Moral Hazard and Capital Regulation Consider an economy where banks could invest either in a safe project that yields G with probability PG and zero otherwise, or in a high-risk project that yields B with probability PB and zero otherwise. The project has constant returns to scale and satisfies G GG > PBB > 1. To develop project G requires additional export with a unitary cost c. Banks are financed by short-term unsecured deposits with a return rD per unit of deposit. Depositors are risk-neutral and will require an expected return equal to the risk-free rate, which is normalized to zero. We assume the participation constraint for banks is satisfied. Capital is costly because equity holders require an expected return of r > 0. 1. Describe the competitive equilibrium in the absence of bank capital, and determine under what conditions the safe project, G, or the risky one, B, will be implemented. 2. Assume that in the absence of bank capital the only equilibrium obtained is characterized by implementing the B project. Determine the minimum level of capital a bank needs in order to restore the possibility of an equilibrium where the safe project G is preferred by banks. 3. Assume depositors observe banks’ capital. What will be the amount of capital a profit-maximizing bank will choose?
Moral Hazard and Capital Regulation Consider an economy where banks could invest either in a safe project that yields G with probability PG and zero otherwise, or in a high-risk project that yields B with probability PB and zero otherwise. The project has constant returns to scale and satisfies G GG > PBB > 1. To develop project G requires additional export with a unitary cost c. Banks are financed by short-term unsecured deposits with a return rD per unit of deposit. Depositors are risk-neutral and will require an expected return equal to the risk-free rate, which is normalized to zero. We assume the participation constraint for banks is satisfied. Capital is
1. Describe the competitive equilibrium in the absence of bank capital, and determine under what conditions the safe project, G, or the risky one, B, will be implemented.
2. Assume that in the absence of bank capital the only equilibrium obtained is characterized by implementing the B project. Determine the minimum level of capital a bank needs in order to restore the possibility of an equilibrium where the safe project G is preferred by banks.
3. Assume depositors observe banks’ capital. What will be the amount of capital a profit-maximizing bank will choose?
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