MEMO. 1 The Firm as a Static Synergy. Date: September 17/24, Tirole: Theory of the Firm

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1 MEMO To: From: File FM Date: September 17/24, 2018 Subject: Tirole: Theory of the Firm These notes follow parts of the introductory chapter of Tirole (T) that lays out the basics of some theory of the firm. The notes are supplemented with additional material not covered in T. T defines 3 views of the firm: (i) a technological view of the firm the firm is a synergy between different units at a given point of time to exploit economies of scale or scope; I insert a historical note on the firm. (ii) a contractual view of the firm hazards of idiosyncratic exchange; (iii) the incomplete contracting view closer to the legal definition of the firm firms and contracts are different governance models. Now we develop these themes. 1 The Firm as a Static Synergy A classic theme in IO is that the size and the number of firms in an industry are related to the degree of returns to scale: higher levels of production permit the use of more efficient techniques: unit costs decrease with output. These are called product-specific economies. Other examples of a similar efficiencies of size are (i) a plant with many machines can sustain a flow of output proportionally higher than one with a small number of machines for with random break down in equipment the firm with larger numbers can more successfully reallocate output to other machines, and (ii) a firm serving several markets with imperfectly correlated variable demand faces less uncertainty than a collection of firms serving these markets independently. and therefore can save on costly peak-load investment. This last example is somewhat problematic for the independent firms could in principle contract with each other to achieve the same efficiency through contract that a single firm can do internally so the efficiency must floe through the choice of contract through the organization or internally versus across organizations or externally. (For that matter, there is no reason why the firms in the first example could not also enter into a contract for mutual assurance of product flow in the face of stochastic equipment failure forced outage in the language of electricity generation.) Another (historical) example of cooperation when there were production complementarities involved daily newspaper production with letter press; U.S.

2 Newspaper Preservagtion Act (1970). This allowed two daily newspapers published in the same city or geographic area to combine business operations while maintaining separate - and competitive - news operations. Some of these disappeared with the use of offset printing as newspapers could contact for commercial printing to use their production facilities when they were not printing their newspapers. What limits the size of firms? Must be that as firms grow large the costs of organization outweigh the enhanced benefits of size and diversification. A formalization of these ideas: 1.1 Simple Model Consider the formalizations of returns to scale and to scope. Start with a single-product firm: Let () denote a firm s total cost of production and output is denoted by. (Wewill say more about the derivation of this cost curve under the next header in the reading list.) For simplicity assume that the cost function is 2x differentiable and defined as follows: Z + 0 () for 0 () = 0 0 otherwise where 0 denotes fixed production cost. Marginal costs are strictly decreasing if 00 () 0 for all possible. Average costs are strictly decreasing is, for all 1 and 2 such that ( 2 ) 2 ( 1) 1 Figure 1 shows 3 shapes of average cost and marginal cost curves used in textbooks. Figure 1a shows the cost curve given by () = + for 0. Figure 1b shows the usual U-shaped curve and Figure 1c shows a range where average and marginal costs are equal so that the minimum efficient scale of plant is not unique. Does size convey a cost advantage? Can a larger firm realize lower unit costs than its smaller rival? Another definition that is used is subadditivity. This will mean that there is an advantage if one firm produces the output more cheaply than several firms can. Baumol et al defined an industry as a natural monopoly if over the relevant range of outputs, the cost function is subadditive. The cost function is said to be strictly subadditive if for any -tuple of outputs given by 1, X X ( ) ( ) =1 Thus it cost less to produce the various ouputs together than it costs to produce them separately. =1

3 Two technical propositions: Proposition 1: everywhere decreasing marginal costs imply everywhere decreasing average costs. Proof: since implies that (() ) = ( )+ µz 0 0 () = () R 0 0 () 0 as 0 () 1 Z 2 0 () 0 () for all (0) 0 () Z () 0 0 () [This is also the same as saying that marginal costs are less than average variable costs is a sufficient condition for downward sloping average cost curves. or ( () = 2 0 = () ] Proposition 2: everywhere decreasing average costs imply subadditivity Proof: Let X Think of the following: ( ) () ( ) () 7 Then ( ) ()

4 which implies X ( ) X () () The reason for this algebraic representation is that it generalizes easily to a multiproduct firm where q becomes a production vector as follows q =( 1 ) and then q 1 q are such vectors. Then the cost function is strictly subadditive if à X X! (q ) q =1 for all q such that P q 6=0. This gives a formulation for economies of scope. For example, let 1 and 2 be two quantities of two different goods. For a strictly subadditive cost function ( 1 0) + (0 2 ) ( 1 2 ) =1 where ( 1 0) and (0 2 ) are the stand-alone costs. 1.2 Critical Question The critical question is: Is this technological view a theory of the firm? The answer is almost surely no. The reason is hinted at above: advantages from firm size could also be realized through contracts among independently owned and operated entities and need not be realized internally. So the question is why these efficiencies are realized in one manner or another. No single manner seems to dominate. 2 Historical Note Coase (1937): The key question is this: why is scale coordination or organization through a firm necessary if this task is typically performed in economics by the price system through a market? That is: outside the firm, price movements direct production; but within the firm entrepreneurs direct production. Coase argues that the distinguishing mark of the firm is the supersession of the price mechanism. The most important reason for establishing a firm appears to be the costs of using the price mechanism. This includes the cost of discovering what the prices are that currently prevail in the market. There are also costs associated with coordinating and monitoring behavior through the conventional price mechanism. For example, if a factor of production wished to cooperate through the price mechanism with other factors of production, that factor would have to make many 2-way contracts. The firm replaces this complex contracting process with a single contract to each factor where the factors obey within limits an entrepreneur s

