Breach of contract in competitive markets
We first examine the effect of the possibility of breaches of contract on market outcomes, assuming that there are no damage measures for breach of contract in place. Consider a competitive market for a good. The marginal cost of production is c > 0. The marginal benefits of consumption are u'(Q ). The efficient outcome in this market is at Q*, where marginal benefit equals marginal cost:
The competitive equilibrium market price is P * = c.
Breaches of contract by buyers
Now consider the same market, but suppose that contractual agreements are not perfectly enforced. Goods are exchanged by means of a contractual arrangement whereby sellers and buyers agree on a price P, sellers then deliver the good, and then after receiving the good, buyers pay the agreed price. However, suppose for goods that are sold, sellers expect that a fraction p of buyers will breach their contractual obligations and refuse to pay the agreed price (alternatively, sellers expect that each buyer will breach the contract and only pay (1 - p)P instead of the agreed price). This means that if the agreed price is P°, each seller's expected marginal revenue is:
where P° is the equilibrium market price in the absence of perfectly enforced contracts. Sellers will produce up until the point where expected marginal revenue equals marginal cost, so in the competitive equilibrium, we have:
In this equilibrium, marginal costs are "grossed up" by (1 minus) the probability that buyers will actually pay the full price, and these grossed up costs are incorporated into the equilibrium market price.
To compute the ex ante welfare loss from imperfectly enforced contracts, note that some buyers in this market breach their contract and do not pay the full market price (that is, a fraction p of them) but still receive the good. Therefore, in this equilibrium, the net benefits to buyers are:
On the other hand, seller profits are:
Hence, total welfare is:
Since total welfare in the presence of fully enforced contractual agreements is W * = u(Q *) - cQ *, the welfare loss from imperfectly enforced contracts is:
This is the shaded area in Figure 8.2.1. Note that in this example, where the long-run market supply curve is perfectly elastic, the incidence of the
Figure 8.2.1 Competitive equilibrium in a market with imperfectly enforced contracts
costs of imperfectly enforced contracts falls entirely on buyers. We can also compute the welfare gain from a marginal improvement in contract enforcement, by computing dW°/dp. We have:
Since the triangle welfare loss is greater if the demand curve is more elastic, this also means that the welfare gain from improvements in contract enforcement arrangements is higher if the demand curve is more elastic.