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INCENTIVES AND CONTRACTS Problem Set 1: Firm Boundaries

Question 1: A manufacturer of pencils contemplates backward integration into the production of rape seed oil, a key ingredient in manufacturing the rubberlike material (called factice) that formers the eraser. Rape seed oil is traded in world commodity markets and its price fluctuates as supply and demand conditions change. The argument that has been made in favour of vertical integration is this: “Pencil production is very utilisation-sensitive -- i.e., a plant that operates at full capacity can produce pencils at much lower cost per unit than a plant that operates at less than full capacity. Owning our own source of supply of rape seed oil insulates us from short-run supply-demand imbalances and therefore will give us a competitive advantage over rival producers.” Explain why this argument is wrong.

Question 2: Besanko, Chapter 4 (a), pp.164-166, Question 3 Shaefer Electronics is a medium-size producer (about 18 million in sales in 1993) of electronic products for the oil industry. It makes two main products – capacitors and integrated circuits. Capacitors are standardized items. Integrated circuits are more complex, highly customized items made to individual customer specifications. They are designed and made to order, they require installation, and sometimes require postsale servicing. Shaefer’s annual sales are shown in the table below. Shaefer’s Annual Sales ($’000)

Capacitors Integrated Circuits Total

1980 5,568 678

1985 6,488 1,679

1989 7,131 4,651

1990 7,052 6,245

1991 7,043 7,363

1992 7,360 8,589

1993 8,109 9,508

6,246

8,167

11,782

13,297

14,406

15,959

17,617

Shaefer relies entirely on manufacturer’s representatives (MRs) located throughout the United States to sell its products. MRs are independent contractors who sell Shaefer’s products in exchange for a sales commission. The company’s

representatives are not exclusive – they represent manufacturers of related but noncompeting products, such as circuit breakers, small switches, or semiconductors. Often a customer will buy some of these related products along with integrated circuits or an order of capacitors. MRs have long experience within local markets, close ties to the engineers within the firms that buy control systems, and deep knowledge of their needs. In the markets in which they operate, MRs develop their own client lists and call schedules. They are fully responsible for the expenses they incur in selling their products. Once an order for one of Shaefer’s products is taken by the MR, Shaefer is then responsible for any installation or postsale servicing that is needed. Shaefer recently hired a marketing consultants to study its sales force strategy. Its report contained the conclusions reported below. Please comment on the soundness of that conclusion. “Shaefer should continue to sell through MRs. Whether it uses MRs or an inhouse sales force, it has to pay sales commissions. By relying on MRs, it avoids the variable selling expenses (e.g., travel expenses for salespeople) it would incur if it had its own sales force. As a result, Shaefer’s selling expenses are lower than they would be with an in-house sales force of comparable size, talent and knowhow.”

Problem Set 1 Answers

Question 1: The argument is founded on supply assurance concerns. By owning its own supply or rape seed oil, this firm would not insulate itself from short-run supply-demand imbalances but put it in the role of commodity speculator. If the price of rape seed oil were to rise, this firm should sell the oil on the market instead of using it itself to manufacture erasers. If the price falls, they lose as well. This illustrates that the market bears some part of risk for you.

Question 2: (a) The conclusion of this marketing consultant is unsound. It is based on the fallacy that says that a firm should buy rather than make because by doing so it avoids production costs associated with making. In this particular case, Shaefer does not avoid variable selling expenses by relying on MR’s. Presumably, the MR's will negotiate a commission rate that will allow them (over some reasonable period of time) to cover their variable selling expenses, such as travel costs. This rate will be higher than the rate that Shaefer would pay to otherwise equally talented, knowledgeable and productive in-house sales people, whose selling expenses will be reimbursed directly by Shaefer, rather than indirectly through the commission.

INCENTIVES AND CONTRACTS

Problem Set 2: Hold Up Problems

Question 1: Some contacts, such as those between municipalities and highway construction firms, are extremely long with terms spelled out in minute detail. Others, such as between consulting firms and their clients, are short and fairly vague about the division of responsibilities. What factor might determine such differences in contract length and detail?

Question 2: For the brave ... Milgrom and Roberts, p.198, Questions 1 – 3: 1. Suppose that there are two firms, Firm A and Firm B, that are considering making a 1/ 2 joint investment in R&D. The total payoff from the project is 200(V A + VB ) , where VA and VB are the values of the two investments. The two firms expect to share this payoff equally while each absorbs the cost VA or VB, of its investment. Show that the value-maximising plans are those where the total investment of the two firms is $10,000. How much total value is created in this way? 2. In question 1, suppose now that the firms cannot enforce a contract specifying levels of investment for each, because they cannot observe the real value of the investments that are made. Show that if Firm A expects Firm B to invest VB, it can do no better than to invest 2,500 – VB. How much, then, will be invested in total? How much total value is created? 3. Suppose that if the firms do not sign a contract, that they can develop their own version of the research project in competition with one another. A marketable produce will result for either firm provided it spends at least 35 percent as much as its 1/ 2 competitor. If V A ≥.35VB , then Firm A’s net profit will be 200(V A −.35VB ) − V A , and correspondingly for B. Show that if each firm expects the other to invest 10000/.65, then it will choose to invest an equal amount. What will total profits be? Would you expect the firms to reach a joint venture agreement under these circumstances?

