weight on the two market segments, an immediate comparison with the pro°t margins in (i) and (ii) shows that in this case it would be optimal for Apple to only cater to the loyalists ²even if their sales are halved, they make a margin of over $300 on each sale, which is better than the total pro°t of about $250 when selling both a high-end and low-end phone in (ii) and the total pro°t of about $200 in (i) when selling both a high-end and a low-end phone. (iv) [10 points] This question has dealt with price discrimination based on self-selection, where the °rm o/ers a menu of alternatives and allows the consumers to self-select into what option they buy. Another form of price discrimination is market segmentation, where the °rm segments the market based on directly observable characteristics and then sets a di/erent price for each segment. Brie±y describe the logic of such market segmentation in terms of how the optimal prices depend on the characteristics of the segment and give at least two examples of such price discrimination. The idea behind direct market segmentation is simply to identify markets with di/erent own- price elasticities of demand based on some observable characteristics and then using the inverse elasticity rule for each segment separately. As a result, inelastic market segments will face higher prices and elastic segments will face lower prices. Some examples include student and senior dis- counts, pricing based on the geographic location (from countries to zip codes), pricing based on your phone³s operating system, and on and on. 16

Bonus question (20 points): To blow o/ some steam after an arduous pre-fall and to forget all about what was STR401, you and your friends decide to go clubbing tonight. You place a value of $15 for just being able to hang out with your friends and commiserate and, on top of it, the club o/ers the ability for you to consume some adult beverages of your choice. Suppose your demand for drinks is P = 20 ± 2 Q and drinks are reasonably priced at P=$10 per drink. (i) [10 points] How many drinks would you choose to consume during the night and how much could the club charge you as a cover charge so that you are still willing to go. Your demand curve is Q = 10 ± 1 2 P so at price of $10, you would drink 5 drinks. Your consumer surplus from the drinks would be 1 2 (20 ± 10) ° 5 = $25 ; so added to the $15 you place on seeing your friends, the maximum cover charge would be $40. (ii) [10 points] Suppose now that one of your friends has the brilliant idea that you could go to a restaurant instead. You value the time with your friends the same, you place a $35 value on the meal you expect to eat and you expect to pay $25 for it. And on top of it, you can have drinks at P=$10 per drink. However, the restaurant drinks don³t give you quite the same value, so your demand for drinks is now P = 15 ± 2 : 5 Q: How many drinks would you have in the restaurant and how high could the cover charge for the club be now so that you would prefer the club over the restaurant? (the restaurant has no cover charge). Your demand curve is Q = 6 ± 1 2 : 5 P , so you would choose to drink 2 drinks, for a total surplus of 1 2 (15 ± 10) ° 2 = $5 : Adding the $15 value of friends, and $10 from the meal, your total consumer surplus from the restaurant option is $30. As a result, the maximum cover charge that the club can charge is now $10 for you to prefer the club over the restaurant. 17

final exam 2022 - answer key (1)

Related Documents