Holmstrom (1999) - The Firm As A Subeconomy

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Reference(s)

  • Holmstrom, Bengt (1999), "The Firm As A Subeconomy", Journal of Law, Economics, and Organization Vol. 15, Issue 1, pp. 74-102. pdf


Abstract

This article explores the economic role of the firm in a market economy. The analysis begins with a discussion and critique of the property rights approach to the theory of the firm as exposited in the recent work by Hart and Moore ('Property Rights and the Nature of the Firm'). It is argued that the Hart-Moore model, taken literally, can only explain why individuals own assets, but not why firms own assets. In particular, the logic of the model suggests that each asset should be free standing in order to provide maximal flexibility for the design of individual incentives. These implications run counter to fact. One of the key features of the modern firm is that it owns essentially all the productive assets that it employs. Employees rarely own any assets; they only contribute human capital. Why is the ownership of assets clustered in firms? This article outlines an answer based on the notion that control over physical assets gives control over contracting rights to those assets. Metaphorically, the firm is viewed as a miniature economy, an 'island' economy, in which asset ownership conveys the CEO the power to define the 'rules of the game', that is, the ability to restructure the incentives of those that accept to do business on (or with) the island. The desire to regulate trade in this fashion stems from contractual externalities characteristic of imperfect information environments. The inability to regulate all trade through a single firm stems from the value of exit rights as an incentive instrument and a tool to discipline the abuse of power.


Free Rider Problem

What follows is essentially a simple elaboration of the basics of the Holmstrom 1982 (Team's Problem) model, but rather than considering the principal as a budget breaker, it will primarily be used to discuss monitoring.

The set up is as follows:

  • There are [math]n\;[/math] workers, each is identical and risk neutral
  • Each worker exerts effort [math]e_i\;[/math], which is unobservable to either a principal or the other workers, at a cost of [math]e_i\;[/math]
  • Ouput is observable to all and is [math]y=y(e_1,\ldots,e_n)\;[/math]
  • There is a sharing contract [math]s_i(y)\;[/math] that denotes the share of output that [math]i\;[/math] gets paid
  • Initially shares are choosen in a partnership without disposal, so that [math]\sum_i s_i(y) = y\;[/math]


The "Team's Problem" is then simply whether [math]s_i\;[/math] can be chosen to induce workers to provide inputs efficiently (i.e. [math]e_i=e^*\; \forall i\;[/math]), that is so that output will maximize total surplus (i.e. [math]y=y(e^*)\;[/math]).


Assuming [math]y\;[/math] is diffentiable (which is not innocuous) and strictly concave (diminising returns to scale, or increasing costs of effort), then [math]e^*\;[/math] is completely characterized by (marginal benefit equals marginal cost):

[math]\frac{\partial \lt math\gt y(e^*)}{\partial e_i} = 1 \quad \forall i=1,\ldots,n\;[/math]


Assuming sharing rules are differentiable (which again may not be innocuous), then a non-cooperative Nash equilbrium must be characterized by (again marginal benefit equals marginal cost):

[math]\frac{ d s_i(y(e^{NE})) }{d y} \frac{\partial y(e^{NE})}{\partial e_i} = 1 \quad \forall i=1,\ldots,n\;[/math]


So for [math]e^{NE}=e^*\;[/math], it must be that:

[math]\frac{ d s_i(y(e^{NE})) }{d y} = 1 \quad \forall i=1,\ldots,n\;[/math]


But from the budget constraint:

[math]\sum_i s_i(y) = y \quad \therefore \sum_i \frac{ d s_i(y(e^{NE})) }{d y} = 1\;[/math]


The above two equations are clearly inconsistent. The problem is simply that in a partnership each worker can not (credibly and under self-imposition) face the full social marginal benefit in his maximization. There are two solutions:

  • The solution presented in Holmstrom 1982 which uses a budget breaker
  • A solution based on Alchian and Demsetz (1972) which uses monitoring


Budget Breakers

The budget breaker solution is loosely to let [math]\sum_i s_i(y) \le y\;[/math], and then create a sharing rule as follows:

[math]s_i(y) = \begin{cases} \frac{y}{n} \quad &\mbox{if } y \ge y(e^*) \\ \frac{y(e^*)}{n} + y - y(e^*) \quad &\mbox{if } y \lt y(e^*) \end{cases} \;[/math]

This requires the team to credible commit to destroying output if the efficient output is not reached (and is not renegotiation proof). In equilibrium this isn't a problem as first best is achieved. And this maybe overcome by including a principle as a residual claimant.


Monitoring

The Alchian and Demsetz (1972) solution is to add a principle who monitors the inputs in some fashion (ignoring the problems of how this person is compensated or incentivized). Again, the monitor may be the residual claimant. A long term reputation game may prevent the monitor from cheating.

The question here is when will an additional performance measure [math]z=z(e_1,\ldots,e_n)\;[/math] add value?

Suppose we rewrite [math]y=e_1 + e_2\;[/math] (with just two team members now), and that [math]c_i(e_i)\;[/math] is now strictly convex (to give an interior solution).


Imagine there is another performance measure:

[math]z = e_1 + \gamma e_2\;[/math]


Restricting to linear sharing rules we have:

[math]s_1(y,z) = \alpha y + \beta z + \delta \;[/math]
[math]s_2(y,z) = (1-\alpha) y - \beta z - \delta \;[/math]


The FOCs for effort (under the sharing contract) are then:

[math]\alpha + \beta = c_1'(e_1)\;[/math]
[math](1-\alpha) - \beta = c_2'(e_2)\;[/math]


We should call the terms on the left the incentive coefficients.

And the workers will respond to changes in \beta:


[math]\frac{d e_1}{d \beta} = \frac{1}{c_1''}\;[/math]
[math]\frac{d e_2}{d \beta} = \frac{- \gamma}{c_2''}\;[/math]


As net output is [math]y-c_1-c_2\;[/math], the effect of a change in [math]\beta\;[/math] is in total:

[math]\left ( (1-\alpha) \frac{1}{c_1''} + \alpha \frac{- \gamma}{c_2''} \right ) d\beta\;[/math]


Thus [math]z\;[/math] is valuable iff the term in the bracket is non-zero. It is easy to show that this is true - in brief:

  • If [math]\gamma = 1\;[/math] then [math]z=y\;[/math] and the term is zero
  • If [math]\gamma \ne 1\;[/math] then [math]z \ne y\;[/math] and the term is non-zero


Thus as long as the measure is not collinear with output, it provides additional info and can be used to strengthen incentives. This extends directly to n workers.

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