Question 3:

Noted fashion expert Sid Sims had been asked by New World Movie Studios to design the wardrobe for the forthcoming file “Bananas and Fog.” The wardrobe will test Sims’ abilities -- the fashions are to be made entirely of old newspapers, dead leaves and scrap iron. The studio offers Sims the following contract: It will pay $500,000 upon acceptance of the wardrobe by the movie studio. Sims estimates that he can get the newspapers and leaves for free, must pay $50,000 for the scap iron, and must commit an additional $350,000 in labour to produce the wardrobe. Full of excitement, Sims signs the contract. a. What is the profit that Sims hopes to realise prior to signing the contract? b. After the wardrobe is complete, what is the gross profit earned? assumptions, if any, did you make to obtain this figure?

What

c. Offer a scenario whereby the studio holds up Sims. d. Can Sims hold up the studio? Explain.

Question 4: Consider two different sorts of transactions between a buyer and a seller. In both transactions, the buyer can potentially choose between many vendors at the initial contracting stage. Both transactions involve relationship-specific assets. In the first sort of transaction, the relationship-specific assets are physical assets (e.g., specialised presses and dies). In the second sort of transaction, the relationship-specific assets are human assets, such as expertise and know-how about the production process. Without knowing anything further about these two different sorts of transactions, why would we expect that vertical integration is more likely to be chosen for the transaction involving human assets than for the transaction involving physical assets?

Question 5: (Milgrom and Roberts, p.52, Question 5) Cable television companies lay cables to individual households in the communities they serve to carry the television signal. How specific is this investment? What kind of arrangements would you expect the cable companies to make with local communities about the pricing and taxation of cable services?

Question 6 (Exam 1996):

Suppose X is an intermediate good in the production of a final good Y. Firm A has a patent on good X, which it produces at zero marginal cost. Firm B is considering buying a machine which it can use to turn up to 10,000 units of X into Y on a onefor-one basis. The machine costs $30,000, once purchased it cannot be resold, and it wears out completely once 10,000 units of Y are produced. Firm B can sell good Y for $5 per unit. Firm B is A’s only potential customer. (a) Prior to B buying the machine, suppose that it could negotiate with A over the price of X. Under efficient bargaining, at what price would Firm A offer to supply good X to firm B? (b) Suppose that this price agreement is not binding. Thus, having bought the machine, A might decide to renegotiate the price. What price results from negotiations after B has bought the machine? What are B’s resulting profits? (c) If price agreements are not binding, would B choose to buy the machine in the first place? (d) Now suppose that A can enter into a licensing agreement with another firm C, under which C can produce good X, incurring a marginal cost of $c per unit. Briefly, describe, in words, the affects of such an arrangement. Why would A wish to license its product to a competitor?

INCENTIVES AND CONTRACTS

Problem Set 2 Answers

Question 1: In the case of the highway construction contract, it may be easier to specify the terms of performance than in the case of the consulting project. That is, it may be easier to specify design specifications, timing, what equals acceptable road quality, etc. When performance under a contract is difficult to specify as one would expect to be the case in the consulting contract, it may be extremely hard to sufficiently elaborate each party’s rights and responsibilities within a written contract. The language in such contracts is often left vague and open-ended because it is not always clear what constitutes fulfillment of the contract.

Question 2: This is a computationally difficult question. 1. The net payoff, or total value, is: R = 200(VA + VB ) 2 − (VA + VB ) = 200V 2 − V 1

1

where we define V to be VA + VB. The total value is maximised at the point where the derivative with respect to V is zero: 1 dR −1 = 100V 2 − 1 = 0 ⇒ V = 1000 ⇒ 200V 2 − V = 10000 dV

So, the value is created is 10,000. 2. The profit earned by A is π A = 12 200(VA + VB ) 2 − VA . A’s prfots are maximised at the point where the marginal return is zero: 1

dπ A −1 = 50(VA + VB ) 2 − 1 = 0 ⇒ VA = 2500 − VB dVA So, the total investment 1 200(2500 ) 2 − 2500 = 7,500 .

is:

VA

+

VB

=

2,500.

Total

value

3. A’s profits will be: π A = 200(VA − 0.35VB ) 2 − VA . These are maximised when: 1

is:

dπ A −1 = 100 (VA − 0.35VB ) 2 − 1 = 0 ⇒ VA = 1000 + 0.35VB dVA This eqution is satisfied when VA = VB = 10000/.65. 1   10000 0.35  2 10000  − 10000 −  = 9231 . Total profits are then: π A + π B = 2  200   0.65 0.65 0.65  

Since total profits are larger in a collaboration, the firms would be tempted to enter a joint venture. The success of this attempt is likely to depend on how costly the joint venture is, that is, on what transaction costs the joint venture incurs. Each firm can get 4,615.50 if it works on its own, or 5000 in a joint venture. Thus, transactions costs have to be less than 384.50 for each firm to make the venture attractive.

Question 3: (a) Sims hopes to get the price of $500,000 for the good less the costs of its production ($50,000 + $350,000). Thus, the net profit Sims hopes to get is $100,000. (b) Gross Profit (or Quasi-rent) = amount Sims will earn if the deal falls through (payoff minus next best opportunity) = $500,000 - $50,000 = $450,000. This calculation assumes he can sell the scrap iron for the same price at which he bought it. Therefore, Sims could suffer from a hold-up. (c) The studio has the opportunity to holdup Sims because he has made a relationshipspecific investment in the production of the wardrobe. The studio may decide not pursue the film production leaving Sims with scrap iron he paid for. The high quasirent in this problem indicates that this could be a risky venture for Sims. (d) If Sims were the only wardrobe supplier the studio has hired, he may be in the position to withhold the wardrobe for a higher royalty. Also, if the studio is on a strict deadline and Sims waits until the last minute, he could holdup the studio. The studio would have nowhere to turn and may have to delay or halt the production of the film (both very costly).

