The set-up is very similar to the bilateral model of accidents that we examined in Chapter 5. Efficiency requires that the following two conditions hold:
- • The buyer should invest in reliance up to the point where the marginal benefit of reliance equals the marginal cost; and
- • The seller should invest in precaution up to the point where the marginal benefit of precaution equal the marginal cost.
Therefore, at the optimum (x*,x*) we have: and:
Note first a key point: in most cases it will be efficient for the seller to breach the contract with some positive probability. Note also what the first of these conditions states. Under conditions of complete certainty, the buyer would invest in reliance up the point where the marginal value of reliance, V'(xB), was equal to marginal cost, wB. Call this level x°. Condition (8.10) above states that where there is some possibility that the contract may be breached, the buyer should invest up to the point where the discounted marginal value of reliance equals its marginal cost, where the value is discounted by the probability that the contract will be performed. Thus, we have:
Figure 8.4.1 Efficient reliance by the buyer
and since V() is concave, this implies that x* < x°. The efficient level of reliance investment is less than that which would be chosen under conditions of complete certainty.