5 instructions for production and these factors receive an agreed-upon remuneration. The claim is that the firm is a nexus of contracts. Uncertainty: Some argue that what distinguishes entrepreneurs who form firmsisthe willingness of entrepreneurs to assume risk. But many markets deal with uncertainty without firms, e.g., buying and selling commodity futures. Coase s argument is that if entrepreneurs for example have a superior ability to forecast more accurately uncertain future events or are willing to accept more risk, then these skills or features can be traded in the marketplace. Government Regulation: Government regulation may encourage firms to form by, for example, taxing market transaction and not identical transactions organized within a firm. This permits us to say that a firm becomes larger as additional transactions are organized by the entrepreneur and smaller as the entrepreneur abandons the organization of such transactions. Now there is a question of what defines the upper limit to the size of the firm? That is, if by organizing you can eliminate costs and reduce the cost of production, why not eliminate all market transactions and have production carried on by on firm? Possible Answers: 1. there may be increasing marginal costs of transactions organized within the firm as the firm grows; 2. as transactions which are internally organized grow in number,it may be increasingly difficult for the manger/entrepreneur to allocate the factors of production in a manner that maximizes output to achieve efficient production; 3. there may be a spatial component if sectors of firm are separated by space, the question is one of coordinating across this space. These factors imply a diminishing return to management in the production process. One problem with these answers is that these coordination costs appear to be a simple transportlike cost some unit cost that increases with the size of the organization. But the real issues are ones of drafting and completing contracts more on this later. I will deal with 2 specific issues (1) monitoring (2) asset specification. Both permit us to say same things about the definition of the firm. Alchian and Demsetz (AER December 1972) (AD) (selected as one of the top 20 paper in 100 years of the AER.) This paper is in the Coase tradition. Their goal is to explain whether gains from specialization and cooperative production can better be explained with an organization such as the firm or across markets. Further AD seek to explain the structure of the firm. The emphasis in the paper is the firm as a nexus of contracts. AD de-emphasize the authoritative nature of entrepreneurial decisions and considers the

6 entrepreneur as a centralized contractual agent in a team production process. They focus on measurement activity. Somehow rewards from production have to be positive correlated to productive effort. To do this requires accurate measurement of input productivity and rewards. Sometimes the market performs this task more effectively; sometimes not. AD suggest that an economic organization that meters well induces greater productivity and therefore has survival value. Suppose that we ignore capital and consider a productive activity which requires a team and cooperation amongst the members of that team. Each member of that team owns the scarce productive resource, his/her own time, and contributes time according to some individual tastes. Further, assume that the team s goal is to maximize the team s profits. The team produces only one good and sells that good into a competitive output market. The production function is given by: = ( 1 2 ) where (critical) 2 0. This relationship specifies the number of units of the good produced by employing in the most efficient fashion the time of the members of the team, e.g. = the number of units of time contributed by the member of the team. The fact that the cross-partial is strictly positive identifies team production; otherwise an individual piece rate would suffice as an efficient form of organization. Under our case, there are gains from cooperative activity. Here team is defined in terms of the type of production that became feasible because of industrial revolution. Consider ideal condition to maximize profits: = X Than Or max : =0or = factor price = or = real wage The issue arises because not all of the resources used in the team production belong to a single person. How can member of the team be rewarded and induced to work efficiently? There is a market for the team s output that will reward the team s productivity but not necessarily the productivity of the individual team member. There are costs associated with monitoring the performance of team members. Question: Will each member of the team have an incentive to shirk (to adjust consumption of goods and leisure) in the presence of monitoring costs relative to the situation where no monitoring exists.

7 AD then show that it will pay for the team to bear the costs of monitoring: there is a collective benefit from a sharing of the monitoring responsibilities. First, let us demonstrate the problem (use simple algebra): Think of a linear sharing rule where factor gets a share of gross revenues defined by such that P =1or revenues are exhausted in their distribution to all factors of production. Each factor then tries to max or to set = But the only way this will be first-best optimal is if =1 But by definition P =1so that each individual 6=1. Central problem is that shirking (i) cannot be detected and (ii) there does not appear to be an easy assignment rule to prevent shirking. It is the combination of the externality plus the nonmeasurable input effort that causes the problem. To break this shirkingdeadlock,accordingtoad,anatural solution would be to introduce monitoring. Now illustrate gains from the sharing of the monitoring costs. (Use simple diagram that appears as Figure 1 at the end of these notes.) Assume that there is one team member to be monitored say person and assume that this team member bears the cost of monitoring.. In Figure 1, the traditional labor supply curve for factor, labelled,isupwardslopingto right, i.e., leisure is a normal good; and the traditional downward sloping to right demand schedule for production is given by =. While is the profit-maximizing equilibrium, it cannot be costlessly determined according to AD. If worker bears the cost of monitoring, then worker s input (effort) drops from to. As 2 0, the reductionineffort by the worker reduces the productivity of all other workers in the team whose cross-partial with worker is positive. This means that the marginal productivity curve of the other workersshiftsinandtheseworkersareworseoff. SeeFigure2attheendofthesenotes. 2 represents a utility reducing equilibrium over 1 for the worker. And this reduction in well-being is attributable to the decision by the worker to cut-back his/her input efforts as they now have to pay a monitor. Are there gains to another arrangement? Imagine other negatively affected workers consider collectively paying some of the monitoring costs of the worker. They will continue to incur additional costs until the marginal cost of their portion of the monitoring fee just equals the gain that accrues to these other workers from the increase in the input efforts of worker.