Question 4:: At the initial contracting stage, before any relationship-specific investments are made, a buying party has many alternative trading partners. Once relationship-specific investments have been made, however, competitive bidding is no longer possible. At this point, selling firms have already made investments in site assets, physical assets, dedicated assets, or human assets. A relationship involving physical assets referes to one in which the physical properties of assets are specifically tailored to a particular transaction. This would include special molds, dyes etc., used in manufacturing a product. Physical asset specificity would inhibit the firms from switching partners. Once firms are involved in such a relationship, they typically can negotiate a contract that assigns ownership of the assets to the part most at risk of being held up. This gives that part flexibility to leave the relationship and find another trading partner if its current partner tries a hold up. A relationship involving human asset specificity refers to one in which a worker or group of workers have acquired skills, know-how, or information that is more valuable inside this particular relationship/firm than outside it. Such specificity involves not only tangible skills (computer expertise) but also intangibles such as ability to work within the organisation’s culture. Knowing one company’s culture may not be of use in another organisation. Because human assets are likely to be so specialised to the particular parties in the transaction, they cannot be transferred to other parties to safeguard against hold up as can physical assets. With human assets, there is always the danger that they would quite to start their own firm, etc. Knowing that a partner has made an RSI, one party to a contract is in the position to exploit contractual incompleteness by attempting hold up. One would expect the hold up problem to be less severe when there are physical assets involved rather than human assets because physical assets are more likely to be specialised to the transaction but not to the current trading partner.

Question 5: The cable system is highly specific: If the community chose (through political action) to deny the cable firm more than its operating costs, with no return on the investment, the firm would have little recourse. At the same time, if the firm decided ex post to raise prices to the monopoly level, the town would have little commercial recourse, because a second cable system would be expensive and its owner would worry that either competition with the firms firm or a hold up by the community would prevent recovery of the investment costs.

Previously, towns in the US regulated cable companies’ pricing and service provision while granting them monopoly franchises. This protected the community, while the right of appeal of regulatory rulings to the courts and the US constitutional prohibition of taking private property, without compensation gave some protection to the cable firms. This regulation is no longer allowed, however. Consequently, we would expect to see long-term contracts that cover pricing and service, perhaps with ascalator clauses to ensure profitability under efficient management. In recent years, the rights of local governments to regulate cable television prices have been eliminated. It is claimed that prices have risen exorbitantly, and cable TV firms stock prices have certainly risen. There is now pressure for re-regulation.

Question 6 (Exam 1996): (a) Under efficient bargaining, A’s outside option is $0 as the patent has no value without firm B purchasing good X. If B invests in the machine, B’s costs is the sum of its fixed and variable costs. Its fixed costs are the costs of the machine, $30,000 and its variable costs for $10,000 are zero per unit. Thus, B’s outside option is $30,000. The total surplus created are from B’s revenues. 10,000 units of Y can be sold for a total of $50,000. Subtracting the outside option from this amount gives B’s net revenues and the negotiated surplus, i.e., $50,000 - $30,000 = $20,000. Assuming A and B are equally proficient negotiators or there are delay costs in negotiations that are equally borne by either party, this amount is split evenly. This results in profits of $10,000 to A and a net profit of $10,000 for B (after subtracting the costs of the machine). This can be achieved with a negotiated price for X of $1 per unit. (b) If the price agreement is not binding, it can be renegotiated after B has bought the machine. At this stage, while A’s outside option is the same, B’s is now $0 as the machine costs are already sunk. The total surplus is still $50,000. But now the amount to be negotiated over is also $50,000. Splitting this equally, results in $25,000 to firm A and firm B, with a price per unit of X of $2.50. (c) Note that if B anticipates purchasing X at $2.50 per unit, it earns only $25,000 and this is insufficient to cover the costs of the machine of $30,000. Therefore, B would not choose to buy the machine in the first place. (d) If B does not buy the machine, then both A and B earn no profits. Therefore, A has an incentive to incur personal costs in making a credible commitment to B not to raise its price. By licensing the good to C, A creates competition. If C’s marginal cost is $c per unit of X, then A is able to make a credible commitment not to price above this amount. This is because in any subsequent negotiations, B’s outside option is a negotiation with C. Now so long as c < 1, B’s outside option in bargaining with A is at least $10,000 leaving a negotiated surplus of $40,000 and hence a payout to B

of at least $30,000 covering the cost of the machine. A still receives $20,000 from this arrangement making it better than the situation without any license agreement.

INCENTIVES AND CONTRACTS

Problem Set 3: Vertical Integration

Question 1: In each of the following situations, why are firms likely to benefit from vertical integration? a. A grain elevator is located at the terminus of a rail line. b. A manufacturer of a product with a national brand name reputation uses distributors that arrange for advertising and promotional activities in local markets. c. A biotech firm develops a new product that will be produced, tested, and distributed by an established pharmaceutical company.

Question 2: (Besanko, Chapter 4, pp.164-166, Question 1) Explain why the following patterns seem to hold in many industries: a. b.

Small firms are more likely to outsource production of inputs than are large firms. “Standard” inputs (such as a simple transistor that could be used by several electronics manufacturers) are more likely to be outsourced than “tailormade” inputs (such as a circuit board designed for a single manufacturer’s specific needs).

