Theories of Firm

Theories of the Firm

Dr. Margaret MeyerNuffield College

2014

Coase (1937)

If the market is an efficient method of resource allocation, asargued by neoclassical economics, then why do so manytransactions take place within firms?

Coases (informal) answer:

There are costs of making transactions through both themarket and the firm: transaction costs.

The firms size is determined by optimizing with respect tothese costs.

But what exactly are these costs? When do they matter? Why dothey differ in the market and in the firm?

A theory of the firm should explain the costs and the benefits oftransacting in the market vs. the firm.

The neoclassical theory of the firm

Production function f (x1, ..., xn) and input prices {wi}ni=1 Cost function: C (Q) = minni=1 wixi s.t. f (x1, ..., xn) Q With fixed costs and increasing marginal costs, C (Q) /Q has

a U-shape, reaching a minimum at some Q. So economies of scale (or scope) explain why production

activities up to scale Q should be concentrated within onefirm rather than being distributed across multiple producers.

But this isnt a theory of the firm. Rather it is a theory ofplant size.

Need to go further: What determines whether several plantshave the same owner or different owners?

A theory of the firm has two possible meanings:

1. a theory of the boundaries of the firm

2. a theory of the internal organization of the firm, i.e. itsinternal structure and policies.

Here, we focus on the first meaning.

We also focus (largely) on decisions about vertical integration:Where a supplier produces an intermediate good for a producer,should the producer own the supplier (backward integration),should the supplier own the producer (forward integration), orshould the supplier and producer be separate firms(non-integration)?

This is often referred to (ignoring the second option) as themake or buy decision.

Sources of transactions costs and the need for contracts

Some transactions occur in spot markets

e.g. casual labor; wholesale fish market efficient spot markets have many participants on each side

Thin spot markets often generate inefficiencies:

Ex post inefficiencies: if parties have specific investments inplace (investments whose value is greater in the currenttransaction than in any alternative use), these investmentsgenerate quasi-rents (i.e. an ex post surplus). The partiesmay waste resources in haggling over how to split this ex postsurplus.

Ex ante inefficiencies: the parties may make inefficiently lowlevels of specific investments ex ante (even if ex postbargaining is efficient).

The need for contractsTo illustrate ex ante inefficiencies, consider a transaction between a seller(S) of an intermediate good (a widget) and a buyer (B).

Ss production cost is 0, but by exerting ex ante effort e, at convexcost C (e), S can improve widgets quality. B values widget at (e) = pie. B has no alternative supplier, and S has no alternative purchaser. The socially optimal (first-best) effort maximizes pie C (e), so

satisfies pi = C (eFB).Suppose there is no contract between B and S , so ex post, they bargainover the price.

Ex post, Ss investment in quality has been sunk, and both partiesoutside options are 0, so Nash Bargaining Solution = p = pie2 . Ex ante, S anticipates this outcome, so S chooses e to maximize

pie2 C (e) = Ss effort satisfies pi2 = C (eSB): there is ex ante

underinvestment by the seller.

Complete vs. incomplete contractsIf Ss effort could be verified by a court, an ex ante contract could solve theunderinvestment problem: contract would specify price p = pie k . This contract would give the seller efficient incentives on the margin, and

the constant k could be chosen to give any desired split of the surplus.

Is this a theory of the firm? No!

The contract p = pi (e) k could work between two independent firms orbetween two units of the same firm. In the presence of this (complete) contract, the boundaries of the firms

would be irrelevant.

In practice, the widget transaction is likely to be much more complex.

There may be many states of the world, in each of which B needs aslightly different widget. And it may be very difficult to describe each state and each type of widget

in a way verifiable by a court. Thus, in practice, the contract signed will be incomplete, and ex ante

contract design cannot completely eliminate ex post bargaining.

Complete vs. incomplete contracts (cont.)A complete contract specifies actions and payments in all possible futurecontingencies. Hence, a complete contract never needs to be revised or addedtothere is never any need for ex post decision-making. If all contracts werecomplete, it wouldnt matter whether the parties to the contracts weremembers of the same or different firms.

Therefore, incompleteness of contracts is necessary for a theory ofthe boundaries of firms.

Why are contracts incomplete in practice?

Difficult to foresee all future contingencies. Difficult to decide in advance what should be done in each case. Difficult to describe the above in a way enforceable by a court.

Whenever contracts are incomplete, there is a need for ex post decision-making.And the boundaries of firms (ownership of the assets used in transactions) willmatter because they will affect how decisions are made ex post.