8 One difficulty in general is that it will not pay a single worker to secure the optimal sharing rule for the monitoring costs as all workers will benefit from the sharing of costs by a single worker a contractual efficiency. These gains are not captured by (say) worker alone and so this worker does not have the correct incentive to seek an optimal sharing arrangement (a free riding problem). This means that it pays a collective of workers to internalize all of these benefits so that the correct proportion of the monitoring costs are borne. AD ask whether competition from the market for membership on the team will cure the problem of shirking? They claim that the answer is no for (i) it is difficult and costly for any potential team member to discover shirking, and (ii) the incentive for shirking still exist that is, as shirkers bear less than the full costs of shirking (there is a real externality), there is an incentive to shirk excessively. One method of reducing the incentive to shirk to the optimal level is to have a central specialized monitor who receives a residual income payment. This arrangement guarantees that the monitor has no incentive to shirk (the old problem of who monitors the monitor?). But this means a vesting of the classical attributes of an entrepreneur in a single individual or set of owners. These important features are: (i) (ii) (iii) (iv) (v) residual income claimant, observation of input behavior, central party common to all contracts with factors of production, ability to alter membership in the team, ability to sell rights as owner/entrepreneur. (What is the impact of limited liability on this package of rights?) This coalition of rights emerges as the most efficient, i.e., least cost method of resolving the shirking-information problem of team production. Some criticisms of the AD approach (Holmstrom and Tirole in the Handbook: p.68): (i) those who do the monitoring in firms are rarely the residual claimants; (ii) horizontal mergers are hard to understand from a monitoring perspective unless there are some economies of scale in monitoring; (iii) monitoring is not the distinguishing feature of corporations for partnerships and cooperatives could also have monitoring; (iv) monitoring does not offer an explanation of firm boundaries: that is, nothing precludes the monitor from being an employee of a separate firm with a service contract that specifies his reward as the residual output. This is also true for the workers they could be monitored and paid as independent agents rather than employees.

9 Some (Williamson) argue that the key is not the comprehensive contract story that is being told here but an incomplete contracting story with sunk or irreversible investments. We continue to examine the impact of sunk costs on contracting. Sunk costs = asset specificity and permits hold-up or opportunistic behavior. What follows is from Tirole. 3 The Firm as a Long-Run Relationship The central idea is that ownership accrues to the party with the residual authority to make decisions not covered by the contract that govern trade. So thecontracthassometermsthatseektogovernexchange. Butsomeissueswill remain outside the contract and who controls these decisions owns the firm (key idea). Within this set-up that authority could be either a seller of a good or a buyer of a good. 3.1 A simple numerical example taken from Aghion and Holden (2011) (need idea of Nash Bargaining see Binmore et al) Consider an upstream firm that supplies one unit of an intermediate good to a downstream firm. Label the upstream supplier as and the downstream buyer as. The downstream firm uses this intermediate good to produce a final good that is sold to a consumer. The consumer values the good at. can make a privately costly investment that lowers the cost of producing the good upstream. If invests $5, the cost of producing the good upstream is $10. Otherwise the good costs $16 to produce. The downstream firm can make an investment that increases the value of the good to the consumer. If makes an investment also of $5, the value of the good to the consumer is = $40; otherwise =$32 so that the investment of $5 increases the value of the good to the consumer by $8. These two investments are specific tothetwoplayers and. Notice the following feature of these numbers: If invests $5, the cost of the good is reduced by$6andthissavingincostaccruesto. If invests $5, the value of the good increases by$8andthisincreaseinvalueaccruesto. If firm ownership meant picking only one of { } to be the party with the residual authority to make decisions (implement the respective investment) which party should dominate? These two players would like to write a contract where each undertakes the specific investment for doing so leads to a total surplus of $( ) = $20. But suppose that the parties cannot contract on this production nor on any cost-sharing rule nor on the investments. For example, a third-party trier of fact cannot determine whether these investments have been made. If they cannot write a contract, then they will bargain about the price pays to but after the investment stage. Assume that and are not integrated so they bargain; with zero threat points, the Nash outcome is to split any rents. Consider the motives facing : if invests, incurs a cost of $5. The value of the surplus

