# Economics 2106 (Fall 2012) — Prof. Greg Trandel — Homework Ass.docx

31 de Oct de 2022
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### Economics 2106 (Fall 2012) — Prof. Greg Trandel — Homework Ass.docx

• 1. Economics 2106 (Fall 2012) — Prof. Greg Trandel — Homework Assignment # 4 (first part) Answers due: Beginning of class, Friday, November 9th. Instructions/Information: Depending on how much material is covered in class by Wednesday, November 7th, it’s possible that students won’t have to answer the last question on this assignment. A definite announcement will be made in class. 1. Suppose that a firm is currently charging \$45 for its product. The firm knows that its marginal cost of producing the product is \$25, and it believes that the elasticity of demand for the product (at least at its current price) equals 3. Given this belief, does it appear that setting its price at \$45 is a profit-maximizing decision? If not, and if the firm’s goal is indeed to maximize its current profit, should the firm raise or lower its price? 2. Suppose that a monopoly firm produces a good at a constant marginal cost of \$30 per unit (to keep things simple, assume that the firm has no fixed cost, so that its average total cost of production also always equals \$30). The firm sells its product to consumers in two di!erent markets. [Market A and Market B are two completely separate markets; the firm can charge a di!erent price is each.] Market A has the following characteristic: if the firm wants to increase its sales in that market by one unit, it can do so only by lowering its price in that market by
• 2. \$1. In order to sell one additional unit in Market B, in contrast, the firm must lower its price there by only \$.50. (a) Use the information given above and the formula (from class) for marginal revenue to complete the accompanying table. Market A Market B Marginal Marginal Unit Price Revenue Unit Price Revenue 8 46 39 8 41 37.5 9 45 37 9 40.5 36.5 10 44 35 10 40 35.5 11 43 11 39.5 12 12 13 13 14 14 15 15 16 16 (b) Considering Market A alone, what quantity should the firm sell in that market in order to maximize its profit there? What price should it charge in that market? What profit does the firm make on its sales in Market A? (c) Considering Market B alone, what quantity should the firm sell in that market in order to maximize its profit there? What price should it charge in that
• 3. market? What profit does the firm make on its sales in Market B? (d) Assume that the firm can charge di!erent prices in each market, and that a consumer located in one market can only buy at the price set in that market (i.e., a consumer in the market in which the firm sets the higher price can’t switch to the other market in order to buy at the lower price). In other words, assume that the firm can practice direct price di!erentiation; that it can simply maximize its profit by charging the prices (and earning the profits) found in parts (b) and (c). Adding together those profit values, what total profit does a price-di!erentiating firm make on its sales? (e) In contrast, suppose that the firm has to charge the same price to all its customers (i.e., it can’t practice price discrimination). In this case, the following table shows the quantity and price combinations at which the firm can sell.! Given the numbers in the MR column, what quantity this firm should sell to maximize its profit. When it sells this Q, what is the firm’s profit? !Here’s an example of how the numbers in the table are computed: to sell a total quantity of 24, the firm sets a price of \$40 and sells 14 units to customers in Market A and 10 units in Market B. (f) How would the ability to price discriminate a!ect the profit that this firm can earn? [In
• 4. other words, how do your answers to parts (d) and (e) compare?] Quantity Price Marg. Rev. 18 42 3613 19 4123 35 2 3 20 4113 35 21 41 3413 22 4023 33 2 3 23 4013 33 24 40 3213 25 3923 31 2 3 26 3913 31 27 39 3013 28 3823 29 2 3 29 3813 29 30 38 2813 (g) Considering a small change in price around the profit-maximizing Market-A price you found in
• 5. part (b) produces the following values: "Q = .2, "P = .2, Q = 12, and P = 42. Inserting these values into the elasticity formula from earlier in the year [("Q/Q)/("P/P)] tells us that the demand elasticity at the profit-maximizing price in Market A equals 3.5. Use this elasticity to find the profit-maximizing price with the P = [elas./(elas. ! 1)] " MC formula. Do the two ways to find the profit-maximizing price produce the same answer? (h) The corresponding values at the profit-maximizing Market-B price are: "Q = .4, "P = .2, Q ̄ = 15, and P̄ = 37.5. Using these numbers shows that the elasticity of demand in market B at the profit-maximizing price equals 5. Again use this elasticity in the appropriate formula to compute the profit-maximizing price and confirm that the formula method gives you the same value for profit-maximizing price you found earlier. 3. The following passage appears in a story (“Seeking Perfect Prices, CEO Tears Up The Rules” by Timothy Aeppel) that appeared in the March 27, 2007 edition of The Wall Street Journal. For as long as anyone at the 89-year-old [Parker Hannifin Corp.] could recall, Parker used the same simple formula to determine prices of its 800,000 parts — from heat- resistant seals for jet engines to steel valves that hoist buckets on cherry pickers. Company managers would calculate how much it cost to make and deliver each product and add a flat percentage on top, usually aiming for about 35%. Many
