Tutorial 4
Q1. Consider the following ISLM model with the central bank controlling
the interest rate:
C = 200 + 0:25YD
I = 150 + 0:25Y 1; 000i
G = 250
T = 200
(
M
P
)d = 2Y 8; 000i
i = i0 = 0:05
a. Derive the IS relation. (Hint: You want an equation with Y on the left
side, all else on the right.)
b. Derive the LM relation. (Hint: It will be convenient for later use to
rewrite this equation with i on the left side, all else on the right.)
c. Solve for equilibrium real output. (Hint: Substitute the value for the
interest rate into the IS equation and solve for output.)
d. Solve for the equilibrium real money supply. (Hint: Substitute the value
you obtained for Y in (c) into the LM equation and solve for MP .)
e. Solve for the equilibrium values of C and I and verify the value you
obtained for Y by adding up C; I and G.
f. Now suppose that the interest rate, i0 was cut to 3 per cent (that is, 0.03).
Solve for Y ,M=P , C and I, and describe in words the e¤ects of an expansionary
monetary policy.
g. Set the interest rate back to 5 per cent. Now suppose that government
spending increases to G = 400. Consider the following two scenarios: Scenario
1: the central bank keeps the money supply unchanged. Find the e¤ects of
this …scal expansion on Y and C. Scenario 2: the central bank responds by
increasing the money supply by enough so that the equilibrium interest rate
remains at 5 per cent after the …scal expansion. What would be the e¤ect on
Y , i and C? Summarise the e¤ects of an expansionary …scal policy on Y , i and
C.
Q2. The following is a linear representation of an IS LM model:
Goods Market (IS Curve)
C = c0 + c1YD
1
YD = Y T
T = t0 + t1Y
I = b0 b1i
G = G0
X = X0
IM = m0 +m1Y
Equilibrium in the Goods Market requires
Y = C + I +G+X IM
Money Market (LM Curve)
(M=P )d = + Y i
(M=P )s =Ms0=P0
Equilibrium in the Money Market requires
(M=P )d = (M=P )s
The money supply is set by the central bank and is taken to be exogenous.
Questions:
a. Interpret the coe¢ cients and .
b. In order to get the economy out of a recession, the government embarks
on an expansionary …scal policy by increasing government expenditure from G0
to G1 whilst keeping the money supply unchanged.
(1) Illustrate the impact on output and interest rates by means of a diagram.
(2) For the expansionary policy to have a large e¤ect on output, is it desirable
that c1 be large or small, t1 be large or small, b1 be large or small, be large
or small? Give reasons for your answers.
c. Use the IS=LM model to predict the likely consequences for output and
interest rates of the following disturbances:
(1) a decrease in consumer con…dence
(2) an aggressive sale of govt. bonds in the money market by a Central Bank
targeting the money supply
(3) an increase in government expenditure on a national environment pro-
gramme
(i) funded by borrowing from the nonbank public
2
(ii) funded by borrowing from the Reserve Bank
(iii) funded by the part sale of Telstra
(4) a recession in the USA.
Q3. Ch. 6 Q3.