3. Consider an economy in which there are 1,000 people who specialize in producing online games. Each online game requires 50 units of the consumption good as an investment. These providers lack the resources to start their project. There are also 1,000 people who are savers and could potentially invest in an online game. Each saver has only 20 goods to invest. For each online game creator, the project either succeeds and returns 75 units of the consumption good next period or the project fails and returns zero units of the consumption good next period. Further, assume the outcome of the project is private information; in other words, the online game creator is the only one who know whether the project succeeds or fails. There does exist a monitoring technology that allows an investor to determine whether the project succeeded or failed. Such monitoring costs 8 units of the consumption good. The probability that a project succeeds is 80 percent and the probability of failure is 20 percent.

a. Suppose an investor can spread their savings across ten different projects. Compute the expected real return for this investor.

b. Suppose the investor puts all their savings into one project. Compute the expected return for this investor.

c. In one or two sentences, explain why there is a difference between the two expected returns.

d. Suppose a bank is allowed to form. The bank costs nothing to operate. Suppose the bank allocates the aggregate level of savings to online game projects. How many projects could the bank finance?

e. Compute the expected return that the bank could offer to its depositors.