BEM/Ec 146 ANSWER KEY

BEM/Ec 146 ANSWER KEY Winter 2007 Prof. Colin Camerer

Homework #2: Available Tuesday 13 February 4 pm, due Tuesday 20 February 230pm (in my Baxter mailbox or email to TA Maggie McConnell [email protected]) Homework must be typed although mathematical symbols can be handwritten if that saves you time and if they are legible to the TA. Think carefully before you write. Many questions only require a paragraph—essentially a one-phrase answer with some elaboration. Some questions have 1 or ½ page limits; any material longer than these (12 point font, 1.5 line spacing) will be ignored. Late homework will be reduced in grade by 50% for each day late and not accepted after two days. The only standard exception is a medical excuse approved by me at least 24 hours in advance (and certified in writing by a health care professional). You can try to email me for other extensions but I am generally very unsympathetic to granting an extension for a reason that was foreseeable in advance. (For example, if you are on a recruiting or science trip that you knew about at the beginning of the term, I won't grant an extension.) The collaboration policy is to work alone.

1. Tournaments: In the theory of tournaments, players choose effort levels ei>0 (i.e. e1 and e2). Each person’s output is measured by ei plus some random luck (or measurement error) term xi. In a two-person tournament, the person with the highest total wins a fixed prize H and the person with the second-highest total wins L. If they tie they win (H+L/2) each. Suppose the luck components are independent and identically distributed with a uniform distribution over [-e, + e] (i.e., the partial distribution function f(x)=1/(2e) for – e

a. (5 points) First compute the probability that player 1 wins if efforts are e1 and e2. (Hint: Compute the distribution of the difference in the two luck components. The sum of this difference and e1-e2 is what is crucial, because if (e1+x1)-(e2+x2) is positive then player 1 wins).

For 1 to win, (e1+x1)-(e2+x2)>0 => (e1-e2)+(x1-x2)>0 => x1>x2+(e2-e1), where |e2-e1|> 0. If e2-e1>2e, then the minimum of x2 + (e2-e1) = e, then P(1 wins| e1, e2) = 0; If e2-e1<-2e, then the maximum of x2+(e2-e1) = -e, then P(1 wins| e1, e2) = 1; If -2e

To find the symmetric equilibrium, At -2e e1* = e2* = (H-L)/(4eb) Similarly, we will obtain the same solution if we calculate in the regime 0 < e2- e1<2e Thus e* = (H-L)/(4eb) c. (2 points each) How do the equilibrium efforts in (b) change if the amount of luck goes up (e goes up) and if the prizes change?

If the amount of luck goes up, e* goes down. If the prizes change, if H-L decreases, then e* goes down; if H-L increases, then e* goes up. d. Discrimination: Now suppose that player 1 has an advantage A (where 0x2+(e2-e1-A), we will obtain the probability that 1 will win under the following condition If e2-e1-A>2e, then P(1 wins| e1, e2) = 0; If e2-e1-A<-2e, then P(1 wins| e1, e2) = 1; If -2e e1* = e2* = (H-L)(2e-A)/ (8be^2) We will obtain the same result in the regime 0

hus e* = (H-L)(2e-A)/(8be^2)

2. (3 points) Give an intuitive explanation for the result you derived in (1).

The resultant e* from (1) intuitively make sense, that the larger A is the easier for x1 to win, and then both 1 and 2 will input less effort.

3. (3 points) If you were running a firm and trying to get the most effort from workers, what value of A would you pick (holding e and b constant)?

Clearly from the formula of e*, we see that in order to get the most effort from the workers, A = 0. This shows that in a firm the only way to get the best effort from the workers is to create an atmosphere of fair competition, the firm should not give any one any advantage or favor.

2. (10 points, ½ page). Fast food. A national fast-food chain regularly adds new items to its menu. Its contracts with independently-owned franchisees, however, do not require the franchisees to add the items. The chain uses very expensive national roll-out advertising (i.e. advertising in many local markets at the same time, as on network TV shows which are broadcast widely) when it introduces new products. Why might the chain want to own a lot of stores, rather than franchise them?

3. (10 points) (10 points 1 page) Makeup exam: In department stores, many employees in different departments—sporting goods, shoes, electronics-- work on a small sales commission, say 10%. (For most of those products, by the way, the profit is a modest percentage of the sale price.) The cosmetics counters typically work differently. Many people working there are not employees of the department store at all— they actually work for the company whose counter they staff and they exclusively sell one line. For example, if you go to the sporting goods section, a Bloomingdale’s employee will sell Callaway golf clubs, Taylormade clubs, and so forth. But if you go to the Estee Lauder counter in Bloomingdale’s, a salesperson who works for Estee Lauder will help you. Furthermore, compared to other departments in a department store, in cosmetics a lot of sales are repeat sales (the customer comes back and asks for the same salesperson). The salespeople also are usually generous with free samples (small “trial” size samples) for their regular customers.

