14.2 Moral Hazard in the Credit Market

We now analyze a credit market characterized by moral hazard. Here, asymmetric information no longer concerns the nature of the project, but the entrepreneur’s behavior after receiving financing: the bank cannot observe whether the entrepreneur exerts effort or not, and this choice affects the project’s probability of success.

As in the previous section, we assume that the project costs $60$ and yields $100$ in case of success. If the entrepreneur exerts effort, the probability of success is 75%, but effort is costly: the entrepreneur incurs a disutility of 10. If instead they do not exert effort, the probability of success is only 50%, with zero disutility.

We assume, as before, that both parties are risk-neutral, that the entrepreneur is protected by limited liability, and that all bargaining power lies with the entrepreneur: banks earn zero expected profit in equilibrium.

Unlike the previous section, we now assume that the entrepreneur has own capital equal to $A<60$, and must therefore borrow only $60-A$. As we shall see, it is this variable (which we had assumed to be zero in the previous section, for simplicity) that determines whether the market succeeds in allocating credit efficiently.

Observable Effort: Efficient Allocation of Credit

Let us start by noting that it is socially efficient to finance an entrepreneur who exerts effort. In this case, the expected value of the project is $0.75\times 100=75$, while the total cost is $60+10=70$: the social surplus is thus positive (equal to $5$). If the entrepreneur does not exert effort, the expected value is only $0.5\times 100=50$, which is lower than the cost, which in this case is $60$. Financing an entrepreneur who does not exert effort is therefore socially inefficient.

If effort were observable and could be the subject of legally binding contracts, bargaining between the parties would lead to the socially efficient outcome. If the bank, rather than the entrepreneur, held all the bargaining power, it would propose a similar contract, but with repayment equal to $100-(A+10)/0.75$. The bank would thus capture the entire surplus: its profit would be \(0.75\times\Big(100-\frac{A+10}{0.75}\Big)-(60-A)=5.\) The entrepreneur would offer the bank a financing contract in which they commit to (i) exerting effort and (ii) repaying $(60-A)/0.75$ to the bank in case of project success. The bank would accept, because the expected repayment would exactly cover the loan:

\(\begin{gathered} 0.75\times\frac{60-A}{0.75} = (60-A) \end{gathered}\)

The entrepreneur would capture the entire surplus, obtaining a payoff $5$ euros greater than in their initial situation:

\(\begin{gathered} 0.75\times \Big(100 - \frac{60-A}{0.75}\Big) - 10 = A + 5 > A. \end{gathered}\)

Unobservable Effort: Credit Rationing

Let us now turn to the case in which effort is unobservable and therefore cannot be included in the contract. As in the previous section, a financing contract is defined by the amount $R$ that the entrepreneur commits to repay to the bank in case of success.

First of all, observe that the bank and the entrepreneur cannot find a mutually beneficial contract (and therefore will never both sign it) if the contract does not provide the entrepreneur with an incentive to exert effort. Indeed, if the entrepreneur does not exert effort, the total surplus is negative: $0.5\times 100-60<0$. This means that, for any value of $R$, we have:

\(\begin{gathered} \big[0.5\times R - (60-A)\big] + \big[0.5\times(100-R) - A\big] < 0 \end{gathered}\)

Therefore, either the bank expects a negative profit, or the entrepreneur prefers not to be financed and to keep their $A$ euros — or both.

Assuming that the contract induces the entrepreneur to exert effort, it will be acceptable for the bank only if the bank’s expected profit is at least zero, i.e. $0.75\times R \geq 60-A$, or:

\(\begin{gathered} R \geq \frac{60-A}{0.75} \end{gathered}\)

But under what conditions does the contract induce the entrepreneur to exert effort? For this to happen, the entrepreneur’s expected payoff from exerting effort must be at least equal to the expected payoff from not exerting effort. That is, the following incentive compatibility condition must hold:

\(\begin{gathered} 0.75\times(100-R) - 10 \geq 0.5\times(100-R) \end{gathered}\)

which simplifies to:

\(\begin{gathered} R \leq 60 \end{gathered}\)

In other words, if the entrepreneur knows they will retain less than $40$ of the $100$ euros obtained in case of success, they will not exert effort. For both conditions $R\geq (60-A)/0.75$ and $R\leq 60$ to hold, it must be that $60\geq(60-A)/0.75$, or equivalently $A\geq 15$.

In conclusion, the bank finances the project if and only if the entrepreneur has sufficiently high own capital: $A\geq 15$. Otherwise, there is no contract compatible with the incentive to exert effort and at the same time sustainable for the bank: credit rationing arises. The project is efficient when carried out with effort, but unless the entrepreneur contributes enough of their own capital, the unobservability of their actions prevents the market from allocating credit efficiently. The excess demand for credit is not absorbed by an increase in the “price” of credit, i.e. $R$. Raising the repayment $R$ does not solve the problem, because above 60 the entrepreneur no longer exerts effort, and the project becomes inefficient.