10 goes from $32 to $40 so that half of this is $(40-32)/2 = $4 $5. So will not invest. Consider the motives facing : if invests, incurs a cost of $5 but the production cost falls to $10 from $16 so that half of this is $(16-10)/2 = $3. So will not invest. The main point is that under no contact and bargaining the investing agent when the agents are independent of each other, the investor gets only 50% of the incremental outcome. Now consider two scenarios: (i) and are vertically integrated with owning s machine that produces the final good (forward integration) but with independent decision making at each level; and (ii) and are vertically integrated with owning s machine (backward integration) again with independent decision making at each level. Integration simply removes the bargaining but does nothing else. Forward Integration: no longer needs to bargain with as owns s machine. now gets all of the cost reduction or $( ) 0andso invests. does not make an investment in enhanced quality as gets none of the benefit as no longer owns the machine but according to the assumption would have to incur any investment cost. cannot force to invest nor by assumption contract on making the investment. The resulting surplus is $( ) = $17 $(32-16) = $16 so a net improvement. Backward Integration: invests but does not. This yields a surplus of $( ) = $19 an even better incremental result. While this is better, it is worse than complete contracting (which yields $20 as seen above) but this is better than any other arrangement. This is better as the investment by is relatively more important than the investment by. Bothcost$5but s investment has a benefit of $(40-32) = $8 while s investment has benefit of$(16-10)=$6. This illustrates two insights from Grossman and Hart. (i) with incomplete contracts, asset ownership can mitigate inefficiencies that would otherwise arise from underinvestment in productive activities (bargaining disincentives); and (ii) the party whose marginal investment is more productive should own the assets. With this example, the expectation is that the equilibrium arrangement is that should be the owner and collect the residual return. (See more of this theme in Mathewson and Winter (1994) Territorial Rights in Franchise Contracts.) Now move on to the development in Tirole. Here the critical question is: why should the rules that govern trade tomorrow be determined today? In answering this question we focus on a vertical relationship between a buyer and a supplier where both parties are risk neutral. Asset specificity plays a key role. 3.2 Idiosyncratic Investment and Asset Specificity: Intro The ingredients here are switching costs or specific investments. Switching costs are an example of specific investments. For example, switching costs include the need of a new team to learn the ropes; these can be substantial, especially when an old team is reluctant to transmit information to the new team. Such costs may prevent a buyer from repeatedly

11 using a spot market to purchase certain goods or services from suppliers. So once parties have traded with each other staying together can yield a surplus relative to trading with others. More generally, idiosyncratic investment can be associated with the prospect of future rather than current trading. Consider sunk investment and all of the examples given by B. Klein. One aspect of this is that even though the supplier and buyer may select each other ex antefromapoolofcompetitivesuppliersandbuyers,theyendupinanexpostbilateral monopoly in that each has an incentive to trade with the other rather than outside parties. But each wants to appropriate the common surplus ex post. Knowledge of this can be imputed to the parties ex ante and this can jeopardize the investments required to complete the ex post trade. Let s model this (after Tirole on p. 22) and in doing so illustrate the problems that arise when there is asymmetric information on essential values in this bargaining problem. There are two periods =1,theexanteperiod,and =2, the ex post period. A supplier and a buyer may or may not contract in period 1. For the moment ignore the first-period specific investments. At the beginning of period 2, the 2 parties learn how much they will gain from trade. Suppose that the parties trade 1 unit of the indivisible good and so the volume of trade is either 0 or 1. The value of the good to the buyer is and its production cost to the seller is. Thus the gains from trade somehow to be slit between the two is. Let be the trading price so the at the buyer s surplus is and the seller s surplus is. 3.3 Bargaining and State of Knowledge: No Investment Bargaining with common knowledge: Provided that, we expect trade to occur. Suppose that no trade were to occur, then one of the parties could suggest a price that left positive surplus with each. If, on the contrary,, then one of the parties would be better off refusing to trade. So bargaining under symmetric information is efficient (a version of the Coase theorem). Bargaining with asymmetric information: Suppose that the cost is known to both partiesbutthevalue is private known only to the buyer. Represent beliefs on the part of the supplier wrt by () with 0 () =() 0 on [ ] with () =0and () =1. Assume that gains from trade exist with positive probability (i.e., ) and that this probability is less than 1 (i..e., ). Suppose that the supplier has all of the bargaining power and makes a take-it-or-leave-it offer of a price. The buyer accepts only if. This means that the probability of trading is 1 () and the supplier s profit problemis max ( )[1 ()] The solution is given by [1 ()] ( )() =0 [Notice that this FOC is similar to the bidding solution in the problem presented in the preliminaries notes.] The two terms are interpreted as follows: A slightly higher