Speculate about why sporting goods salespeople are employees of the department store, while cosmetics counter salespeople are employees of the cosmetics company. Feel free to use any other information or impressions you have about these products and sales practices, or to give answers which make sense conditional on facts that you are not sure about.

4. (10 points, ½ page) Drug dealing: At a recent NIDA (National Institute of Drug Abuse) conference, several social scientists discussed their field research on the economic organization of drug dealing (e.g., for crack cocaine). Here are some background assumptions: (1) In street-level drug transactions, individual dealers stand around a street corner and wait for customers to approach; customers usually are buying a small amount of drug (one or a few vials). (2) A large percentage of the street-level operatives who handle the drug transactions use crack themselves. (2) It is common for street-level dealers to have to throw away crack vials when police come. (3) Street- level dealers often get robbed by rivals or in other ways that they cannot verify or report (e.g. theft by police themselves).

Here is a stylized fact: None of the street-level dealers handle *both* the crack itself and cash. (That is, there is usually an organizational separation in which a buyer pays cash to one person and receives the crack from somebody else nearby.) Given the background facts above, speculate as to why the optimal “job design” separates handling of crack and cash by street-level dealers.

5. (10 points, ½ page). Cars: Ted delivers pizzas. When an order is taken by the company, it is conveyed to Ted who can decide whether to deliver the pizza or not. (He can turn it down if it will take too long to get there, if he thinks the neighborhood is dangerous, and so on.) Ted’s identical twin, Fred, works as a movie location scout. His work requires him to go to rugged and sometimes dangerous locations at strange hours (e.g., to take location photos at 3 a.m. to see how a street will look when it is being used for filming at night). Fred has no choice about where to go; if he refused to scout a location he’ll be fired. Which one of Ted or Fred is more likely to own the “tool” he uses—namely, his car or truck? Explain.

6. Explain whether the following skills are general or firm-specific human capital or a combination of the two: a. Speaking Spanish. b. Learning code numbers for sections of a company’s work manual (which is not used elsewhere). c. Knowing which people in the organization can really be trusted. d. Learning to make PowerPoint software presentations in a particular color scheme, for your boss who has an unusual kind of color blindness. e. Learning a secret recipe which your company uses, and other companies would love to have. (Assume nothing legally prevents you from using the recipe at another company if you left.) f. You work in a talent agency (e.g. representing film stars). You learn which of the stars are trustworthy, and which of the people those stars work with— directors, accountants, family and friends—can be trusted. If you switched jobs you would run into some of these other people occasionally even if the major star continued to be tied exclusively to your old firm. BEM 146 HW#2 KEY

2. (10 points, ½ page). Fast food. A national fast-food chain regularly adds new items to its menu. Its contracts with independently-owned franchisees, however, do not require the franchisees to add the items. The chain uses very expensive national roll-out advertising (i.e. advertising in many local markets at the same time, as on network TV shows which are broadcast widely) when it introduces new products. Why might the chain want to own a lot of stores, rather than franchise them?

The chain would want to own a lot of stores because they have very expensive national roll-out advertising regularly. If the stores were franchised, the owners of the franchise would have the decision of whether or not to add the new items to their menu. From the stand point of the national chain, they want as many stores as possible to carry the new items because they are paying a fixed cost of advertising this new item. The more new items that are sold will decrease the cost of advertising/item. Unfortunately, if these items are not carried at a store, the chain loses a potential sale or put another way, the chain wants to capture every opportunity they can get to make a sale. The more sales made, the more worthwhile their advertising cost becomes. And most likely, the franchises may be reluctant at first to add the new items before seeing how they perform else where. Owning the stores themselves prevents this problem because the decision right of whether or not to add the new item falls with the chain.

3. (10 points) (10 points 1 page) Makeup exam: In department stores, many employees in different departments—sporting goods, shoes, electronics-- work on a small sales commission, say 10%. (For most of those products, by the way, the profit is a modest percentage of the sale price.) The cosmetics counters typically work differently. Many people working there are not employees of the department store at all— they actually work for the company whose counter they staff and they exclusively sell one line. For example, if you go to the sporting goods section, a Bloomingdale’s employee will sell Callaway golf clubs, Taylormade clubs, and so forth. But if you go to the Estee Lauder counter in Bloomingdale’s, a salesperson who works for Estee Lauder will help you. Furthermore, compared to other departments in a department store, in cosmetics a lot of sales are repeat sales (the customer comes back and asks for the same salesperson). The salespeople also are usually generous with free samples (small “trial” size samples) for their regular customers.

