final exam 2022 - answer key (1)

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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
(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
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