CECN 506 Young Workers Economy Worksheet
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CECN 506 – Problem Set 4
Provide a short answer to each point`. A sentence or a few formulas would
suffice.
1. 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 (i.e. n = 1). There is a constant stock of fiat
money Mt = M (i.e. 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 are the average real rates of return 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 deposits in the economy are Ht and total currency is Qt.
1
What is the price of the good?
(k) Find a relationship between the monetary base Mt and the money stock (M1)t.
2. What is fully-backed central bank money? Why is it important to consider a model with fully-backed
central bank money?
3. What are open-market operations?
2
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