Speculate about why sporting goods salespeople are employees of the department store, while cosmetics counter salespeople are employees of the cosmetics company. Feel free to use any other information or impressions you have about these products and sales practices, or to give answers which make sense conditional on facts that you are not sure about.

Several reasons: a) Makeup runs out quickly, so cosmetics sales are usually repeat sales. The customer comes back and asks for a specific salesperson, so if that salesperson were to go and work for a different store, they would likely take their customers with them. This is great for the makeup companies. b) Selling makeup requires a lot of specialized knowledge about the product line offered by the company and requires a lot more than just recommending the most expensive/popular stuff, which is what department store employees would do. c) Markup on cosmetics is so high that it allows high commission rates resulting in dedicated selling e.g. giving out free samples etc, which wouldn’t occur with department store employees who have a much higher turnover rate.

4. (10 points, ½ page) Drug dealing: At a recent NIDA (National Institute of Drug Abuse) conference, several social scientists discussed their field research on the economic organization of drug dealing (e.g., for crack cocaine). Here are some background assumptions: (1) In street-level drug transactions, individual dealers stand around a street corner and wait for customers to approach; customers usually are buying a small amount of drug (one or a few vials). (2) A large percentage of the street-level operatives who handle the drug transactions use crack themselves. (2) It is common for street-level dealers to have to throw away crack vials when police come. (3) Street- level dealers often get robbed by rivals or in other ways that they cannot verify or report (e.g. theft by police themselves). Here is a stylized fact: None of the street-level dealers handle *both* the crack itself and cash. (That is, there is usually an organizational separation in which a buyer pays cash to one person and receives the crack from somebody else nearby.) Given the background facts above, speculate as to why the optimal “job design” separates handling of crack and cash by street-level dealers.

Two main reasons here: a) Splitting up cash and drugs helps keep the dealers in check. When they return to the man in charge, the money better be equal to the amount of missing drugs. If the cash doesn’t add up to the drugs “sold”, then you know that either the drug handler is using the drugs on his own, or the money handler is cheating you. The idea is that they would both have to cooperate together to cheat you, i.e. corroborate each other’s stories about thefts/police interference, whereas with one dealer he could do the drugs, spend the money, and claim it was all stolen/confiscated.

b) There is also the idea of not putting all your eggs in one basket. Splitting up the money and drugs cuts your expected losses in half since both dealers would have to be caught/robbed in order for you to lose everything, plus there’s no crime in just having money, so only one guy is really at risk from the police.

5. (10 points, ½ page). Cars: Ted delivers pizzas. When an order is taken by the company, it is conveyed to Ted who can decide whether to deliver the pizza or not. (He can turn it down if it will take too long to get there, if he thinks the neighborhood is dangerous, and so on.) Ted’s identical twin, Fred, works as a movie location scout. His work requires him to go to rugged and sometimes dangerous locations at strange hours (e.g., to take location photos at 3 a.m. to see how a street will look when it is being used for filming at night). Fred has no choice about where to go; if he refused to scout a location he’ll be fired. Which one of Ted or Fred is more likely to own the “tool” he uses—namely, his car or truck? Explain.

Ted is more likely to own his “tool” since he gets to choose whether or not to deliver the pizzas, and so will only deliver if expected gain > expected loss from damage, muggings etc. Similarly, since pizza delivery boys are often in a rush, you want them to be responsible for the car, otherwise they would constantly be getting in wrecks. Fred has no choice about where to go and so the scouting agency should pay for his car, since it is in the position to decide whether or not the expected benefit exceeds the expected cost.

6. Explain whether the following skills are general or firm-specific human capital or a combination of the two: g. Speaking Spanish. GENERAL h. Learning code numbers for sections of a company’s work manual (which is not used elsewhere). SPECIFIC i. Knowing which people in the organization can really be trusted. SPECIFIC j. Learning to make PowerPoint software presentations in a particular color scheme, for your boss who has an unusual kind of color blindness. COMBINATION—POWER POINT IS GENERAL, SPECIFIC COLORS ARE FIRM SPECIFIC k. Learning a secret recipe which your company uses, and other companies would love to have. (Assume nothing legally prevents you from using the recipe at another company if you left.) GENERAL l. You work in a talent agency (e.g. representing film stars). You learn which of the stars are trustworthy, and which of the people those stars work with— directors, accountants, family and friends—can be trusted. If you switched jobs you would run into some of these other people occasionally even if the major star continued to be tied exclusively to your old firm. COMBINATION—YOU LEARN ABOUT FIRM SPECIFIC STARS BUT ALSO ABOUT OTHERS YOU WILL DEAL WITH IN OTHER FIRMS.