Let there be 100 investors each of whom has 10 goods to invest. Let there be 100 entrepreneurs each of whom requires 15 goods in order operate their business, a restaurant, say. Each restaurant is successful with probability 0.75 and fails with probability 0.25 . When successful, the restaurant yields a return of 1.6 and should it fail, the restaurant yields a return of zero. Any report of failure is met with the investor (or bank) paying a monitoring cost of 2 goods per failed restaurant.

a. Suppose that each investor allocates their investment equally to 20 entrepreneurs. Calculate the expected payoff to the investor per restaurant in which they invested.

b. Suppose that each investor allocates their entire investment to a single entrepreneur. Calculate t expected payoff to the investor.

c. Calculate the expected rate of return to an investor when they allocate their entire investment to a single entrepreneur.

d. Suppose that there is a bank that accepts deposits from investors and makes loans to entrepreneurs. Calculate the bank's expected payoff on its loan to a given restaurant.

e. Calculate the expected payoff that each depositor receives from the bank.

f. Calculate the (deterministic) rate of return per depositor, r .

g. In what two ways is an investor better off using the bank (intermediated investment) rather than investing directly (unintermediated investment) into one restaurant? Briefly explain.

Thank you so much for helping! Please help with a-g if you can! Very appreciated it your time!