Provide a short answer to each point. A sentence or a few formulas would be fine.
Consider an OLG economy with an infinite horizon where individuals live for two periods. Suppose the number of young born in a period is constant at Nt = N (e.g., n = 1). There is a constant stock of fiat money Mt = M (e.g., z = 1). In each young generation there are three types of individuals born: workers, bankers and entrepreneurs.
Workers and entrepreneurs both have y units of time available and use all of this time to work. Each unit of time spent working produces one unit of the consumption good. Here we assume that individuals only care about consuming when old. Each worker produces a different amount (some are more productive than others). Denote the amount produced by each young worker by si. Entrepreneurs have an additional ability to create capital, which has a one period return of x > 1 (and matures after one period).
Finally, bankers have no endowment and do not care about consumption. Bankers in this economy simply take deposits and promise a one-period return rd and make loans at the rate r. Bankers can perfectly locate entrepreneurs to make loans and can be easily located by depositors. Finally, when a depositor needs to make a withdrawal, there is a fixed cost ? that they must pay to do this that does not depend on the size of the withdrawal. You can think of this cost as the cost of going to the bank, periodically answering security questions, signing-in to your account etc.
(a) Young workers can either acquire money or deposit with a banker. How many goods do they receive in the next period if they acquire fiat money?
???????(b) How many goods do they acquire in the next period if they deposit?
(c) What is the rate rd that must be offered by bankers?
(d) What is the average rate of return received on money and deposits?
(e) Explain why some individuals will deposit and others will acquire money. (f) What does the banker do with deposits?
(g) At what rate r does the banker lend to entrepreneurs?
(h) What do entrepreneurs do with the goods they produce?
(i) Assume bankers loan at rate r = x and pay rate rd = x on deposits and do not consume. Why do we include them in our model?
(j) Suppose the total real deposits in the economy are Ht and total real currency is Qt. What is the price of the good?
(k) Find a relationship between the monetary base Mt and the money stock (M1)t.