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COMPARING FIRMS, CONTRACTS, AND MARKETS

Birger WernerfeltMIT

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Some simple points about the theory of the firm

• Firms are “common”, so the theory should be driven by “common” factors

• It is unlikely that one institution solves two problems (TCE: Ex ante and ex post distortions)

• It is unlikely that two institutions are driven by the same force (PRT: Asset ownership and employment)

• It is a plus if the theory resonates with managers• It should portray one party as giving “orders”

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Combination of old premises gives new insights

• Bargaining costs (Coase, 1937)• Gains from specialization (Adam Smith, 1776) Adapting without losing gains from specialization

• Why Markets, Firms, or Contracts?• When?• Other implications of the theory• Scope of the firm

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About bargaining costs

• Many kinds: Incurred before, during, or after• Have a bad name• Some can be micro-founded: For ex. investment in

information/bargaining power (also rent seeking literature)

• Sub-additive – exhibit economies of scale

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Experiment on bargaining cost

• Bilateral, 30 sequential trades, full information• Offer a price for the current trade or an

average price for rest of them• Small cost of pooling the residual trades:

Domains overlap and all trades have to be executed under a pooling contract.

• Results point to positive, sub-additive bargaining cost

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Gains from many kinds of specialization

• Performing the same service many times (Plumber) – service specialist

• Working for the same business many times (Superintendent) – business specialist

• Doing everything in the same way (Min time or cost, Max durability, appearance, or quality …) - standardization

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Workhorse model: Fixed firm size

• Three periods t = 0, 1, 2. Time preference δ• Services (S, s) and businesses (B, b)• Workers (W, w) and entrepreneurs (E, e)• In every period, each business needs a specific

service and each worker can perform one • For now │B│=│W│=│E│• “Type” of b is εb ~ F(0, σB), type of s is εs ~ G(0, σS)

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Two frictions

Adaptation vs. standardization:-If w performs s for b, the ideal “level” is qw = εb + εs

-However, standardization requires that the level is constant over time. With standardization, second period base costs are c* instead of c. (Assume: Non-standardization is prohibitively costly)Bargaining costs-Positive for bilateral price determination-Sub-additive, taking values between K and K

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Bargaining bins

Players in a bargaining bin may negotiate a single price in every period. The bin is defined by a set of services to which this price applies. For example, among {0, 1}│S│ x {0, 1}│B│ possibilities, it can be “service s’ for any b ”, “service s’ for b’ ”, “any s for b’ ”, or “no services”.

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Strategies

• An entrepreneur selects first and second period bargaining bins as functions of her needs for those periods.

• A worker selects first and second period bargaining bins as functions of his assignment in the immediately prior periods and, in the first period, a level at which to standardize.

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Sequence of events: Period 0

-Each entrepreneur is randomly and permanently matched with a business. Workers and entrepreneurs are randomly matched. All εb, εs are realized.

-Business (entrepreneur) needs for period 0 are realized. Workers learn the εb of the business with which they are matched and the εs of the service it needs.

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Sequence of events: Period 1

-Business needs for period 1 are realized.-Entrepreneurs and workers distribute themselves into bargaining bins and negotiate as indicated.-Entrepreneurs and workers in each bin are randomly matched.-Workers choose the levels qw on which they standardize.-Workers perform the agreed upon services and learn the associated εb, εs.

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Sequence of events: Period 2

-Business needs for period 2 are realized.-Entrepreneurs and workers distribute themselves into bargaining bins and negotiate as indicated.-Entrepreneurs and workers in each bin are randomly matched.-Workers perform the agreed upon services (and learn the associated εb, εs).

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Equilibria

• An equilibrium is a Market if all bargaining bins consist of │E│/ │S│ entrepreneurs needing the same service as well as │E│/ │S│ workers who are service-specialists on it, and the members negotiate a price for that service only

• An equilibrium is Employment if all period 1 bargaining bins consist of one worker and the entrepreneur for whom he worked in period 0, and the members negotiate a single price for all services.

• An equilibrium is Sequential Contracting if all bargaining bins consist of one worker and the entrepreneur for whom he worked in period 0, and the members negotiate a price for the service needed by the entrepreneur in the current period.

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Proposition 1There exists three regions in [σB

2, σS2, K, K, δ] where Markets, Employment, and

Sequential Contracting are weakly more efficient that all other sub-game perfect equilibria.

σB2 – σS

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Sequential Contracting Employment Market δ

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Firms are more likely to be used when frequent adaptation is necessary

A car consists of 36 “systems”Changes in one may require changes in others36x36 matrix of frequency w. w. “coordinated change is needed”

Which systems should be co-produced?Data from 8 cars, very different solutions

This is an enormously big optimization problemFirms do extremely well: 4 of 8 beat 99,995/100,000 random designs, 1 beats all.

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Asset ownership

• An asset is owned by the player whose decisions most influence its depreciation

• 50 carpenters, 41 tools• Employees own 40% of the tools• “A hammer is easily lost or stolen” - employee• “Some projects are more likely to damage a hammer”- boss• Brand specific skills do not matter – no effect

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Growing a business

• Some workers can be both business – and service specialists. Very efficient

• Worthwhile to expand to different but “adjacent” businesses

• This stops when the portfolio becomes too “unfocused”

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PROPOSITION 2

If the εbs are uniformly distributed on [0, 1] and

an entrepreneur can meet all needs from n [0, 1] businesses by hiring n service-specialists as employees,

The optimal scope is an interval and profits are maximized at n = Min{2½(2v – c – c* - K)½, 1}

PS: 2v-c-c*-K is average net profit per worker

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Discussion 1: Summary

• Firms vs Markets vs Contracts: New forces- Advantages of specialization - Frequency of change - Magnitude of demand - Size of firms

• Limits to firm size: Resonate with practitioners-Leverage excess capacity of resources-Focus on what you are good at

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Discussion 2: Turning things upside down

• Asset ownership -I own the assets because I am the boss

• Flatter incentives in firms -boss may ask employees to do other things

• Delegation -it is too costly to agree on everything

• Incomplete contracts - because they can be renegotiated

• More communication inside firms -loss of bargaining power matter less