Description

Consider the problem of an entrepreneur/borrower with no money and a project requiring L=200 to be carried out. Assume that the borrower cannot use his illiquid assets to finance the project.

The entrepreneur

Once the entrepreneur undertakes the project, she decides either to work hard or to shirk.

If she works hard, then she earns a high return R=$500 with probability p=0.75 and earns nothing with probability (1-p)=0.25.

If she shirks, she earns a high return with probability q=0.25 and earns nothing with probability (1-q)=0.75.

The borrower has ex-post utility u(y)=y-D if she works hard and u(y)=y if she does not work hard, where y is her income (after loan payments) earned from the project. Assume D=125.

The bank:

A bank is willing to finance the project and lend $200 to the borrower. The bank charges the agent an interest rate of i on the loan.

The borrower always repays the loan when she succeeds. If she fails, she is protected by limited liability: she repays nothing to the bank.

Finally, assume that the bank could also purchase $200 in risk-free bonds with a return of r=0.10, and that the financial markets are perfectly competitive.

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