• 6. managers liked the method because it was straightforward. While straightforward, the described pricing system was unlikely to maximize the selling firm’s profit. How would you recommend that the company change its pricing method in order to attain more profit? 4. Think about the goods and services one might purchase for a wedding ceremony/reception: a banquet hall, a photographer, flowers, musicians (or a d.j.), etc. Some people have observed that the purchasers of apparently identical items are charged more when tell the seller they are planning a wedding than they would have been charged if they said they were planning some other type of party/gathering. Explain why this might happen. 5. For some of its ticket o!ers, Universal Orlando Resort o!ers a lower price to residents of Florida than it o!ers to residents of other states (and appears to o!er a lower price to residents of the United States and Canada than to those who live elsewhere in the world). [At least as this ques- tion is being written, see: http://www.universalorlando.com/Theme-Park-Tickets/Flor- ida-Resident-Tickets.aspx and http://www.universalorlando.com/Theme-Park-Tickets /General-Admission.aspx for examples of such pricing policies.] (a) Is such a pricing pattern better viewed as an example of direct or of indirect price dis- crimination? (b) Does this pricing pattern imply that Universal believes that the elasticity of demand of
• 7. Florida residents is larger or smaller than the elasticity of demand of residents of other states? (c) Can you speculate on a reason why the elasticity of demand for tickets to Universal might (on average) di!er depending on state of residence in the way you described in part (b)? 6. Universal studio also o!ers (for \$20 to \$30 for one day) an Express Pass option; buyers can use the pass to bypass the regular waiting lines. Is such a pricing scheme better viewed as an example of direct or of indirect price discrimination? 7. When the purchase of a product qualifies the buyer for a rebate, he or she often has to mail a form and wait to receive a check in the mail. An alternative approach would be for the manufacturer to reduce the price it charges the retail establishment, and then require the retailer to lower the price it charges customers. Explain one reason (and there may be more than one) why a manufacturer would choose the rebate approach. 8. Watch the Priceline commercial archived at: http://www.adstorical.com/commercial/369/ priceline-com-big-deal-no-one-deals-like-we-do. Which characteristic(s) that makes an item a strong candidate for price discrimination is emphasized in the script of the commer- cial?
• 9. 11. Each of two movie studios has to pick the week during which it will begin showing (or “open”) its potential summer block- buster movie. There are three possible weeks during which the movies could open. Suppose that the interaction between the studios can be con- sidered a simultaneous game, and that the accompanying table shows the payo! (the profit over the whole summer) that each studio receives for each possible combination of opening weeks. [In each box, the lower, left-hand number is the payo! of Studio X and the upper, right- hand number is the payo! of Studio Y.] Use the equilibrium-finding technique demonstrated in class to find the equilibrium (actually, to find all the equilibria) of this “game.” Studio Y: week 1 week 2 week 3 45 55 50 week 1 55 70 65 Studio 60 45 55 X: week 2 65 55 55 55 50 40 week 3 60 60 50
• 10. 12. Other things equal, Sam prefers to spend the evening at a game rather than at a movie. Other things equal, Jordan prefers to spend the evening at a movie rather than at a game. Both Sam and Jordan, other things equal, prefer to be with the other person rather than spend the evening alone. The accompanying game table shows one set of payo!s that is consistent with all these preferences. Assume that both players know how each ranks the game’s four possible outcomes. Jordan movie game 4 1 movie Sam 3 1 2 3 game 2 4 (a) What is (what are) the equilibrium (equilibria) of this game? (b) Suppose that Sam and Jordan did not finalize their plans for the evening and therefore did not agree on what event to attend. If it’s impossible for either person to communicate with the other, is it obvious to what event either player should go? (c) Now suppose that, before each person has to make his or her independent decision about which event to attend, it’s — for some unknown reason —
• 11. possible for Sam to get a message to Jordan, but it’s impossible for Jordan to get a message to Sam. When this is true, which player is likely to be able to attain his or her highest-possible payo!? What message should be sent to enable that player to attain that highest payo!? 13. The accompanying table is also consistent with the prefer- ences described in the previous question. The change in the table is due to a change in the relative importance of Jordan’s two desires. Again assume that both players know all the payo! values in the full game table. Jordan movie game 4 1 movie Sam 3 1 3 2 game 2 4 (a) Does either player have a dominant strategy in this game? If so, which player, and which strategy? (b) What is the equilibrium of the game? (c) Suppose that only one player can communicate with the other before each has to make an independent decision about which event to attend. Is that
• 12. communication likely to change either player’s action? 14. This question concerns two pairs of roommates — Andi and Bobbi are one pair; Charley and Danny are the other. Each of these people has to decide whether to devote the time needed to “Clean” the apartment, or “Not” to clean. A person’s level of satisfaction depends on both the choice that person makes and on the choice made by his or her roommate. Each of Andi and Bobbi agree that the four pos- sible outcomes are ranked in this order. Best my roommate does all the cleaning jobs; I do none 2nd best my roommate and I both share the cleaning jobs 2nd worst I do all the cleaning; my roommate does none Worst neither my roommate nor I do any cleaning Each of Charley and Danny, in contrast, agree that the outcomes are ranked in this order. Best my roommate does all the cleaning jobs; I do none 2nd best my roommate and I both share the cleaning jobs 2nd worst neither my roommate nor I do any cleaning Worst I do all the cleaning; my roommate does none (a) Using a “4” to represent the best outcome, and a “1” to represent the worst, put payo!
