Question 1. Suppose a firm is owned by an entrepreneur who knows whether the firm's prospects are good or bad. Outsiders do not know the firm's prospects. The entrepreneur has to raise funds from outsiders to finance the firm's investment. The financial market is competitive, the entrepreneur and investors are risk neutral, and the risk-free interest rate is 0. The entrepreneur's reservation is $110. The firm has two projects. The first requires an investment of $120 and the second requires an investment of $240. Each investment generates a combination of a risk-free cash flow of $100 and an additional risky cash flow of $400. The probability of the risky cash flow based on the investment in the project and the firm's type are as follows: Risky CF 400 Investment of $120 Good Bad 0.6 0.4 Investment of $240 Good Bad 0.8 0.5 Restrict attention to limited liability financing contracts where each contract pays out non-negative fractions of the risk free cash flow of $100 and the risky $400 cash flow. For example, a feasible contract will be of the from 0.4 of the risk free cash flow and 0.2 of the risky cash flow. a. Can the entrepreneur signal the firm's type if he invests $120 regardless of the firm's type? b. What is the optimal pair of contracts that allows the entrepreneur to signal the firm's type if the firm's investment can vary with its type? c. Suppose that the outsiders believe that the firm is type G with probability 95%. Is it optimal for the entrepreneur to signal the firm's type? Question 1. Suppose a firm is owned by an entrepreneur who knows whether the firm's prospects are good or bad. Outsiders do not know the firm's prospects. The entrepreneur has to raise funds from outsiders to finance the firm's investment. The financial market is competitive, the entrepreneur and investors are risk neutral, and the risk-free interest rate is 0. The entrepreneur's reservation is $110. The firm has two projects. The first requires an investment of $120 and the second requires an investment of $240. Each investment generates a combination of a risk-free cash flow of $100 and an additional risky cash flow of $400. The probability of the risky cash flow based on the investment in the project and the firm's type are as follows: Risky CF 400 Investment of $120 Good Bad 0.6 0.4 Investment of $240 Good Bad 0.8 0.5 Restrict attention to limited liability financing contracts where each contract pays out non-negative fractions of the risk free cash flow of $100 and the risky $400 cash flow. For example, a feasible contract will be of the from 0.4 of the risk free cash flow and 0.2 of the risky cash flow. a. Can the entrepreneur signal the firm's type if he invests $120 regardless of the firm's type? b. What is the optimal pair of contracts that allows the entrepreneur to signal the firm's type if the firm's investment can vary with its type? c. Suppose that the outsiders believe that the firm is type G with probability 95%. Is it optimal for the entrepreneur to signal the firm's type