12 brings in expected revenue of [1 ()] buthasthecostofpossiblyexceedingthebuyer s reservation value with probability () and therefore a loss of surplus of ( ). Notice that this equation leads to and therefore to a loss of total surplus. The reason for the loss is as follows: evaluate at = and the result is =1 () 0 which means that increasing price above = permits profits to accrue to the supplier as any loss of profit associated with a reduction in the volume of trade associated with () is zero when the initial price-cost margin is zero. Notice that the profit function above looks like a conventional profit function with the demand curve given by = () =1 () or a continuum of buyers with unit demands and valuations distributed according to some cumulative distribution ( ) is equivalent to a single buyer with unit demand and a random valuation determined by ( ). Remark: As long as there is some asymmetry of information and some probability that (gains from trade do not arise with certainty) there exists no efficient bargaining process (Myerson and Satterthwaite 1983), i.e., bargaining creates some inefficiency. Contracting: This ex post trade inefficiency gives rise to an incentive to contract ex ante to avoid or to limit the inefficiency. The way to do this is to give the buyer the right to set the price. Doing this gives rise to a price of = wherethesellerisjustindifferent. Since is known, no inefficiency will arise. In general, the contract tries to create the largest possible surplus where the division of this surplus depends on ex ante relative bargaining powers. Similarly if the buyer s is common knowledge and the seller s is private, the supplier will fix the price that is =. In general this allocates power as follows: the one with the private information sets the price and the other has only the authority over the trade/no trade decision. So in the former case, the contract is: The buyer determines the quantity to be delivered (0 or 1). The delivery price is. Theruleisthatpowershouldgo to the informed party. 3.4 Bargaining and Idiosyncratic Investment Add Investment and use Bargaining: (Uses the concept of Nash solutions) Consider a production cost as a function of supplier s investment where this cost is given by () where 0 0 and Let as before denote the value to the buyer and assume that (0). The price will be determined by the ex post Nash bargaining solution to split the ex post gains from trade. The ex post gains from trade are () and so if the splits these then is determined to give () =( ())2 (or equivalently () () =( ())2) or solving yields () = ()+ 2 once has been invested. The supplier s ex ante profit isgivenby max () () = max2 ()2

13 and the solution is given by 0 (ˆ)2 =1 Or at the solution value (ˆ), $1 of investment yields $2.00 of cost reduction to the supplier and therefore investment is too little. Clearly the socially optimal investment is given by 0 () =1or a (not surprisingly) larger investment. So the problem is that the ex ante investor does not capture all of the cost savings. This has been labelled opportunism or hold-up. One amendment to this involves the possibility of other potential buyers. This limits the degree of hold-up by the buyer and in doing so limits the ability of the original buyer to hold-up the quasi-rent on the investment. Assume that and are common knowledge. Characterize this opportunity to trade with other buyers (many of them) in the following manner. Define to be a parameter that reflects the specificity of the investment. That is. if the seller trades with any other buyer, then the investment cost corresponds to a fictitious investment where =0indicates extreme specificity and =1indicates the absence of specificity; that is [0 1]. To appreciate this specification, let s see how it works. Suppose that a supplier has invested. If he does not trade with a specific buyerbutcan trade with others, the supplier can receive as there is competition among the buyers to buy the stuff. If there is competition among the buyers, the competitive outcome is that the winning buyer will bid the full value to purchase the product. The seller gets surplus defined by () or the value to the other buyer (transferred through the competitive process to the seller) less the avoidable cost no longer sunk dependent on the fictitious investment. This is the clever point of the specification. If =1, then the full benefit of the fictitious investment is applicable to the trade with the other buyer or the investment is fungible to another buyer. If =0, then none of the benefit is transferable to the other buyer (i.e., all is specific to the original buyer) and the seller in this other trade would face an avoidable unit cost of (0) or the avoidable unit cost if there had been no investment. Then the threat point of the supplier is to trade with one of these other buyers and the Nash solution has to be corrected for any threats. Then the ex post gains to trade are split correcting for the threat potential. The seller expects to receive a gross payment of () ( ()) or (selling price less the gains from trade with another buyer who competes for the good) and the buyer expects to receive (). The Nash fair solution is given by max () and the solution is given by seller surplus buyer surplus z } { [() () ( ())] [ z } ()] { () [() () ( ())] = 0 or () = + () () 2

14 This yields an ex ante profit problem for the supplier of max () () = max ()+() 2 and a solution of [ 0 ()+ 0 ()] = 2 so that when =1(no asset specificity) 0 () =1 the efficient solution with = and when =0,wehavetheprevioussolution,namely that 0 ()2 =1. So provided curvature of cost function is not too great, the supplier s incentive to invest increases with. The proviso comes from the following: = ()+ 00 () 0 ( 00 () ()) = ( )+(+) 0 provided (+) 4 The Firm as an Incomplete Contract We can identify 4 types of contracting costs, 2 of which occur at the date of contracting and the other 2 occur later. Here they are: (i) some contingences which will ultimately occur are simply unforeseen (ii) even if these are foreseen, there may be too many to write into the contract (iii) monitoring the contract may be costly (iv) enforcing contracts may involve considerable legal costs. Claim: minimization of transaction costs is a major factor in organization design. We have already investigated the nature of bargaining outcomes. There are other intermediate forms of contracting (between no contract and a complete contract). One possibility is that the two parties resort to a third party whose role is to strive to achieve those efficient decisions that would result from a complete contract. That is, whatever rules put forward by this third party must seek to achieve both ex post efficient volumes of trade and encourage ex ante the efficient levels of investment. The other possibility is to relegate residual authority to one of the two trading parties in any unspecified contingency. 4.1 Authority to One Trading Party Let s consider the impact of the latter where one of the two trading parties has authority. The important point here is to recognize that such an allocation of authority alters the