• 13. numbers (for both players) in the following game tables to make them consistent with the rankings described above. Bobbi Clean Not Clean Andi Not Danny Clean Not Clean Charley Not (b) Is the “game” between Andi and Bobbi best described as a prisoners’ dilemma or as a chicken game? How about the game between Charley and Danny? 15. Suppose now that Andi and Danny (from the previous question) live together. (a) Based on the preferences given above, fill in the payo!s 1–4 (for both players) in the accom- panying game table. (b) Find the equilibrium of the game between Andi and Danny. (c) We’ve analyzed games by assuming that each
• 14. player knows the payo! values of the other player(s). Suppose that isn’t necessarily true. In this game, which player has an incentive to try to conceal his or her true rankings of the various possible outcomes? Danny Clean Not Clean Andi Not 16. An article entitled “Airlines, Now Flush, Fear a Downturn” (New York Times, June 11, 2011) is posted on eLC. (a) According to the article, what happened to airline revenue per passenger in the first few months of 2011? (b) One reason for the change you noted in part (a) is that airlines changed their fares and fees. One reason for the change in ticket prices is probably the rise in fuel prices noted in the article. The article, however, also mentions another factor that might help to explain why the airlines changed their ticket prices. What is this factor? (c) Explain the possible connection between the factor you cited in when answering (b) and the fact “that mergers have left fewer airlines”. (d) Using terminology from class, what is it that airlines appeared to be doing more e!ectively
• 15. (in mid-2011) than they had done previously? 17. When we (earlier in the semester) studied a perfectly- competitive market, we concluded that when all sellers in a market are motivated by their own private self interest, the resulting outcome was the best possible one for the overall society. More recently, when we studied a prisoners’ dilemma, we concluded that when all sellers are motivated by their own private self interest, the resulting outcome was not the best possible one for the the overall group. Explain why these two conclusions are perfectly consistent with each other. 18. The accompanying table contains data on three things. The second column of the table shows the marginal value that consumers receive from various units of good Y that might be produced. The third column shows the marginal private cost of pro- ducing those units. The fourth column shows the marginal external cost that results from a negative externality that is associated with the production/ consumption of the good. Unit MV MPC MEC MSC 100 \$120 \$83 \$4 200 115 84 6 300 110 85 8 400 105 86 10 500 100 87 12 600 95 88 14 700 90 89 16 800 85 90 18
• 16. 900 80 91 20 (a) Complete the table by filling in the marginal social cost of producing each unit of Y. (b) Assume that both firms and consumers ignore the MEC associated with producing Y, and that this market reaches a competitive outcome (i.e., goods are produced as long as the value of the good to consumers exceeds the cost to producers). To the nearest hundred, how many units of Y will be produced? (c) To the nearest hundred, how much Y should be produced into order to create the most (socially-)e#cient possible outcome? (d) Is the the market equilibrium quantity less than or more than the e#cient quantity of output? By (to the nearest hundred) how many units? (e) Why is it privately profitable to produce some units of this good even though the pro- duction of those units makes society worse o! (i.e., reduces social surplus)? not provide positive social benefits? 19. The accompanying table shows data on the marginal private value (or marginal benefit) that the buyers of a good receive from various units of good Z that might be produced, the marginal private cost of pro- ducing those units, and the marginal external value that results from a positive externality that is asso- ciated with the production/consumption of good Z. Unit MPV MPC MEV MSV
• 17. 100 \$90 \$69 \$22 200 86 70 21 300 82 71 20 400 78 72 19 500 74 73 18 600 70 74 17 700 66 75 16 800 62 76 15 900 58 77 14 (a) Complete the table by filling in the marginal social value of each unit of Z. (b) Assume that both firms and consumers ignore the external value associated with Z, and that this market reaches a competitive outcome (i.e., goods are produced only as long as the value of the good to a buyer exceeds the cost to producers). To the nearest hundred, how many units of Z will be produced? (c) To the nearest hundred, how much Z should be produced into order to create the most (socially-)e#cient possible outcome? (d) Is the the market equilibrium quantity less than or more than the e#cient quantity of output? By (to the nearest hundred) how many units? (e) Why is it not privately profitable to produce some units of this good even though the production of those units would make society better o! (i.e., would raise social surplus)?