Three theories of the firm

1. transaction cost economics: due to Coase (1937), Williamson(1975,79,85) and Klein, Crawford, and Alchian (1978)

2. property rights theory: due to Grossman and Hart (1986) and Hartand Moore (1990)

3. incentive system theory: due to Holmstrom and Milgrom (1991,1994)

Each theory assumes that contracts are incomplete. Each theory gives a different explanation for why and how decision making

is different when the parties belong to the same firm (backwardintegration or forward integration) than when they belong to differentfirms (non-integration). Consequently, the theories yield different predictions about how the

boundaries of firms affect the efficiency of transactions.

Transaction cost economics (1)

The famous case of General Motors and its supplier Fisher Body

In 1919, General Motors (GM) entered a 10-year agreementwith Fisher Body (FB) for the supply of metal closed bodies

exclusive dealing clause by which GM purchased closed bodiesonly from FB

price fixed Demand for closed bodies later increased dramatically GM wanted to reduce the price, since FBs average costs had

decreased FB refused to locate plants near GMs assembly plants Thus, inefficient haggling ex post and inefficient ex ante

investment decisions

By 1924, GM began negotiations to purchase FB, which it didin 1926


Coase (1937), Klein, Crawford & Alchian (1978), Williamson(1975,79,85) The theory is informal Stresses incompleteness of contracts and lock-in Lock-in describes a situation where the parties to the contract have

made specific investments (investments whose value is greater in thecurrent transaction than in any alternative transaction). The specificinvestments generate quasi-rents (i.e. ex post surplus).

Costs of market transactions (non-integration): ex post haggling overthe quasi-rents (and also, potentially, underinvestment in specificassets ex ante).

These costs are greater for transactions characterized by greaterspecificity of assets and more uncontracted-for contingencies.

These transaction costs of using the market disappear underintegration where decisions can be imposed by fiat. (Focus is usuallyon backward integration.) But integration has bureaucratic costs.


Main empirical prediction: higher quasi-rents are more likely tolead to integration.

Generally, this is confirmed. For ex., Joskow (1985) examines the transactions between

coal mines and electric utilities and finds that electricity plantslocated next to a coal mine are more likely to own their coalsource than are plants not so located.

Interpretation: degree of lock-in, and hence size of quasi-rents,is greater for plants located next to a coal mine.

Problems with the transaction cost theory of the firm: Why does haggling stop inside the firm? What about

rent-seeking behavior inside firms? (see Gibbons (2005) andMeyer, Milgrom, and Roberts (1992))

What are the bureaucratic costs?

The property rights theory of the firmOverviewGrossman and Hart (1986), Hart and Moore (1990)

Distinguish between human assets (human capital) and physicalassets (machines, buildings, land, patents,...) In this theory, the firm = set of jointly-owned physical assets. Contracts are incomplete: in at least some states of the world,

future uses of physical assets are left unspecified. Ownership of physical assets matters because, in states where

contract is silent, owner of assets has residual control rights overhow the assets are used. Residual control rights influence ex postbargaining power, hence ex post distribution of surplus.Anticipated ex post distribution of surplus influences ex anteincentives for investments in specific human capital. The theory predicts that the ownership of physical assets will be

determined so as to maximize ex ante expected surplus from thetransactions.

The property rights theory of the firmAn example (1)Aghion-Holden (2011): Transaction btw. seller (S) of an intermediate good(widget) and buyer (B), who uses widget to produce a final good.

S can make a privately costly investment (cost=5) in the widgetmachine which reduces his cost of producing the widget from 16 to 10. B can make a privately costly quality investment (cost=5) in the

final-good machine which raises his sales revenue from 32 to 40. Only S can make cost-reduction investment, and only B can make

quality-enhancement investment. S (B) has no alternative purchaser (supplier) of the widget. S and B can both observe whether or not the other has invested, but a

court cannot verify these investments. Hence S and B cannot write acontract making Bs payment to S contingent on the investmentchoices: incomplete contract assumption. Therefore, the price will be determined by ex post bargaining, after the

investment decisions.

Socially efficient outcome: S and B both invest, and widget is sold by Sto B. First-best social surplus= 40 10 5 5 = 20.

The property rights theory of the firmAn example (2) Non-integration: S owns widget machine and B owns final-good machine Ex post (after the investment decisions), S and B bargain over the price.

Assume price determined by Nash Bargaining Solution S and B split expost surplus from trade 50:50.

B anticipates that if he invests (cost=5), surplus rises by 8 but his sharerises by only 12 (8), so B will choose not to invest. Similarly, investment by Swould cost 5 but raise Ss share by only 12 (6), so S, too, will not invest. Social surplus under non-integration = 32 16 = 16.

