Download MACROECONOMICS. FALL 2010. EXAM 1.

MACROECONOMICS. FALL 2010. EXAM 1.
Time: 1 and ½ Hs.
Date: September 20th, 2010.
To score full points on a question carefully document all steps taken to reach a solution. An
answer that does not demonstrate your thinking process is unlikely to score full points.
1) [20 POINTS]
Consider an economy described by the following equations:
Y  C  I  G Where: Y  5,000 G  1,000 T  1,000
C  250  0.75(Y  T ) I  1,000  50r
a. In this economy, compute private saving, public saving, and national saving.
b. Identify the equilibrium interest rate.
c. Now suppose that G rises to 1,250. Solve for private saving, public saving, and
national saving.
d. Find the new equilibrium interest rate.
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MACROECONOMICS. FALL 2010. EXAM 1.
2) [20 POINTS] In Ghana, the velocity of money is constant. Real GDP grows by 10% per
year, the money stock grows by 25% per year and the nominal interest rate is 21%.
Calculate the real interest rate?
The real interest rate is the difference between the nominal interest rate and the inflation rate.
The nominal interest rate is 21 percent, but we need to solve for the inflation rate. We do this
with the quantity identity expressed in percentage-change form:
% Change in M + % Change in V = % Change in P + % Change in Y.
Rearranging this equation tells us that the inflation rate is given by:
Inflation = % Change in P = % Change in M + % Change in V – % Change in Y.
Substituting the numbers given in the problem, we thus find:
Inflation = % Change in P = 25% + 0% – 10%
= 15%.
Thus, the real interest rate is 6 percent: the nominal interest rate of 21 percent minus the
inflation rate of 15 percent.
3) [20 POINTS] Suppose government increases taxes (T) and government (G) purchases
by equal amounts. Explain what happens to the interest rate and investment in response to
this balanced-budget change? Does your answer depend on the marginal propensity to
consume?
To determine the effect on investment of an equal increase in both taxes and government
spending, consider the national income accounts identity for national saving:
National Saving = [Private Saving] + [Public Saving]
= [Y – T – C(Y – T)] + [T – G].
We know that Y is fixed by the factors of production. We also know that the change in
consumption equals the marginal propensity to consume (MPC) times the change in disposable
income. This tells us that
∆National Saving = [– ∆T – (MPC × ( – ∆T))] + [∆T – ∆G]
= [– ∆T + (MPC × ∆T)] + 0
= (MPC – 1) ∆T. Remember that ∆T = ∆G.
The above expression tells us that the impact on saving of an equal increase in T and G depends
on the size of the marginal propensity to consume. The closer the MPC is to 1, the smaller is the
fall in saving. For example, if the MPC equals 1, then the fall in consumption equals the rise in
government purchases, so national saving [Y – C(Y – T) – G] is unchanged. The closer the MPC
is to 0 (and therefore the larger is the amount saved rather than spent for a one-dollar change in
disposable income), the greater is the impact on saving (Saving increases). Because we assume
that the MPC is less than 1, we expect that national saving falls in response to an equal increase
in taxes and government spending. The reduction in saving means that the supply of loanable
funds curve shifts to the left. The real interest rate rises, and investment falls.
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MACROECONOMICS. FALL 2010. EXAM 1.
4) [10 POINTS]
Suppose you are advising a small country e.g. Ghana on whether to use its own money or
to use the money of a large country e.g. the US. Itemize and critically access the costs
and benefits of having a national currency? Does the relative stability of the US
compared to Ghana play a role in this decision?
5) [10 POINTS]
Explain the term Inflation Tax. Illustrate with an example.
The inflation tax is closely linked with the idea of seignorage or when the government
prints money. The inflation tax is paid by all consumers in the economy when the
government prints money. Instead of using taxes to generate revenue to fund its
expenditure, the government can print money. When government prints money, inflation
rises and the real value of the money in the wallets of consumers falls. So inflation is like
a tax on holding money. For example instead of increasing total taxes in Ghana by 20%
to fund the building of new roads, the Ghana government can coordinate with the bank of
Ghana to print enough new money to build roads. The new money dilutes the existing
Ghanaian currency so that every GHC note now has reduced purchasing power.
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MACROECONOMICS. FALL 2010. EXAM 1.
6) [20 POINTS]
a. Write the quantity equation and explain it.
b. What does the assumption of constant velocity of money imply?
a. The quantity equation is an identity that expresses the link between the number of
transactions that people make and how much money they hold. We write it as
Money × Velocity = Price × Transactions
M × V = P × T.
The right-hand side of the quantity equation tells us about the total number of transactions that
occur during a given period of time, say, a year. T represents the total number of times that any
two individuals exchange goods or services for money. P represents the price of a typical
transaction. Hence, the product P × T represents the number of dollars exchanged in a year.
The left-hand side of the quantity equation tells us about the money used to make these
transactions. M represents the quantity of money in the economy. V represents the transactions
velocity of money—the rate at which money circulates in the economy. Because the number of
transactions is difficult to measure, economists usually use a slightly different version of the
quantity equation, in which the total output of the economy Y replaces the number of transactions
T:
Money × Velocity = Price × Output
M × V = P × Y.
P now represents the price of one unit of output, so that P × Y is the dollar value of output—
nominal GDP. V represents the income velocity of money—the number of times a dollar bill
becomes a part of someone’s income.
b. If we assume that velocity in the quantity equation is constant, then we can view the quantity
equation as a theory of nominal GDP. The quantity equation with fixed velocity states that
MV = PY.
If velocity V is constant, then a change in the quantity of money (M) causes a proportionate
change in nominal GDP (PY). If we assume further that output is fixed by the factors of
production and the production technology, then we can conclude that the quantity of money
determines the price level. This is called the quantity theory of money. It simply says that
change in the quantity of money exactly determines inflation. Therefore, to reduce inflation, just
stop printing money.
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