• 18. 20. The growers of “standard” produce (fruits and vegetables) use pesticides and fertilizers to in- crease yield and decrease per-unit costs. Assume that some of those pesticides/fertilizers soak into the soil, are washed away by rainwater, accumulate in lakes, rivers, or oceans, and harm the organisms (perhaps including people) that rely on that water. [I.e., fertilizer use can create so-called “dead zones”.] [There is also the possibility that harmful amounts of pesticides might remain on produce when it is sold to consumers (and might, therefore, directly harm buyers). As far as this question is concerned, however, assume that whatever pesticide residue is left on the produce (if any) is not harmful (i.e., assume there isn’t any direct impact on the purchaser of the produce).] In contrast to these items, assume that “organic” produce is grown without the use of any artificial pesticides or fertilizers. Quick observation at any grocery store indicates that consumers must pay a higher price to buy organic produce than to buy standard produce. This price di!erential presumably (at least in part) reflects the fact that it’s more expensive for a grower to produce using organic methods than to produce using standard methods. The existence of this price di!erential, of course, discourages consumers from buying organic produce. Explain why the di!erence between the grocery-store consumer prices of standard and or- ganic produce does not accurately reflect the true di!erence in the costs of producing these products.
• 19. 21. The accompanying graphs shows the demand and supply curves for a particular good. The right-hand graph also shows a marginal social cost curve associated with the production of the relevant good. The small numbers inside each figure give numeric values for the sizes of the relevant areas. Use these figures to answer the following questions. To find answers for economic surplus, add or subtract (if needed) the appropriate areas. !!!!!!!!!!!!!!! "" "" "" "" "" "" "" " 100 60 20 800 D S(=MPC)
• 21. 40 20 600 800 D S(=MPC) MSC \$ Q 18000 12000 2000 2000 (a) Assume that there is no external cost associated with the production of this good. I.e., use the left-hand-side graph to answer this question. In this case, how many units of the good are produced, and what economic surplus is created? (b) For the rest of the question, assume that the production of the good does create a marginal external cost. I.e., when you — as an independent, outside analyst — evaluate (correctly) the performance of this market, you need to use the right-hand-
• 22. side graph. Assuming that firms and consumers totally ignore the external costs of their actions, how many units of the good are produced? (c) In this market-equilibrium outcome, what economic surplus (measured correctly) is cre- ated? (d) If the only way to reduce the extent of the external e!ect is to reduce production of the good, how many units of the good should be manufactured if society’s goal is to create the largest possible economic surplus? How big is that economic surplus? 22. This question is optional. From an economic point of view, is there some positive amount of crime that could be considered to be the (socially) e#cient amount of crime? If there is such a thing, briefly explain how one could (conceptually) determine the e#cient amount of crime. 23. Table I shows, for a variety of levels of industry-wide (daily) output, the marginal value, the marginal private cost, and marginal external cost created by the production/consumption of a good. This good is produced by a number of firms in a competitive market. Table I Quantity MV MPC MEC 1000 63 27 4.5 2000 60 28 5
• 23. 3000 57 29 5.5 4000 54 30 6 5000 51 31 6.5 6000 48 32 7 7000 45 33 7.5 8000 42 34 8 9000 39 35 8.5 10000 36 36 9 11000 33 37 9.5 Table II With-Tax Marginal Private Cost tax tax tax tax tax tax Quantity = 0 = 2 = 4 = 6 = 8 = 10 1000 27 29 31 33 35 37 2000 28 30 32 34 36 38 3000 29 31 33 35 37 39 4000 30 32 34 36 38 40 5000 31 33 35 37 39 41 6000 32 34 36 38 40 42 7000 33 35 37 39 41 43 8000 34 36 38 40 42 44 9000 35 37 39 41 43 45 10000 36 38 40 42 44 46 11000 37 39 41 43 45 47 (a) Based on the numbers in Table I, if consumers and producers ignore the external cost of their actions, what quantity of the good would be produced and sold? (b) Based again on Table I, what is the (socially) e#cient quantity of production of the good? (c) Suppose that a tax is imposed on all the firms that produce
• 24. this good. The tax is a fixed amount that any firm must pay for each unit of the good it produces. Such a tax raises the marginal private cost of producing the good (which in turn shifts up the supply curve of the good). Table II shows the with-tax marginal private cost of the industry’s firms for various levels at which the tax could be set. What size tax will cause the with-tax private-market outcome (demand = supply) to match the (socially) e#cient outcome? (d) Briefly explain how a tax set at the level you found in part (b) will internalize the exter- nality.