15 threat point or the status-quo point in the bargaining process. To illustrate this point, consider the following set-up: Suppose that a buyer and seller must make some decision. The monetary payoffs aregivenby () where =1 2. Giving authority to, say, party 1 means that this party is allowed to choose ex post his/her preferred. If the2partiescannotagree,party1chooses 1 (that is 1 =argmax 1 ( 1 ). Similarly 2 =argmax 2 ( 2 ).) If, however, this decision does not maximize party 2 s pay-off, then the two parties have an incentive to renegotiate to maximize their joint pay-off given by 1 ()+ 2 (). Define as follows =argmax 1 ()+ 2 () Assuming a transfer from party 2 to party 1 that implements the Nash bargaining solution we have = 1( )+ 2 ( ) [ 1 ( 1)+ 2 ( 1)] 2 or maximized joint pay-off less status quo points or upon rearranging terms we have [ 1 ( 1)+] 1 ( )=[ 2 ( ) ] 2 ( 1) If we let, =1 2 denote the final benefits after the transfer and the decision,thenwe have 1 = 1 ( 1)+ 1( )+ 2 ( ) [ 1 ( 1)+ 2 ( 1)] 2 and 2 = 2 ( 1)+ 1( )+ 2 ( ) [ 1 ( 1)+ 2 ( 1)] 2 (gains even distributed). By definition, it is clear that party 1 benefits relative to party 2 as 1 2 as 1 ( 1) 1 ( 2) and 2 ( 1) 2 ( 2) so that 1 ( 1) 2 ( 1) 1 ( 2) 2 ( 2) This says that party 1 gains more than party 2 through the renegotiation process this makes sense. If ex post benefits depend on ex ant investment as well as the ex post decision (as above), then the distribution of authority affects the parties decisions to invest in specific assets. Party 1 s investment cannot be expropriated as 1 is the decision maker here; party 2 s could be however. Thus in the absence of renegotiation. party 1 s authority affects both parties incentives to invest. Under renegotiation, the status quo even if it is not observed influences final payoffs and thus the distribution of authority still affects the incentives for investment.

16 4.2 Grossman and Hart (JPE) Grossman and Hart call supplier (buyer) control as the setting where the supplier (buyer) has authority over decision. Integration is the allocation of residual rights of control to one of the parties. Nonintegration is where the decision space has 2 dimensions and each party has control over one of these dimensions. The optimal arrangement is that one that best protects the specific investments. (Example on p. 31 that illustrates the Grossman-Hart analysis.) A buyer and seller contract at =1to trade at =2. While a basic design is contracted for initially, there will an as yet undefined possibility that quality could be improved when the trade is to occur. Both parties learn the improvement, should it occur, at =2. Suppose that the second-period cost of production incurred by the supplier is. The buyer selects an investment in =1. The buyer s second period value for the improvement is with probability and 0 with probability 1. The cost of investment is equal to 2 2 (The specification here appears to be that additional investment increases the likelihood of a higher second period valuation; the cost function is quadratic for ease of illustration and should yield closed solutions where relevant.) Investment levels are unobservable and therefore non-contractable That is, the investment level is private and not public information and therefore cannot appear in a contract. Note that and are extra valuation and cost beyond those value associated with the basic design. Consider first the social optimum. Quality improvement should be made only if buyer has value. That is the optimal investment (made prior to the realization of value) is given by or max [( ) 2 2] = Substitute this solution into the surplus relation above to define joint surplus as: =( ) 2 2 Now move to the set-up where the parties act in their self-interest. Tirole considers the 3 possibilities (already listed when no specific investment was at stake): (i) unconstrained bargaining parties bargain over whether to make improvement at =2,(ii) supplier control seller has the right, and (iii) buyer control buyer has right to decide. In theselasttwocases,thepartywithpower canoffer to give away this authority. Also assume in bargaining that gains are split (Nash fair solution). Finally parties choose an arrangement or institution that maximizes expected joint surplus as any gains from switching can be redistributed ex post. (i) Unconstrained Bargaining: Parties trade iff. and each gets ( )2 Buyer s investment solves ( ) max 2 2 2

17 or = ( )2 = 2 This is just the underinvestment-under-unconstrained-bargaining result. Joint surplus may be calculated as = ( ) ( ) 2 2 = 3( )2 8 (ii) Supplier Control: The solution here is equivalent to unconstrained bargaining as the status-quo point in the bargaining game is the same: if the parties disagree, the supplier chooses not to make the improvement, which is the less costly action for the supplier. Supplier control means that the supplier can use strict compliance with the original contract as a threat to elicit a good bargaining position. Thus similar to unconstrained bargaining the buyer underinvests. (iii) Buyer Control: Improvement would always be made if the status quo were not renegotiated. When the value to the buyer is zero, the buyer is indifferent between imposing the improvement and not (as it is the seller who incurs the cost ) so the assumption is that the buyer imposes the improvement The buyer would certainly impose the improvement if the value were only slightly positive. If the value is the status quo is efficient and no bargaining occurs. The buyer gets by imposing the improvement. If the value is 0, the status quo is inefficient and bargaining divides evenly the gain () ofnotmakingthe improvement. In particular, the buyer gets 2. The optimal choice of investment for the buyer is given by 2 2 max +(1 ) 2 or 2 =0 or and the surplus is or = 2 = ( ) ( ) 2 2 = ( 2 )( ) 1 2 ( 2 )2 = 1 2 ( 2 )( ) = 1 2 ( 3 )( 2 2 )

