Monetary Economics

Question 1 (35 points)
In the Republic of Pecunia 1100 individuals are born in period t. The population grows
according to Nt = 1.1Nt−1. Each citizen in Pecunia is endowed with y1 = 15 units of the
consumption good when young, and y2 = 5.5 units when old. Preferences are such that
individuals will always want to consume more than their endowment when old.
The fiat money stock in period t amounts to 2500. The Pecunian government is increasing
the stock of fiat money in circulation by 5 percent each period (z = 1.05). The additional
units of money printed every period are used to purchase Gt units of the consumption good
for government consumption which is wasteful from the perspective of the Pecunian citizens.
Assume stationarity throughout the exercise.
(a) (5 points) Define total uses and total sources of goods in this economy in period t and
derive the (per-capita) feasible set. Use gt =
Gt
Nt−1
.
(b) (5 points) Now look at the monetary equilibrium. Combine the constraints on first- and
second-period consumption for a typical person into a lifetime budget constraint. Hint:
Make sure to consider all available endowments.
(c) (5 points) Derive the real rate of return of fiat money. Plug into the lifetime budget
constraint.
(d) (5 points) Now assume that the government raises lump-sum taxes τ from young individuals to finance its government consumption Gt and does not print new fiat money
(z = 1). Show how this policy affects the life-time budget constraint of an individual
born in t both directly and indirectly through changes in the rate of return to fiat money.
(e) (5 points) Express the feasible set in terms of τ .
(f) (5 points) Considering the welfare of all future generations, explain in your own words
why the second policy option (lump-sum taxes g = nτ and z = 1) is preferable to the
expansionary monetary policy in the first scenario (τ = 0 and z > 1).
Question 2 (25 points)
Consider a 2-period overlapping generations economy with an initial population N0 = 500.
Each generation is n = 1.5 times larger than the previous one. Each individual is endowed
with y = 100 units of the consumption good when young, and nothing when old. The only way
to acquire consumption in old age is by exchanging part of the endowment when young for fiat
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money. The initial old are endowed with M0 = 20, 000 units of fiat money. The money stock
grows at rate z = 1.01 every period. Newly created fiat money in every period t is distributed
as a lump-sum transfer to old individuals worth a units of the consumption good. Assume
stationary allocations of consumption throughout the exercise.
(a) (5 points) Write down total sources and total uses of goods in this economy in period t
and find the per-capita feasible set that a central planner faces in this economy.
(b) (5 points) Turning to the monetary equilibrium, write down equations that represent the
constraints on first- and second-period consumption for a typical person born in period t.
Combine these constraints into a lifetime budget constraint. (Hint: Make sure to consider
all sources of funds for the old.)
(c) (5 points) Find the equation representing the equality of supply and demand in the market for money (money market clearing) in an arbitrary period t. Starting from this
equation, derive the real rate of return to fiat money, υt+1
υt
.
(d) (10 points) Assume that a = 0.8. Use a graph that combines the feasible set, the lifetime
budget constraint, and arbitrarily drawn indifference curves to argue whether or not the
monetary equilibrium attains the Golden Rule in this economy. Clearly label all axes and
other relevant elements in the graph. Explain in your own words.
Question 3 (25 points)
Consider an economy with a constant population of N = 2, 000. Individuals are endowed with
y = 50 units of the consumption good when young and nothing when old. All seigniorage
revenue is used to finance government expenditures. There are no subsidies and no taxes other
than seigniorage. Suppose that preferences are such that each individual wishes to hold real
balances of fiat money worth y
1+ υt
υt+1
goods.
(a) (10 points) Write down the budget constraints in the first and second period of an individual’s life. Determine consumption when young and when old as a function of υt
υt+1
.
Show that the lifetime budget constraint is satisfied.
(b) (10 points) Use the equality of supply and demand in the money market to determine
the real rate of return to fiat money. Using this, determine the total real balances of fiat
money in a stationary equilibrium as a function of the rate of fiat money creation z.
(c) (5 points) Use your answer in part (b) to find total seigniorage revenue as a function of
z.
Question 4 (15 points)
Suppose the monetary authority prints fiat money at the rate z but now does not distribute
the newly printed money as a lump-sum subsidy. Instead, the government distributes the
newly printed money by giving each old person α new dollars for each dollar acquired when
young. Assume that there is a constant population of people endowed only when young.
(a) (5 points) Use the government budget constraint to find α as a function of z.
(b) (5 points) Find the individual’s budget constraints to when young and old. Combine
them to form the individual’s lifetime budget constraint.
(c) (5 points) Explain in your own words why the rate of return to fiat money is no longer
given by just υt+1
υt
.
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