Question 3: (Besanko, Chapter 4, pp.164-166, Question 2) The following is an except from an actual strategic plan (the company and product names have been changed to protect the innocent): Acme’s primary raw material is PVC sheet that is produced by three major vendors within the United States. Acme, a small consumer products

manufacturer, is consolidating down to a single vendor. Continued growth by this vendor assures Acme that it will be able to meet its needs in the future. Assume that Acme’s chosen vendor will grow as forecast. Offer a scenario to Acme management that might convince them that they should rethink their decision to rely on a single vendor. What do you recommend Acme do to minimise the risk(s) that you have identified? Are there any drawbacks with your recommendation?

Question 4: In problem set 1, Question 2 you considered the sales force strategy of Shaefer Electronics. Dissatisfied with the first consultant, they hired another. Their conclusion was: “Selling through MRs made sense for Shaefer when it was first getting started and specialised in capacitors. However, given its current product mix, it would not want to set itself up the way it is now if it were designing its sales force strategy from scratch. But with what it has got, Shaefer should be extremely cautious about changing.” Please comment on the soundness of this conclusion.

INCENTIVES AND CONTRACTS

Problem Set 3 Answers

Question 1: (a) A grain elevator owner would benefit from vertical integration: • Coordination Costs: Use of market firms often present coordination problems. This is especially problematic for inputs with design attributes that require a careful fit between different components. It may be that storage bins and rail cares need to be so designed. Another factor that may be an issue with grain is timing. The grain operator would want to ship the grain as soon as possible to avoid spoilage etc. Arranging these elements through contracts would be extremely difficult and costly to achieve. • Costs of Using the Market: Locating assets side-by-side may allow the operators to economise on transportation or inventory costs or to take advantage of processing efficiencies. (This is a concept called site specificity, which is introduced in Chapter 3 of the text.) • Economies of Scale: The grain operator may also be able to achieve distribution economies by having its own rail operation as opposed to contracting with individual transportation providers. (b) The manufacturer would benefit from vertical integration for several reasons: Coordination Costs: • The firm could better coordinate the release of any new items with advertising. (Timing) • Moreover, since the manufacturer will certainly want to run national as well as local advertising, it would be better able ot coordinate/convey consistent messages across local markets. (Sequencing) • A manufacturer’s own distributors are more likely to sell/push its own brand name products than they would be if these distributors were also selling rival brands. (Transactions Cost). (c) The biotech firm would benefit from vertical integration for several reasons: • Coordination Costs: The level of sophistication of the design attributes (size and fit of components, performance specifications, timing of delivery with other products etc.) of the new product would be critical to determining how costly any potential mistakes made by an outside firm (the pharmaceutical firm) may be.

• Leakage of private information: Does the biotech firm have to divulge proprietary product information in order for the pharmaceutical firm to manufacture it? This may suggest making or vertically integrating would be benefical, especially if the larger pharmaceutical firm would then manufacture a competing product. Does the pharmaceutical firm already produce a substitute product? If so, there may be conflict of interest here that prevents the pharmaceutical firm from adequately promoting the product.

Question 2: (a) A firm gains less from vertical integration the greater the ability is of outside market specialists to take advantage of economies of scale and scope relative to the firm itself. A small firm might not be able to take advantage of economies of scale and scope while a large firm might produce enough inputs that it will have the same economies of scale and scope that an outside firm would have. (b) There are two reasons why “standard” inputs are more likely to be outsourced than “tailor-made” inputs. First, an outside firm can reach economies of scale and scope if it is producing these inputs for several different electronic manufacturers. An outside firm might not be able to take advantage of economies of scale and scope with tailor-made inputs, because they would be making them for one firm, not several firms. Second, complexity of contracting becomes an issue for a “tailor-made” item; it becomes more difficult to specify what good performance is in a contract and a firm incurs larger transactions costs. Scott Maston’s study of the aerospace industry (p.140) indicates that more complex components were more likely to be manufactured internally.

Question 3: Acme’s primary raw material is PVC sheet that is produced by three major vendors within the United States. Acme, a small consumer products manufacturer, is consolidating down to a single vendor. Continued growth by this vendor assures Acme that it will be able to meet its needs in the future. Assume that Acme’s chosen vendor will grow as forecast. Offer a scenario to Acme management that might convince them that they should rethink their decision to rely on a single vendor. What do you recommend that Acme do to minimize the risk(s) that you have identified? Are their any drawbacks with your recommendation?

There is a potential for hold-up problems if Acme consolidates down to a single vendor. Of course, the likelihood of hold-up problems would depend on the degree of asset specificity involved and switching costs. In order to minimize its risks, Acme could second source or backward integrate (partially or fully). This assumes that Acme must have a valid reason for using a single supplier. A key merit of Acme's approach is that it might encourage the vendor to make specific investments. (Yes, asset specificity has two sides.) Alternately, Acme could maintain two suppliers. Second sourcing protects the firm from hold-up but may drive up costs by reducing purchasing discounts and requiring additional investments by the second source. A third solution would be for Acme to consider tapered integration. Tapered integration poses the usual make problems -- high costs and poor incentives. Full integration seems totally implausible, unless Acme is a very large buyer of PVC sheet. The problem implies that Acme is small. The problem tells us that there are three major suppliers in this industry and at least one of them is planning to grow much larger. This strongly suggests that Acme does not control a large share of this market, and that Acme’s deal will not materially affect the size of each firm. If Acme was a big buyer, then how could its future partner plan to grow independent of Acme’s growth?

