# 1. Suppose that a firm is currently charging \$45 for its product. The firm knows that its marginal cost of…

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 different markets. [Market A and Market B are two completely separate markets; the firm can charge a different 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 \$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.
(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 market? What profit does the firm make on its sales in Market B?
(d) Assume that the firm can charge different 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 differentiation; 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-differentiating 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 andpricecombinationsatwhichthefirmcansell.∗ GiventhenumbersintheMRcolumn, 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.
Market A
Market B
Unit
Price
Marginal Revenue
Unit
Price
Marginal Revenue
8
9 10 11 12 13 14 15 16
46 45 44 43
39 37 35
8
9 10 11 12 13 14 15 16
41 40.5 40 39.5
37.5 36.5 35.5
(f) How would the ability to price discriminate affect the profit that this firm can earn? [In other words, how do your answers to parts (d) and (e) compare?]
(g) Considering a small change in price around the profit-maximizing Market-A price you found in 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 P ̄ = 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 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 offers, Universal Orlando Resort offers a lower price to residents of Florida than it offers to residents of other states (and appears to offer 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 Florida residents is larger or smaller than the elasticity of demand of residents of other states?
Quantity
Price
Marg. Rev.
18 19 20 21 22 23 24 25 26 27 28 29 30
42 412
3
411 3
41 402
3
401 3
40 392
3
391 3
39 382
3
381 3
38
361 3
352 3
35 341
3
332 3
33 321
3
312 3
31 301
3
292 3
29
281 3
(c) Can you speculate on a reason why the elasticity of demand for tickets to Universal might (on average) differ depending on state of residence in the way you described in part (b)?
6. Universal studio also offers (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. In class, we identified senior citizens, students, and members of the military as groups that are often offered lowered prices for certain products. Obviously, members of all three of these groups may also (on average) have lower incomes than do those working full time. Our explanation for why firms profit from price discrimination, though, didn’t focus on how much money the members of a group had; rather it focused on differences in the behavior of these groups relative to the behaviors of the rest of the population.
(a) Basing your answer on behaviors, explain why sellers might offer lower prices to the members of the three relevant groups.
(b) Explain the connection between those behaviors and the limited incomes possessed by many members of the three groups.
10. Ignoring a few quite-small industries (like oil royalty traders (don’t ask me)), the two industries that had the largest values for ad-spending-as-a-percent-of-sales revenue in 2011 were perfumes, cosmetics, and other toilet preparations (SIC code 2844) and transportation services (code 4700). [Data for over 300 industries is available at: http://www.wensmedia.com/assets/Media %20Free%20Stuff/ADtoSalesRatios2011.pdf.] What characteristic do these two industries share that likely distinguishes them from many other industries? [To guide your answer, you’ll probably want to think about the formula (presented in class) for a firm’s profit-maximizing level of advertising.]
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 week 1 which the movies could open. Suppose that the
Studio Y:
week 2
week 3
45
55
55
70
50
65
60
65
45
55
55
55
55
60
50
60
40
50
interaction between the studios can be con- sidered a simultaneous game, and that the accompanying table shows the payoff (the profit over the whole summer)
week 1
Studio that each studio receives for each X: week 2
possible combination of opening weeks. [In each box, the lower, left-hand number is the payoff of Studio X and the upper, right- hand number is the payoff of Studio Y.] Use the equilibrium-finding technique demonstrated in class to find the equilibrium (actually, to find all the equilibria) of this “game.”
week 3
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 payoffs 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
3
1
1
2
2
3
4
Sam
movie
game
(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 — 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 payoff? What message should be sent to enable that player to attain that highest payoff?

Business & Finance homework help