Forward integration: S owns both machines Ex post, S no longer needs to reach agreement with B: S can operate both

machines and capture the whole ex post surplus. S therefore chooses to invest, since cost = 5 < 6 = Ss gain. B chooses not to invest, since he captures none of the increase in surplus. Social surplus under forward integration = 32 10 5 = 17.

Backward integration: B owns both machines Ex post, B no longer needs to reach agreement with S: B can operate both

machines and capture the whole ex post surplus. B therefore chooses to invest, since cost = 5 < 8 = Bs gain. S chooses not to invest, since he captures none of the increase in surplus. Social surplus under backward integration = 40 16 5 = 19.

The property rights theory of the firmAn example (3)

Conclusion from the example: None of the three ownershipstructures achieves the first-best surplus, but backward integrationis best here.

Key messages:

1. When contracts are incomplete, asset ownership mattersbecause it affects ex ante inefficiencies from underinvestmentin specific assets.

2. Residual rights of control over assets should be allocated tothe party whose marginal investment is more productive.

The property rights theory of the firmA model (1)Manager 1 uses asset a1 to produce final good with an input (widget)produced by manager 2 with asset a2. Timeline of the game:

At t = 0, managers can buy and sell the two assets. At t = 1, manager i invests ei , at cost c(ei ) = 12e2i , in human capital

specific to ai . At t = 2, bargaining determines whether or not widget is produced and

exchanged, and its price.

Assumptions:

Incomplete contract: contract written at t = 0 cannot specifyinvestments at t = 1 or decisions at t = 2. Ownership of asset(s)confers control rights over their use at t = 2, which determinedisagreement payoffs for period-2 bargaining. Managers have symmetric information throughout the game, so at t = 2, both can observe (e1, e2) chosen at t = 1. Period-2 bargaining

is efficient, with outcome described by the Nash Bargaining Soln.; at t = 0, trading of assets results in ownership structure that maximizes

ex ante expected surplus.

The property rights theory of the firmA model (2)

Denote by Ai {a1, a2} the set of assets owned by manager i Ownership structures: no integration: manager i owns ai

A1 = {a1},A2 = {a2} type-1 integration: manager 1 owns both assets

A1 = {a1, a2},A2 = {} type-2 integration: manager 2 owns both assets

A1 = {},A2 = {a1, a2} Ownership of assets affects who has control rights over their

use at t = 2, but does not affect who can invest in assets att = 1: only manager i can invest in ai .

Asset ownership does not affect managers information orpreferences.

The property rights theory of the firmA model (3)

At t = 2, transacting yields revenuepi (e1, e2) = pi1 e1 + pi2 e2 First-best investments (benchmark if complete contract were

feasible) would solve:

maxe1,e2

pi (e1, e2) 12e21

1

2e22 pii = eFBi for i = 1, 2

Disagreement payoffs at t = 2: Di (ei ,Ai ) = di (Ai ) ei di (Ai ) measures the marginal effect of i s investment on his

disagreement payoff and depends on Ai i s disagreement payoff is not affected by ej

Assume pii di ({a1, a2}) di ({ai}) di ({}), for i = 1, 2. Hence, for all ownership structures,pi (e1, e2) D1 (e1,A1) + D2 (e2,A2) = ex post, alwaysefficient for widget to be traded.

Solving the modelAt t = 2, investments (e1, e2) are observable. Managers bargain expost under symmetric information (Nash Bargaining Solution) =widget is traded, and price p paid by manager 1 solves

maxp

(pi(e1, e2) p D1(e1,A1)) (p D2(e2,A2)) .

Hence bargaining yields a payoff, Si , for manager i at t = 2 of

Si = Di (ei ,Ai ) +1

2[pi (e1, e2) D1 (e1,A1) D2 (e2,A2)] .

At t = 1, given ownership structure (A1,A2), manager i solves

maxei

Si (e1, e2;A1,A2) 12e2i =

1

2[pii + di (Ai )] = e

eqmi

Since first-best efforts satisfy pii = eFBi , we conclude that for any

ownership structure, eqm. investment levels of bothmanagers are inefficiently low: eeqmi eFBi , i = 1, 2.

Solving the model

1

2[pi1 + d1 (A1)] = e

SB1 and

1

2[pi2 + d2 (A2)] = e

SB2

Effects of ownership structure:

Ownership of assets increases incentives: Sincedi ({a1, a2}) di ({ai}) di ({}), it follows that

eeqmi ({a1, a2}) eeqmi ({ai}) eeqmi ({}) . Therefore, changes in ownership structure have both

benefits and costs: type-i integration increases manageri s incentives at the expense of manager js.