Question 4: (b) However, if Shaefer was designing its sales force strategy from scratch in 1993, it would not want to rely on MR’s. Shaefer has grown, and its product mix has changed in a way that has significant implications for the make-or-buy decision. Integrated circuits (ICs), which now account for more than half of its sales, are complex, hightech, and non-standardized. For such products, the salesperson's personal relationship with the customer is particularly important. The salesperson's role is not just to take orders from the catalog, but also to provide product information and technical advice. When Shaefer uses MR’s to sell its products, it is the MR, not a Shaefer employee, that deals personally with the customer. For this reason, a customer’s primary loyalty will probably be to the MR and not to Shaefer. All of this implies that MR's client list is an important relationship-specific asset. Once Shaefer forges a relationship with a MR, it becomes extremely difficult to “fire” a MR and replicate the access to that rep’s clients through another MR. When transactions involve relationship-specific assets, “making” is often preferred to “buying.” In this case, MR’s “ownership” of the client list gives it considerable bargaining power over Shaefer. This bargaining power is enhanced by the fact that the MR’s do not have exclusive relationships with Shaefer; they sell other products as well. The bargaining power enjoyed by the MR’s would make it difficult for Shaefer

to: (1) keep sales commission low; (2) enforce sales quotas; (3) control the time the MR's spend pushing Shaefer’s products versus other products. High sales commissions (1) directly raise the costs to Shaefer of using reps; (2) and (3) reduce the effectiveness of using reps to push Shaefer’s products. We don't know for sure that any of these problems are actually occurring, but one slight bit of evidence that may be suggestive of a problem is that since 1990, Shaefer’s sales of integrated circuits have grown less rapidly that the industry as a whole. Another potential problem with the use of MR’s is they may compromise coordination between design, manufacturing, sales and installation and post-sale customer service. While such coordination is probably not unimportant in the capacitor business, it is likely to be keenly important in a business like ICs, where customization is key. Under the current arrangement, the sale is made by an MR, who then has to communicate with Shaefer's design and manufacturing people to develop the specs for the customer's order. And after the sale has been completed, the MR would have to arrange with Shaefer for installation and debugging. This in not a good set-up. It leaves Shaefer vulnerable to competitors who can perform the ordertaking, design manufacture, delivery and installation more quickly than Shaefer. Finally, MR’s are probably not the best way to sell a customized product such as ICs. In the IC business, Shaefer is not just selling a physical product; it is selling its capabilities to custom design, produce and install a device that will solve a particular need for a prospective customer. An in-house sales person is likely to have more specific knowledge of Shaefer's ability to adapt its designs to solve particular customer needs than an MR who carries many different products. While it is true that MR’s know a lot about their clients’ needs, and probably know something about the capabilities of the manufacturers, the key question is: is their knowledge about Shaefees products deep enough to allow Shaefer to compete effectively against rivals who are aggressively pushing their abilities to solve specific customer problems. Of course, this line of argument begs the question of why Shaefer couldn't provide training for its MR’s to enhance their knowledge about Shaefer's products. A possible answer relates to the earlier discussion of asset specificity. Providing an MR with training about the capabilities and technological specifications of Shaefer's products creates a relationship-specific assets that further cements the dependence on Shaefer on its manufacturer reps. The possibility that its MR’s might engage in hold up reduces the marginal value of any investment Shaefer might make in its relationship with them. Thus, while providing training to the MR’s may seem like a good idea in principle, it is far from clear that its benefits outweigh the costs. The above considerations would argue against using MR’s in the first place. But the irony of relationship-specific assets, is that they can create dependency relationships that are difficult or costly to break. This, then, explains the third part of the consultant's conclusion: Shaefer should be extremely cautious about changing from its

current situation. Since the MR’s have already incurred the upfront costs of developing relationships with clients and learning how to sell Shaefer’s products, it might be better to stick with the MR’s, despite the fact that they may “holdup” Shaefer for higher commissions or work less hard than an in-house sales force because, on balance, that would be cheaper than starting an in-house salesforce from scratch. Note that the trade-off would be different if Shaefer was starting from scratch --- i.e. if MR’s had no experience selling Shaefer’s products. In that case, the alternative to developing an in-house sales force would be to sell through MR’s who have no experience selling Shaefer’s products, and who would have to spend time developing new relationships that would be valuable sources of demand for Shaefer’s IC’s. The cost to Shaefer of starting its own sales force is the same, but the attractiveness of MR’s is higher now than it would have been if Shaefer was designing its sales force strategy from scratch.

INCENTIVES AND CONTRACTS

Problem Set 4: Incentive Contracts

Question 1: (Milgrom and Roberts, p.198, Question 4) (Forcing contracts) In principal-agent problems of effort provision, moral hazard may not be a problem if the structure of uncertainty allows the principal to infer precisely whether the agent has failed to perform as desired. To see this, suppose in the context of the example in the lecture that the matrix relating the probabilities of various outcomes were changed so that the high level of revenues (30) was sure to occur if the workers supplies the high level of effort (e = 2), but either level of revenue could still happen if the low level of effort (e = 1) is provided. Thus, the first row of the matrix corresponding to e = 1, is unchanged, but the entries corresponding to e = 2 become 0 and 1 instead of 1/3 and 2/3. Rewrite the incentive and participation constraints and show that it is possible to design a forcing contract that motivates the worker to work hard, supplying e = 2, without placing any risk on him or her. How much is the worker paid if revenues of 10 are realised? How much when revenues are 30? What are the expected payoffs of the two parties? Is there any cost in this case to effort not being observable, that is, could the parties do better if effort were observed? Would it be possible to achieve this sort of result if the low level of effort surely resulted in revenues of 10, but the high level of effort could result in either revenues of 10 (with probability 1/3) or 30 (with probability 2/3)? Why or why not? Question 2: (Milgrom and Roberts, p.199, Question 5) (Selling the firm to a risk-neutral agent) In many principal-agent problems of effort provision, moral hazard is costly if the agent is risk averse because making his or her pay reflect the full marginal impact of his or her effort choices imposes costs on the agent that could be avoided if the risk-neutral principal absorbed the variability in incomes. Again in the context of the mathematical example in the lecture, show that if the agent is risk-neutral, with payoff function for income w and effort e of u(w,e) = w – (e – 1), then it is possible to achieve the same expected payoffs for both parties as would result if effort were observable by having the agent bear all the risk and the principal receive an amount that is independent of the realised level of revenues.

