Homework Assignment #3
Principles of Macroeconomics
Economics 112
Assigned: Wednesday, November 24, 1999
Due: Friday, December 3, 1999
1. The Multiplier Effect
a. Consider a closed economy in which no investment or government
spending takes place. In this economy, autonomous consumption is equal to 100
(A = 160). The tax bill is equal to 80 (T = 80). Firms in this economy set a fixed
price and sell as much output as people demand. If household consumption is
equal to expenditure which is equal to output:
Y = Expenditure = C = A + mpc  (Y-T)
Solve the above equation for Y when mpc = .75. Now suppose that A
increases by A = 20. How much will Y increase? Why is the increase in Y larger
than the increase in autonomous consumption? What is the multiplier?
b. In Hong Kong, the government does not set some amount of taxes to be
collected. Instead, the government collects a percentage of private income. Now,
suppose that taxes are set equal to
T=tY
where 0< t < 1 is a fraction. Solve for output when A = 160, mpc = .75, and t =
.20. How much are taxes? Suppose that A increases by A = 20. How much will
Y increase? How much will taxes increase? Explain why the increase in output
following the increase in autonomous consumption is smaller than in part A.
2. Investment Demand
Though the British economist John Hicks developed the IS-LM model in the
1930’s, it was based on some of the theories of another British economist, John
Maynard Keynes (which is why this type of macroeconomic theory is called
Keynesian economics). So far we have assumed that investment is strictly a
(negative) function of the interest rate. However, Keynes believed that the main
cause of business cycles is fluctuations in the optimism and pessimism of owners
and managers of businesses. He believed that investor confidence was a major
cause of fluctuations in expenditure on investment. Now, imagine if investment
was a function of the real interest rate, r, and animal spirits B
I = I(r,B)
-+
A decrease in B caused by pessimism will reduce investment expenditure at
any given interest rate. For the remainder of the question assume that prices are
fixed and firms will produce any amount of goods demanded at the given price
level. Use the IS-LM analysis to demonstrate the effects of a wave of pessimism
that reduces investment expenditure by I.
a. A wave of pessimism hits China reducing the level of investment
expenditure. Use the IS-LM model of a closed economy to graphically
demonstrate the effects of this shock on the equilibrium interest rate and output
level. Does this shock cause and increase, decrease, or have no effect on
consumption? Explain.
b. A wave of pessimism hits Canada reducing the level of investment
expenditure. Use the ISX-LMX model of a small open economy with flexible
exchange rates to demonstrate the effect of this shock on the equilibrium exchange
rate and the output level. Will this increase, decrease or have no effect on
consumption and net exports. Explain.
c. A wave of pessimism hits Hong Kong reducing the level of investment
expenditure. Use the ISX-LMX model of a small open economy with fixed
exchange rates to demonstrate the effect of this shock on the equilibrium exchange
rate and the output level. Will this increase, decrease or have no effect on
consumption, money supply and net exports. Explain.
d. A wave of pessimism hits Japan reducing the level of investment
expenditure. Use the IS-LM model of a large open economy to demonstrate the
effect of this shock on the equilibrium interest rate, exchange rate and the output
level. Will this increase, decrease or have no effect on consumption, net foreign
investment and net exports. Explain.
3. The Algebra of the IS-LM Model
a. In a closed economy with no government spending or taxes (G=T=0), the
level of consumption expenditure is
C = A + mpc  Y
while investment expenditure is given by
I = B – ieir
Firms in the short run set the price level P = 1. We can then write the demand
for liquid assets as:
M = Y - iemr
Solve for the equilibrium interest rate and output levels as a function of the
exogenous variables (M, A, B) and the parameter values (mpc, iei, iem). Show that
an increase in B will lead to higher interest rates and an increase in M will lead to
lower interest rates in the short run.
b. In an open economy with flexible exchange rates, and no government
spending or taxes (G=T=0), the level of consumption expenditure is given by
C = 100 + .75  Y
while investment expenditure is given by
I = 100 – 200r
while net exports are given by:
NX = 10 (1-e). Firms in the short run set the
price level P = 1. We can then write the demand for liquid assets as:
M = Y - 1000r
The central bank sets money supply equal to 500 and the world real
interest rate is rw=.10. Solve for equilibrium output, the exchange rate, net
exports, consumption and investment. Now assume that the monetary authority
increases the money supply by 50. Solve for the new equilibrium output, exchange
rate, consumption, investment and net exports.