Choice of ownership structure

1

2[pi1 + d1 (A1)] = e

SB1 and

1

2[pi2 + d2 (A2)] = e

SB2

What can be said about the optimal ownership structure? assets are independent if for both managers, di ({a1, a2}) = di ({ai})

= no-integration (NI) is optimal assets are complementary for manager 1 if d1 ({a1}) = d1 ({})

= type-2 integration (2I) dominates no-integration manager 2s human capital is essential if d1 ({a1, a2}) = d1 ()

= type-2 integration (2I) is optimal

In our earlier example, the assets are complementary for both B and S:neither has a positive outside option unless he owns both machines.

0 = di ({}) = di ({ai}) < di ({a1, a2}) = pii Therefore, both B-integration and S-integration dominate no-integration. B-integration gives B but not S incentive to invest; S-integration does the

reverse. The optimal type of integration is the one where the investment made has a

bigger marginal effect on the disagreement payoff di ({a1, a2}) ei , which inthe example equals pii ei (or pi(e1, e2)).

Choice of ownership structure

The property rights theory of the firm: A critical view Main empirical prediction: transferring ownership raises incentives of

new owner and lowers incentives of previous owner.

More formally, marginal effects of investments on disagreement payoffsD1 and D2 determine ex ante incentives and hence optimal ownershipstructure.

But how to measure these marginal effects? If each partys effort affects outside options of both parties, even harder

to make predictions. Not much evidence, but see Whinston (2003).

The theory better explains small entrepreneurs than large firms. How to explain owners who dont manage and managers who dont

own?

Broader message of the property rights theory: When contracts areincomplete, it is important to understand how decision rights areallocated.

This message has inspired applications of models of incompletecontracts to questions in organizational economics, corporate finance,macro, public economics, and international trade.

The incentive system theory of the firmOverviewHolmstrom and Milgrom (1991, 1994), Holmstrom (1999)

Firms and markets are different approaches to resolving multi-taskincentive problems. Ownership of an asset used in a transaction confers on the owner the

right to receive the return stream from that asset. Incomplete contract assumption: Verifiable measures of changes in

the value of an asset (esp. an intangible asset) may be too costly toproduce, so contracts basing payments on changes in asset valuesmay be infeasible. Assigning ownership of an asset to an agent can provide him with

strong incentives to maintain the value of the asset. But these incentives may divert his efforts away from other activities,

e.g, producing output, unless he is also given strong output-basedincentives. The theory can explain

i) why explicit output-based incentives are weaker for employees (whodont own the assets used) than for independent contractors (who do);

ii) why agents whose effort in producing output can be measured moreaccurately are more likely to be independent contractors.

The incentive system theory of the firm: A model (1)

An agent (A) performs a set of tasks for a principal (P), usinga transferable asset. If P owns the asset, A is an employee ofP; if A owns the asset, A is an independent contractor.Examples:

P=producer; A=retailer P=fast-food restaurant; A=franchisee or employee P=trucking company; A=truck driver Asset can be physical (e.g. machine, vehicle, property) or

intangible (e.g. reputation for quality or service)

Extend the earlier multi-task principal-agent model to analyze:

How do optimal compensation contracts differ for employeesand independent contractors?

Under what conditions is it optimal for A to be an employeeand under what conditions an independent contractor?


Agent privately chooses efforts (e1, e2) at cost C (e1 + e2) = 0if e1 + e2 e and C (e1 + e2) > 0 if e1 + e2 > e. e1: effort on production/sales task; e2: effort to develop value

of asset

Socially efficient efforts maximize B(e1) +V (e2)C (e1 + e2) B(e1) is expected revenue from production/sales, and V (e2) is

expected change in asset value. B(0) = V (0) = 0.

Actual change in asset value accrues to whoever owns assetand equals V (e2) + , where N(0,Var()) . Verifiable performance measure for production/sales task

= z1 = e1 + x1, where x1 N(0,Var(x1)). For now, no verifiable performance measure for

asset-maintenance task.

Linear compensation contract for agent: w = + 1z1.


Recall C (e1 + e2) = 0 if e1 + e2 e and C (e1 + e2) > 0 ife1 + e2 > e.

Socially efficient efforts maximize social surplus (SS)= B(e1) + V (e2) C (e1 + e2).

Define pi1 maxe1 B(e1) C (e1)maxed SS when e2 is setat 0.