INCENTIVES AND CONTRACTS

Problem Set 4 Answers

Question 1:

(a) The new table is: Revenue Action

R=10

R=30

e=1

2/3

1/3

e=2

0

1

Suppose the contract pays y if R = 10 and z if R = 30. The incentive compatibility constraint (ICC) says that: expected utility picking e = 2 ≥ expected utility picking e = 1 z − 1 ≥ 23 y + 13 z ⇒ z − 32 ≥ y The participation constraint (PC) says:

z − 1 ≥ 1.

From PC, we conclude that z ≥ 4. From this and ICC, we see that any increase in y necessitates an increase in z as well (raising the cost of the contract). Thus, y is set at zero, and there is no reason to set z greater than 4. Suppose then that the principal sets z = 4 and y = 0. Then the constraints are satisfied, so the agent chooses e = 2 and gets utility of 1 for sure, i.e., the agent bears no risk. The expected profits for the principal as 30 -4 == 26. In this case there are no costs involved in not being able to observe effort level. If effort were observable, then we would have the same outcome: the agent receives wage 4 if he exerts effort e= 2, and the principal’s profit remains 26. (b) In this case the table is:

Revenue Action

R=10

R=30

e=1

1

0

e=2

1/3

2/3

Intuitively, we see that we will not be able to replicate the previous result. If e = 2 is chosen, a payment schedule based upon the outcome will leave the agent with risk, since R = 30 is not certain. We get ICC: PC:

1 3

( y − 1)+ ( z − 1)≥ y ⇒ z − y ≥ ( y − 1)+ ( z − 1)≥ 1 ⇒ 2 z + y ≥ 6

1 3

2 3

3 2

2 3

Adding these inequalities, we get z ≥ 52 . If ICC holds with equality, then any increase in y necessitates an increase in z to maintain incentives. Since the principal 1 2 is interested in minimising the expected pay to the agent, 3 y + 3 z , subject to ICC and PC, it is clear that the solution is to push down both y and z as much as possible while maintaining ICC and PC. This means the solution is at z = 25/4 and y = 1: the optimal contract has a considerable spread in the payments and leaves the agent bearing risk. It results in the following payoffs: For the agent: the expected wage is 4.5 and expected utility is 1. For the principal, expected profit is 18.83. If effort were directly observable and enforceable, it would be possible to achieve a wage of 4 and expected utility for the agent of 1. The principal would receive a return of 58/3. The lack of information imposes transactions costs in this example. Note: Forcing contracts are generally feasible only when it is possible to make the agent’s utility sufficiently low if the wrong action is chosen. This may require making utility negative. In some models, unlimited liability suffices. In additive separable models (with utility being the value of income less a cost of effort), even that is not generally sufficient if the utility of consumption is bounded below.

Question 2: In this problem u(w,e) = w - (e-1).

Revenue Action

R=10

R=30

e=1

2/3

1/3

e=2

1/3

2/3

(a) Observable effort: if the level of effort could be observed and enforced, then the agent could be made to choose e = 2 and paid a wage of 2, so that the participation constraint was satisfied. (A wage of zero would be paid if the agent shirks, in order to provide the correct incentives). The expected profit for the principal is then 64/3 (b) Unobservable effort: with a risk neutral agent, the parties can do equally well when effort is not observed by paying the agent a wage of 3 when revenue is 30 and 0 when the revenue is 10. This satisfies the participation constraint because 2/3(3-1) + 1/3(0-1) = 1 is the agent’s expected utility from the contract. It satisfies the incentive compatibility constraint because 2/3(3-1) + 1/3(0-1) = 1 ≥ 1/3(3-0) + 2/3(0-0). When the agent is risk neutral, the variation in payments needed to provide incentives and which imposes a risk on the agent nevertheless results in no transactions cost. If the agent has sufficient wealth, a different way to achieve the same result and with less need for fine data about the problem is to sell the firm to the agent. In this case, selling the firm for a price of 64/3 amounts to paying a wage of R - 64/3 for whatever level the revenues R might be. This obviously results in a return of 64/3 for the principal. It is feasible only if the agent can supply the necessary funds when R = 10. If the agent can do that, then a simple calculation shows that the agent’s incentives are always to maximise total value and that, being risk neutral, the agent suffers no cost from having to bear this excess risk.

