## Saturday, 1 August 2009

### Just for fun: the theory of the firm

In a posting over at TVHE Matt Nolan discussed the The basic frame of a firm: Cournot. In the comments to this post I said,
[...] that the standard perfectly competitive, oligopoly and monopoly models don’t have firms in them, they are more models of industries rather than models of firms. This follows from Coase 1937. As Martins Rickets put it “If market transactions were costless there would be no rationale for firms”. In other words, in a model with zero transaction costs, which the standard models are, firms need not exist. Production takes place over the market since it is costless to organise it that way.
Thus for a theory of the firm to make sense in terms of a theory of a definite organisational entity, you need to deal with a positive transaction cost world and move away from the first and second year textbook discussion of the firm. There is now a well known literature which does this, most of which originates from Coase (1937). So for fun I thought I would discuss some new ideas to do with the firm, in particular those ideas based around recent work by Oliver Hart concerning 'reference points' and the theory of the firm. This work by Hart is in turn based on joint work between Hart and John Moore.

One obvious question for the theory of the firm is where is the boundary between markets and firms. Or when are transactions carried out via the market (using an independent contractor) or carried out 'in house' (within a firm using an employment contract)? It is this question that the discussion below addresses.

The basic ideas underlying the 'reference point' approach to the firm can be gathered from a simple example based on Hart (2008). Hart assumes that a seller, $S$, can provide a good, costing 10, to a buyer, $B$, who is willing to pay 20. Let us assume that we are talking about a public lecture on some aspect of microeconomics which $B$ is organising and which $B$ wants $S$ to give. A successful lecture is worth 20 to $B$ and it costs 10 for $S$ to give the lecture.

At this stage Hart ignores the fact that $B$ could engage other economists or that $S$ could give lectures elsewhere. While trade could proceed smoothly, it is also possible that it will not. We will assume that $B$ and $S$ each have some discretion over the 'quality' of performance. For example, $S$ could give a witty, lively, entertaining lecture or a very boring one. $B$ on the other hand could treat $S$ well, give her a nice dinner and pay quickly, or treat her badly.

In the language of Hart and Moore (2008) each party, is able to provide basic (perfunctory) or exemplary (consummate) performance. It is further assumed that only the basic (perfunctory) level of performance can be legally enforced: exemplary (consummate) performance is entirely discretionary. It is assumed that each party is more or less indifferent between providing each level of performance - exemplary performance costs only a little more than basic or may even be slightly more pleasurable - and will provide exemplary performance if they feel they are being 'well treated' but not if they feel they are been 'badly treated'. Cutting back on exemplary performance is called 'shading'. Such behaviour cannot be observed or punished by an outsider. Shading hurts the other party.

Hart emphasises that each party will feel 'well treated' if they receive what they think they are entitled to; that a contract between the parties is a reference point for perceived entitlements; and that should there be no reference point, then entitlements can diverge, wildly in some cases.

To return to the example above. First, we will add a time line, see Figure 1 below. The time line tells us that $B$ and $S$ will write a contract some months before the lecture is given, at date 0, rather than at the last minute, date 1. One reason for this is that each party has more options earlier on. In fact it is assumed that there is a competitive market for sellers, at date 0.

Figure 1

Date 0..........................................................................Date 1
|----------------------------------------------------------------------------------|

Parties meet.................................................................Lecture given

Assume, further, that although $B$ and $S$ sign a contract at date 0, they leave the question of how much $B$ will pay $S$ open until the night before the lecture, date 1. This may seem a bad idea, and later it will be shown that it is. If no price is specified, then any $p$ between 10 and 20 is possible. What might each party feel entitled to?

Hart and Moore (2008) take the view that entitlements can diverge. $S$ may feel that the whole success of the talk will be due to her giving it and thus she feels entitled to $p=20$. On the other hand $B$ may have a somewhat different view of $S$'s abilities and likely contribution and thus feel that $S$ is worth much less, say,$p=10$.

Even though they disagree as to what $p$ should be, they are rational enough to arrive at a compromise, say $p=15$. According to Hart and Moore (2008) each party will feel short-changed and therefore aggrieved. Since $B$ is aggrieved by 5, (15-10), $B$ shades to the point where $S$'s payoff falls by $5\theta$, where $\theta$ is the constant of proportionality. And since$S$ is also aggrieved by 5, (20-15), $S$ shades to the point where the payoff for $B$ falls by $5\theta$.

The end result of this is that if $S$ and $B$ leave the determination of the price until the night before the lecture, there will be a deadweight loss of $10\theta$ due to the shading activities of each party. This reduces the value of the relationship between $S$ and $B$ from $10$ to $10-10\theta=10(1-\theta)$.

Next Hart asks the question: Can anything be done to avoid this deadweight loss? His answer is yes. But first note an answer that doesn't do the job. Ex post Coasian bargaining at date 1 doesn't work. The reason is that shading is not contractible and thus an agreement not to shade is not enforceable. Or to put this another way, if $B$ offers to pay $S$ more to reduce her shading, say $B$ offers to pay $p=16$ to $S$ rather than $15$, then this will indeed reduce $S$'s shading, from $5\theta$ to $4\theta$, since $S$ will now feel less aggrieved, but it will also increase $B$'s shading from $5\theta$ to $6\theta$, since he now feels more aggrieved. Total deadweight loss does not change, it remains at $10\theta$. However there is a simple solution; the parties just put the price in the contract at date 0. Since it has been assumed that the market for lectures is competitive at date 0, $B$ will be able to hire $S$ for a price $p=10$. With this price specified in the contract, there is nothing for $B$ and $S$ to disagree about at date 1. The fact that $B$ and $S$ may disagree about the contribution that $S$ makes to the success of the lecture not longer matters. $B$ and $S$ have agreed that $B$ will pay $S$ 10, and neither $B$ nor $S$ will be disappointed or aggrieved when that happens. Importantly, agreeing in advance, at date 0, to a payment of 10 eliminates ex post argument and aggrievement, and thus both parties will be willing to provide exemplary performance. Here we have the first best being achieved and zero deadweight losses as a result. This does raise an obvious question: What changes between dates 0 and 1? Why does a date 0 contract that fixes $p$ avoid aggrievement, whereas a date 1 contract that fixes $p$ does not? The crucial point here is the role of the ex ante market at date 0. This market gives an objective measure of what $B$ and $S$ bring to the relationship. Given the assumption of a competitive date 0 market, there are many sellers willing to supply at $p=10$ and thus $S$ accepts that she cannot expect to receive more than 10, while $B$ understands that he can't expect to pay less, as no one would be willing to give the lecture for less. Thus, neither party is aggrieved by $p=10$. This gives us a model of the contractual relationship between $B$ and $S$, but, as Hart explains, we need one further ingredient to create a theory of the firm.