Define pi2 maxe2 V (e2) C (e2)maxed SS when e1 is setat 0.

Define pi12 maxe1 B(e1) + V (e e1)maxed SS whene1 + e2 = e.

If pi12 > max{pi1, pi2}, there is a strong social preference forbalanced efforts:

SS from low total effort e1 + e2 = e, optimally allocated acrosstasks, exceeds max. surplus if effort is devoted to only 1 task.

The incentive system theory of the firm: A model (4)Claim: If pi12 > max{pi1, pi2}, then

i) if A is an employee, the optimal contract pays a fixed wage: 1 = 0(low-powered incentives are optimal for employees);

ii) if it is optimal for A to be an independent contractor, then the optimalcontract sets 1 > 0 (high-powered incentives are optimal forindependent contractors).

Proof: i) If 1 > 0 for employee, then A chooses e2 = 0 and e1 such that1 = C

(e1). Total certainty equivalent (TCE) equals

B(e1) C (e1) 12rVar(x1)(1)

2 < pi1 < pi12.

If 1 = 0 for employee, then A is willing to allocate total effort e in sociallyoptimal way, so TCE = pi12. Thus, optimal 1 for an employee is 0.

ii) If 1 = 0, then an A who is an indep. contractor sets e1 = 0, and TCE< pi2 < pi12 = TCE when A is an employee and 1 = 0. Hence, if it isoptimal for A to be an indep. contractor, optimal 1 > 0.

The incentive system theory of the firm: A model (5)Claim: If pi12 > max{pi1, pi2}, then

i) depending on the values of (r ,Var(),Var(x1)), either employment orindependent contracting can be optimal;

ii) lowering any of (r ,Var(),Var(x1)) makes independent contractingmore likely to be optimal.

Proof: i) Suppose first Var(x1) = Var() = 0. Then first-best isachievable with indep. contracting and 1 = B

(eFB1 ). But first-best is notachievable with A an employee, since either e2 = 0 (when 1 > 0) or totaleffort is too low (when 1 = 0). Hence indep. contracting is optimal. Butif rVar() gets large, employment becomes optimal.

ii) TCE under optimal employment (1 = 0) is indep. of rVar(x1) andrVar(), while TCE under indep. contracting decreases in these terms. Now suppose new technology generates a noisy but verifiable performancemeasure for task 2: z2 = e2 + x2, where x2 N(0,Var(x2)). Contract can now set w = + 1z1 + 2z2. Prediction: As monitoring of asset-maintenance effort e2 improves (asVar(x2) ), independent contracting is less likely to be optimal.

The incentive system theory: Empirical evidenceIncentive system theory of the firm can help explain empirical findings:

Anderson and Schmittlein (1984) studied employment status andcompensation of sales agents in electronic components industry.

Both employment and independent contracting were common. Difficulty of measuring sales of individual agents (because of

team-selling or costly record-keeping) was best empirical predictor oflikelihood of sales agents being employees. In line with prediction that Var(z1) = employment more likely.

Baker and Hubbard (2004) studied trucking industry, focusing on drivervs. company ownership of trucks.

On long-haul routes, more scope for drivers to shirk onasset-maintenance effort, by driving at highly variable speeds. Empirical findings:

i) Driver ownership is greater for long hauls.ii) Introduction of on-board computers (monitoring speed of driving, etc.)

reduces driver ownership, esp. for long hauls.

Conclusion (1)All of the theories argue that the boundaries of firms matter becausecontracts are necessarily incomplete.

Transaction cost economics: Ownership affects ex post decision governance. Integration reduces costly ex post haggling but entails bureaucratic

costs. Gibbons (2005) argues that there are actually two different theories

here, one focusing on haggling (rent seeking) and one focusing onadapting to uncertainty.

Property rights: Ownership of an asset = control rights over that asset. Ownership affects ex ante incentives for investment.

Incentive systems: Ownership of an asset = receive return stream from that asset. Ownership affects incentives for investments in assets and, indirectly,

for other activities. Ownership is one of many instruments used by firms to manage

multi-task incentive problems.

Conclusion (2)

Other theories (see Cremer (2010)) have provided different answersto the question: What changes when the boundaries of firmschange? For example, a firm that purchases its supplier might

obtain better information about its suppliers costsRiordan(1990) and Cremer (1995) show that this can be adouble-edged sword, lowering the buyers commitment power;

obtain authority over its suppliers personnelMeyer,Milgrom, and Roberts (1992) show that this, too, can have acost as well as a benefit, giving these personnel incentives forinfluence activities (i.e. rent-seeking).

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Theories of Firm