INCENTIVES AND CONTRACTS

Problem Set 5: Compensation

Question 1: (Milgrom and Roberts, pp.243-244, Food for Thought Questions) 1. In the late 1960s and early 1970s, when McDonalds (the fast-food chain) was undergoing a period of very rapid expansion in sales, it considered a variety of different compensation systems for its managers. The company wanted to encourage its managers to increase sales, control costs, and maintain the company’s standards of quality, service and cleanliness. It also wanted local store managers to hire and train people who could become managers of new outlets, which were being added to the chain at a rapid pace. What difficulties would you expect this situation to pose for McDonald’s management? What would you expect to occur if a local outlet manager’s compensation were based primarily on sales growth? On outlet profits? What kind of compensation plan should McDonalds adopt? How would you expect the compensation formula to change as McDonalds moved into its next phase, with fewer new outlets being opened in North America. 2. A common complaint of university students is that professors seem too remote and uninterested in teaching them. How do university systems of compensation, promotion, and tenure contribute to the problem? Is the problem likely to be more severe for tenured or untenured faculty? Why do universities often have rules restricting outside consulting activities? 3. Unlike specialty stores, department stores sell a wide array of products to a single group of customers, and are often especially interested in maintaining their reputations for servicing their customers well. How might this consideration affect the compensation of department store sales personnel compared to the salespeople at specialty outlets?

Question 2: In the United States, lawyers in negligence cases are usually paid a contingency fee equal to roughly 30 percent of the total award. Lawyers in other types of cases are often paid on an hourly basis. Use agency theory to assess the merits and draw-backs of each type of fee arrangement from the client’s (i.e., the principal’s) perspective. Be sure to discuss incentive and sorting effects.

Question 3: Suppose that a principal desires a worker to perform two tasks, but can observe performance on only one task. Under what conditions should the principal closely tie pay to performance on the first task?

Question 4: (Personnel Economics Exam 2000) You manufacture hobs, which are precision tools that grind the gears used in motors and other mechanical devices. Hob machinists have been studied and found they exhibit the behavior listed in the table below. The interpretation of the table is that in order for the hob machinist, otherwise known as a hobbit, to work one hour in a given day, the firm would have to pay $3 for the day. To get the hobbit to work 2 hours in the given day, the firm would have to pay $12 for the day. To get the hobbit to work 8 hours during the given day, the firm would have to pay $192 for the day, and so forth. Labor Supply of Machinists Total $ Wages 3 12 27 48 75 108 147 192 243 300 363 432 507 1000 2000 10000

Hours Worked 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

The firm has 100 hobbits on the payroll and there are no other hobbits available for hire. Hobs sell for $55 each and take one hour to produce. The machine that is used to produce hobs is rented from another firm at a cost of $10 per hour. Assume that there is perfectly elastic demand for hobs at a price of $55. This implies that the hob company can sell as many hobs as it wants to sell at $55, but can sell no hobs at any price above $55. (a)

(5 marks) How much must the firm pay for the first hour to get a hobbit to increase their labor supply from zero hours to one hour per day? How much must the firm pay for the tenth hour to induce a hobbit to increase their labor supply from 9 to 10 hours?

(b)

(5 marks) If the firm announces a wage of $45 per hour, how many hours will each hobbit work per day and how much will the firm pay in total wages per day? Calculate the profit per worker under this scheme.

(c)

(10 marks) The original CEO at the hob company, named Tolkien, is replaced by a new CEO, named Rose. Rose believes that he can make higher profits by changing the compensation scheme, but is unclear as to which scheme to implement. He has three candidate schemes. They are: 1. Pay hobbits on the basis of hobs produced at a price of $55. Each hobbit may choose the number of hours that he works. 2. Pay nothing for anything less than 6 hobs per day. A worker who produces at least 6 hobs receives $102 for the day plus a bonus of $45 for each hob above 6 produced during that day. 3. Pay $25 per hob produced; no minimum number of hobs required. Your job is to advise Rose on the best choice. Make a selection and explain why your answer is correct. Discuss the specifics of this example and the general principle involved in making your choice.

(d) (10 marks) Now suppose that there are two types of hobbits. The very able produce one hob per hour. The less able, called slobbits, produce one hob every two hours. Both types supply labor according to the schedule given in the table above. There are 100 of each type of hobbit, but the firm only has access to 100 hob making machines and so can only have 100 workers on board. Does the compensation scheme that you suggested in (c) attract one kind of hobbit or both kinds to the firm? Explain.

Problem Set 5 Answers

Question 1: 1. This question refers to compensation for managers of company-owned outlets, which over the years have usually constituted about 20-30% of all McDonald’s outlets. The remaining 70-80% of the outlets were owned by franchisees—see chapter 16 for more about this. The formal analysis of a system of incentive compensation always begins by analyzing what the objectives of the system are and what kind of behavior is to be motivated. In this case, McDonald’s values a whole set of different behaviors and has to be concerned about maintaining a proper balance among them and finding appropriate measures of performance for each kind of behavior. For example, if the bonus is based on sales or sales growth or ratings on the company’s quality-service-cleanliness (“QSC”) surveys or other measures of product quality, the store managers may neglect cost control and fail to train assistants to become new store managers. This is an application of the equal compensation principle. One way to overcome this problem is to free the local outlet managers of responsibility for, say, managerial training, assigning that to the regional offices. Failure to compensate the outlet managers for training would present no problem, though it would still be necessary to motivate the regional offices to perform that assignment. This system might work especially well in the next phase of the business, when the North American market is saturated and fewer new outlet managers are needed. If, however, the outlet managers have a comparative advantage in training, centralizing training might be an especially expensive option during the period of rapid growth. In any real incentive pay system, part of the problem is to determine an appropriate conceptual model of what constitutes successful performance. For example, if an outlet manager can, by good efforts, increase market share only at the expense of other nearby restaurants, then sales growth may be a poor measure of performance. The level of sales or market share may be better. Compensating based on sales growth may even create a ratchet effect, in which higher sales this year sets a higher standard for next year. Increasing current sales may then lead to no net increase in compensation over, say, a two year period. If the only effective way to increase sales is to maintain the quality, service and cleanliness standards for the outlet then, according to the informativeness principle, compensation should be based on QSC performance. Variations in sales, given the QSC performance, are uncontrollable and best born by the company. This, again, is a matter of the firm’s conceptual model of what constitutes good performance. If it thinks that there are other, intangible aspects to improving sales performance, then compensation based on sales may be the only effective means of motivation. And, if it thinks that building sales is a matter of creating an ever-expanding base of regular customers, then the ratchet effect is irrelevant (this year’s customers come back more or less automatically) and compensation based on sales growth may be appropriate. An excellent managerial

