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In a simple model of borrowing and lending with asymmetric information we show that the optimal, incentive-compatible debt contract is the standard debt contract. The second-best level of investment never exceeds the first-best and is strictly less when there is a positive probability of costly bankruptcy. We also compare the second-best with the results of interest-rate-taking behaviour and consider the effects of risk aversion. Finally we provide conditions under which increasing the borrower's initial net wealth must reduce total investment in the venture.

Empirical evidence suggests that banking panics are related to the business cycle and are not simply the result of "sunspots." Panics occur when depositors perceive that the returns on bank assets are going to be unusually low. We develop a simple model of this. In this setting, bank runs can be first-best efficient: they allow efficient risk sharing between early and late withdrawing depositors and they allow banks to hold efficient portfolios. However, if costly runs or markets for risky assets are introduced, central bank intervention of the right kind can lead to a Pareto improvement in welfare.FROM THE EARLIEST TIMES, banks have been plagued by the problem of bank runs in which many or all of the bank's depositors attempt to withdraw their funds simultaneously. Because banks issue liquid liabilities in the form of deposit contracts, but invest in illiquid assets in the form of loans, they are vulnerable to runs that can lead to closure and liquidation. A financial crisis or banking panic occurs when depositors at many or all of the banks in a region or a country attempt to withdraw their funds simultaneously.Prior to the twentieth century, banking panics occurred frequently in Europe and the United States. Panics were generally regarded as a bad thing and the development of central banks to eliminate panics and ensure financial stability has been an important feature of the history of financial systems. It has been a long and involved process. The first central bank, the Bank of Sweden, was established more than 300 years ago. The Bank of England played an especially important role in the development of effective stabilization policies in the eighteenth and nineteenth centuries. By the end of the nineteenth century, banking panics had been eliminated in Europe.

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By using graphical representations of simple portfolio choice problems, we generate a very rich dataset to study behavior under uncertainty at the level of the individual subject. We test the data for consistency with the maximization hypothesis, and we estimate preferences using a two-parameter utility function based on Faruk Gul (1991). This specification provides a good interpretation of the data at the individual level and can account for the highly heterogeneous behaviors observed in the laboratory. The parameter estimates jointly describe attitudes toward risk and allow us to characterize the distribution of risk preferences in the population. (JEL D11, D14, D81, G11)