Now let us add a little more realism by assuming that not all of the details of the lecture can be anticipated at date 0. To keep things simple we will assume that two different lectures can be given with values and costs as given in Case 2.
Case 2 gives the payoffs and costs of each lecture. Lecture 1 has a value of 20, costs of 10 giving a surplus of 10. Lecture 2 has a value of 14, costs of 8 giving a surplus of 6.
So lecture 1 - say, a theory of the firm lecture - is the same as above, with a value of 20 and costs of 10. Lecture 2 - say, a microeconometrics lecture - yields value of 14 and costs of 8. Note that lecture 1 is more efficient in that it generates a greater surplus. Assume that the lectures can not be specified in the date 0 contract, since thinking about econometrics is sooooo boring that no one can stay awake long enough to write the contract! At date 1, however, the choice between them becomes clear.

Now we have to compare two organisational forms: an employment contract and an independent contractor. First, let $B$ and $S$ fix the price of the good at date 0, at say 10, and let $B$ and $S$ agree at date 0 that $S$ will be an independent contractor. This is, in other words, a market exchange between two separate economics agents. Independent contractor means here that $S$ gets to pick which lecture to give. That is $S$ has the residual control rights.

Hart then asks, What will $S$ do? Given that the price has been fixed by the date 0 contract, $S$ will pick lecture 2, since it is cheaper for her. But note, this is inefficient. $B$ will be aggrieved because $S$ didn't choose lecture 1, which $B$ feels entitled to; $B$ is short-changed by 6 (20-14), and he will therefore shade enough to reduce $S$'s payoff by $6\theta$. Total surplus in this case will be $6-6\theta$.

The second organisation form to be considered is an employment contract. $B$ and $S$ agree at date 0 that $S$ is an employee of $B$. This we take to mean that $S$ will work for $B$ at a fixed wage, again assume 10. $B$, being the employer, has the right to decide on which lecture is to be given. As the wage is fixed $B$ will choose lecture 1, as this gives him the greater value. This is efficient. $S$ will be aggrieved since lecture 2 wan't chosen, but $S$'s aggrievement is only 2. This induces $S$ to shape by enough to reduce $B$'s payoff by $2\theta$. Total surplus is therefore $10-2\theta$.

Under the conditions specified, the employment contract is better. This is true for two, related, reasons. First, the lecture matters more to $B$ than to $S$. $B$ will lose $20-14=6$ if his favoured lecture is not chosen while $S$ only loses $10-8=2$ if her favoured lecture is not chosen. This means it is efficient for $B$ to chose the lecture. Second, and related, $S$'s aggrievement is low since she doesn't care very much.

Hart now changes the numbers in Case 2 to create Case 3.
Case 3, again, gives the payoffs and costs of each lecture. Lecture 1 has a value of 20, costs of 10 giving a surplus of 10. Lecture 2 has a value of 14, costs of 2 giving a surplus of 12.
Keep lecture 1 as it is, but change lecture 2 so while it still yields 14, it now costs only 2. Lecture 2 is now the more efficient (12 v's 10). Under employment, lecture 1 will be chosen, yielding a total surplus of $10-8\theta$. If $S$ is an independent contractor, lecture 2 will be chosen resulting in a total surplus of $12-6\theta$.

What this suggests is that employment is good if the lecture matters more to $B$ than to $S$, while independent contracting is good if the lecture matters more to $S$ than to $B$.

Hart goes on to say
One point worth emphasizing is that in neither of the above examples is the following contract optimal: to leave the choice of price and method until date 1, i.e. to rely on unconstrained Coasian bargaining. This would always yield the efficient method, but the aggrievement costs would be high. In [Case 2] the parties would agree on method 1; however, since there are 10 dollars of surplus to argue over, shading costs equal $10\theta$: net surplus $= 10(1-\theta)$, which is less than that obtained under the employment contract. In [Case 3] there are 12 dollars of surplus to argue over and net surplus $= 12(1-\theta)$, which is less than that obtained under independent contracting. (Hart 2008: 409.)
Clearly the examples above are toy ones, but Hart argues they contain the basic ingredients of a theory of the firm in that they consider the choice between carrying out a transaction in the market, using an independent contractor, and 'inside the firm', via an employment contract. This was the tradeoff at the heart of Coase (1937).

References:
• Coase, Ronald Harry (1937). 'The Nature of the Firm', Economica, n.s. 4 no. 16 November: 386-405.
• Hart, Oliver D. (2008). 'Economica Coase Lecture: Reference Points and the Theory of the Firm', Economica, 75(299) August: 404-11.
• Hart, Oliver D. and John Moore (2008). 'Contracts as Reference Points', Quarterly Journal of Economics, 123(1) February: 1-48.