18 The result is that the buyer now over invests. The source of this result is that the buyer s authority permits the buyer to avoid paying if his value is. The point is that the authority vested in the buyer (by assumption under buyer control) permits the buyer to avoid paying the incremental production cost when his value is. As the buyer fails to internalize this production cost, the buyer overinvests in that activity that makes production more likely. Here are some more results. If =0(variable unit costs are zero), buyer control is socially efficient there is no noninternalized production cost supplier control is inefficient. If = 0, then no investment is optimal and supplier control or unconstrained bargaining is optimal; buyer control would yield investment and a negative joint surplus. (Opinion: insightful result.) A relevant question is who owns the customers, the firmortheemployee insurance example. Could do the Mathewson and Winter paper on exclusive territories. 5 Basic Incentive Problem This problem reflects the conflicts between incentives and insurance. There are risk-neutral shareholders and a risk-averse manager. Suppose that there is a pie of random size defined by Π which takes on values defined by Π 1 Π Π with probabilities defined by 1 with the usual P =1 =1. Let the allocation to the risk-averse party be (Π) and therefore the allocation to the risk-neutral party is Π (Π). the respective expected utilities are Π ((Π)) = X ( ) and Π [Π (Π)] = X [Π ] where = (Π ). An efficient contract maximizes the utility of one party for any given level of utility of the other and so satisfies X X max ( ) s.t. [Π ] 0 { } The corresponding Lagrangian is = X " # X ( )+ [Π ] 0 and the solutions are given by 0 ( )= so s are independent of with risk aversion.

19 That is, the risk averse individual should get full insurance or have a constant income over all states of nature. But suppose that the risk averse individual takes an action which affects the size of the pie and that this action is costly to this individual. suppose further that this action is unobservable to the risk neutral individual. But if the income of the risk averse individual is independent of his actions, then this individual has no incentive to exert effort. So full insurance conflicts with incentives. On the other hand, suppose that the parties are risk neutral so that 0 is a constant. Then the party who takes the action does not need to be insured and the other party (called the principal) can ensure that the individual taking the action (called the agent) takes the jointly optimal action by selling the entire pie to this individual for a fixed fee. So the principal receives a transfer price independent of the size of the pie (equal say to the expected size of the pie under optimal actions an auction) and the agent becomes the full residual income recipient. Then the agent has the optimal incentive to undertake the first-best action. 6 Example of Principal-Agent Relationship This illustrates the necessity of a confounded observation that cannot be inverted. Suppose that shareholders are risk neutral; this also illustrates the result of selling the full residual claim to the one undertaking the hidden action. Suppose that the manager makes an unobservable decision, sayeffort, in an interval [ ]. Profits, however, are subject to a random disturbance given by. So the profit relationshipisdefined by ( ) which is increasing in. Shareholders observe only the profit outcome and reward managers based on this observation; this reward is defined as (). This leaves the shareholders objective function as [( ) (( ))] The risk neutral manager s objective function is given by ( ) = () (where () represents the disutility of effort) and a participation condition given by ( ) 0 (assumed to be binding).these permit us to rewrite the shareholders objective function as [( ) (( ))] = ( ) [( )+()] = ( ) () 0 Define to optimize ( ) (); thatis is the first-best effort level. Under this set-up of asymmetric information, let shareholders sell the firm ( a sell-out contract) to the manager for the price of = ( ) () 0. If the manager accepts, then the manager

20 is the full residual income recipient. Alternatively the shareholders could put forward a managerial payment scheme defined by () = What is the manager s expected utility in this case? It is ( ) = () () = ( ) () Manager takes as given and maximizes as follows: The manager would accept as max[ ( ) ()] max [ ( ) () ] = max[ ( ) () ( ( ) () 0 )] by design of = 0 So the manager accepts and the shareholders make exactly the same expected profit as under full information. Both offers achieve the same result. The manager bears all of the risk but this is irrelevant with risk-neutral managers. 7 Relative Compensation (also yardstick competition) Model (from Ed Lazear Personnel Economics, Chapter 3, Relative Compensation). Considerafirm with two workers that sets up two jobs, boss and operator. Workers compete against each other with the winner being designated the boss and the loser being designated the operator. The winner receives a wage of 1 and the loser receives a wage of 2. The wages are paid only after the completion of the contest. The probability of winning the contest depends on the effort exerted by each individual. We designate the two individuals as and. We denote their respective random luck components as and (( )=( )=0) and their outputs as and. Unobserved individual effort levels are denoted by and. The production function for each is given by = + = + The problem is solved in an incentive compatible fashion so first the worker s optimal decision is developed and then this is plugged back into the firm s problem to determine the optimal compensation scheme. We proceed to define ( ) where = as the probability