discussion of McDonald’s pay system is found in the Sasser and Pettway article referenced above. 2. Untenured faculty’s chances of becoming tenured depend mainly on their scientific achievements and publications, rather than on their teaching performance. Since teaching and research activities compete for the faculty member’s time, promotion decisions based on research tend to penalize time devoted to achieving excellence in teaching. (At Stanford University in 1991, an attempt to counter this problem was made by limiting the number of publications that could be considered in making a promotion decision. The idea was to reward quality, rather than quantity, of research. Students might want to discuss the likely effects of this strategy.) There are several reasons why universities emphasize research over teaching in their faculty evaluations. One is that good measures of teaching performance are hard to come by. Student rankings are perceived by faculty as too often reflecting how entertaining the instructor is and how seemingly relevant the course material is, neglecting whether the material being taught is up-to-date, actually useful, and reflective of the best current thinking. Faculty evaluations of one another’s teaching performance could, in principle, overcome this problem, but such measures are costly to obtain and highly subjective. Also, collegiality may keep the faculty from judging one another harshly. Even if a single university were to develop reliable internal measures of teaching performance, the professor’s chances of getting good job offers from other universities’ would still depend primarily on research performance. At many research universities, pay in the current job is primarily determined by the faculty member’s outside opportunities, which adds to the emphasis on research output. The problem is probably worse for untenured than for tenured faculty, since the tenured professors have job security and have more nearly reached a plateau in their earnings. If these faculty are personally committed to teaching well, then the financial incentives for doing so, while not particularly strong, are at least not negative. Given the difficulty of measuring teaching performance and the high rates of compensation that many faculty members can earn in outside consulting, permitting unlimited outside consulting is problematic. Many universities attempt to limit their faculty members’ time devoted to outside consulting in order to reduce the resulting problem but, without good sources of information about the time devoted to outside activities, these rules are of limited effectiveness. 3. This is another application of the equal compensation principle. Under the hypothesis of the question, the job of salespeople in a specialty store is selling the store’s product, while the job of salespeople in department stores includes a larger component of customer service (including perhaps advising on the purchase of items from other departments). If a department store pays a large commission for selling and doesn’t monitor service performance, service will be neglected. The alternatives are to lower the commission rate (or use hourly wages) or to measure customer satisfaction and use the result in employee evaluations when wages are being set. In

short, fixed hourly wages are predicted to be more likely for department stores salespeople.

Question 2: In negligence cases, the client will not pay any money to the lawyer unless the suit is victorious. What is the risk profile of a lawyer who will accept such a risky project? Clearly, the selection process will draw risk neutral or risk loving practitioners to these suits. Only certain people will accept this “all or nothing” proposition. The client will know that it is in the interest of the lawyer to win and win quickly however, because there are no other benefits other than the victory settlement.

Question 3: The question gets at the definition of an appropriate proxy. When correctly used, a proxy is a measurement of one outcome that is assumed to be the best alternative to measuring the desired outcome directly. If this correlation is questionable, management will add another variable of uncertainty to the contract, and in most cases, will have to pay more to cover the increased risk. But the principal also runs the risk of getting performance only on the observable factors. Workers may just produce the proxy, since it alone is measured directly. Therefore, it is in the principal’s interest to choose a proxy wisely and to explain the strength of the proxy to the agents.

Question 4: (a) $3; $57. (b) 8 hours; Total wages = 8(45)=$360; Profit = 8(55-10-45) = 0. (c) Best choice is 2. 1. Scheme 1 pays more than 100% of net revenue so worker works too hard (9 hours). Profits with 1 are 9(55 - 10 - 55) = -90. 2. Scheme 2 is just right. Pays worker $45 per unit so he works 8 hours and produces 8 units. Implicitly, the firm is paying 100% of net revenue and “selling” him the job for $168 (i.e., it implicitly reduces piece rate on the first 6 units but this doesn’t affect amount of labor supplied because the first 6 hours are inframarginal.) Profit is 8(55-10) - 102 - 90 = $168. The principle is that the firm rents him the machine at $10 per hob (same as hour) and lets him produce what he wants. Since he is the full residual claimant, he works efficient amount of hours and the firm extracts the most rent possible by charging a lump sum fee of $168. (This fee is collected by only paying him $102 for 6 hobs which are worth $270, leaving a net of $168). 3. Scheme 3 pays too little. The worker chooses to work 4 hours and earns $100. The firm’s profit per worker is 4(55-10-25) = $80. This is worse than $168. The firm makes more per hob, but not more altogether. (d) Only Quobbits will work. Since it takes two hours to produce a hob, slobbits earn half of what quobbits earn each hour. Since quobbits are at just indifferent between working or not (they earn $192 and this is their reservation price), slobbits strictly prefer not to work. To produce 6 hobs, they must work 12 hours. They only earn $102 for 12 hours of work and things only get worse if they produce more.