21 of winning the contest, conditional on the effort level chosen so that worker s optimization problem may be written as max ( ) 1 +(1 ( )) Think of 2 as the monetary value of pay associated with effort level. The corresponding FOC for worker is ( 1 2 ) 0 = (1) andasimilarfocforworker. The probability that defeats is given by = ( + + ) = ( )(or ( )) = ( ) where is the distribution function on the rv. This means that = ( ) But the two workers are ex ante identical. This means that there is a symmetrical equilibrium where the two workers choose the same level of effort so that = = so that (1) becomes ( 1 2 )(0) = (2) This results admits of two interesting implications as follows: 1. Any increase is ( 1 2 ) implies a higher level of effort a bigger raise induces workers to compete harder for promotion, i.e., ( 1 2 )=(0) (See diagram on the nature of (0).)The lower is (0) the lower the level of effort in equilibrium since (0) is the measure of luck in this production tale. If luck is completely unimportant is degenerate and (0) approaches infinity. If luck is important and the distribution of has fat tails, then (0) becomes very small. This leads to the following: as the importance of luck increases, the amount of effort exerted for any given wage spread declines. The interpretation is that if luck dominates the determination of the promotion outcome decision, workers will not try very hard to win the promotion. Another way to put this is the following: in production set-ups where measurements of efforts are noisy, large raises are needed to offset the tendency by workers to reduce effort. Now consider the firm s design problem. The firm wants to maximize its expected profit or equivalently its profit per worker given determined by (1). since the number of workers hired is exogenous to this problem. The design problem facing the firm is given by max ( )2 1 2 ( )2 2 2 or ( ) 2

22 The latter constraint is a participation condition; ( )2 is the expected wage that each risk-neutral contestant can expect to receive; 2 2 is the opportunity cost of the worker. Substitute the constraint into the objective function to obtain The corresponding FOC s are max (1 ) =0where =1 2 The solution to this is =1or the marginal benefit tothefirm of labor is 1 while the marginal cost is so this condition equates marginal benefits to marginal costs. If effort could be contracted on the firm s goal would be to maximize expected profit perworkerfor the firm or and the solution would be given by max = ( ) 2 2 = 2 2 1= which, of course, is the outcome given by the tournament. The wage spread is found by substituting 1 =1into (2) to obtain 1 2 = 1 (0) This equation together with the participation condition given and (3) ( )2 = 2 2=12 (4) can be solved for the wage level and the wage spread. While the wage spread increases with the inverse of (0) so that the size of one s wage is increased to offset any increase in luck as reflected by a fall in (0), the average is invariant with respect to a change in (0). This permits an interpretation of a recent claim: Some feel that US/Canadian CEO s are overpaid relative to say European and Japanese CEO s. While this may be true, it misses a point. The CEO s salary exists not so much to motivate the CEO as it is to motivate all under him or her. The CEO s salary in this story is not determined in relation to output or the CEO s productivity but in relation to the firm s hierarchical structure. The argument is that tournament theory provides a way to think about the entire structure of compensation within the firm. Tournament theory implies a wage spread or a level of variance if wages with an organization. The size of the spread depends only on the amount of noise associated with the production environment. Even though we talk about noise and distributions, all actors here are risk neutral.

23 Eddie Lazear continues to consider Industrial Politics. The idea is that winner-take-all tournaments may spawn espionage where workers may waste resources in undermining the efforts of their competitors to enhance their own chances of success. Workers may also engage in sub-optimal amounts of cooperation. These are inefficient. Lazear continues to consider where workers will self-select, hawks going into one firm and doves to the other. This will not happen for the following reason. In the presence of hawks who will engage in non-cooperative behavior in order to enhance their own chances of success, firms will dampen the wage spread. This will not be the case for firms that employ only doves. Knowledge of this, however, will mean that hawks will flow to the firms with doves where thewagespreadislargerandthusthere willnot be a self-selecting separating equilibrium. This means that firms may have to screen. COMMENTARY: This leads Lazear to comment on a couple of phenomena: First corporate culture may matter in terms of seeking homogeneous worker pools along the attribute lines of hawks or doves. Second, firms may select internal workers for promotion to hierarchical positions from sectors where cooperation is high rather than low. For example, field offices may compete with each other under a corporate umbrella. The rivalry then may be between and among these field offices. If COO s and CEO s are selected from the field, this may prevent competition among the VPs at head office, dampening any hawkish tendencies. The example given by Lazear is that before the breakup of AT&T, the CEO was generally chosen from the ranks of the subsidiary operating companies. It may be that competition among the field offices holds a low potential for wasted noncooperative behavior. Cooperation at head office may be critical to the firm s success. Third, tournament theory is consistent with the view that CEO s tend to be the least compassionate people in an organization. Tournament theory predicts that this follows from having to battle to win the tournament, a natural selection outcome. The claim by Lazear is that tournament theory provides a basis for thinking about industrial politics and suggests a theory of hierarchical structure. From (3) and (4) and 1 2 = 1 (0) = 1 or 1 = 1 2 Substitute for 1 in the above equation to obtain = (0) or 2 = 5 5 (0) and 1 = 1 2 or 1 = 5+ 5 (0)