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a) [1 mark] Derive the IS curve.
(b) [1 mark] Derive the LM curve.
(c) [2 marks] Solve for the equilibrium output and interest rate in the short run.
Due to a drop in consumer confidence, consumers reduce their consumption level, so that the
consumption function now becomes:
C = 0.2 (Y - T),
(d) [1 mark] Compute the new equilibrium output and interest rate in the short run.
(e) [1 mark] Compute the old and new equilibrium investment levels. How does the drop in consumer
confidence affect the equilibrium investment level? Explain the intuition behind this change.
To give a quick boost to the economy and bring the equilibrium output back to the original level
identified in part (c), the central bank decides to launch an expansionary monetary policy by
increasing the real money supply.
(f) [1 mark] Solve for the required interest rate that can achieve such a recovery.
(g) [1 mark] Draw an IS-LM diagram to represent the drop in consumer confidence and the entailing
expansionary monetary policy. Label all axes and curves and mark all the values and equilibrium
points appropriately.
Answer:
(a) IS: i = 1/5 – Y/40
(b) LM: i = Y/10 – 2/5
(c) Y*=4.8, i*=0.08
(d) new IS: i = 0.15 – Y/40, new Y*=4.4, new i*=0.04
(e) old I = 3+0.3(4.8)-20(0.08) = 2.84
new I = 3+0.3(4.4)-20(0.04) = 3.52
drop in Y* leads to a drop in I*; drop in i* leads to a rise in I*; the net result is a rise in I*
(f) from the new IS curve, required i = 0.15 – 4.8/40 = 0.03
Q2. Suppose the economy is described by the following behavioural equations. Assume the central bank
controls the interest rate.
C = c0 + c1(Y –T) Consumption
I = b0 + b1Y – b2i Investment
Md / P = kY – hi Money demand
G = G0 Exogenous government purchases
T = T0 Exogenous taxes
i = i0 Interest rate
(a) Derive the IS curve.
(b) Derive the LM curve.
(c) Solve for the equilibrium output in the short run.
(d) Solve for the equilibrium real money supply.
Now suppose c0 =200
c1 = 0.25
b0 = 150
b1 =0.25
b2 =1000
k= 2
h=8000
G0=250
T0=200
i0=0.05
(e) Solve for the equilibrium values of C, I, Y, and real money supply. Verify the value you obtained for
Y by adding up C, I and G.
(f) Now suppose that government spending increases to G=400. Solve for the new equilibrium values of
C, I, Y, and real money supply.
(g) Now suppose that in response to the fiscal expansion, the central bank increases the interest rate to
20%. Solve for the new equilibrium values of C, I, Y, and real money supply.
Answer: (a) = 1
1−1−1
(0 − 10 + 0 − 2 + 0) IS
(b) / = kY – hi LM
(c) = 1
1−1−1
(0 − 10 + 0 − 20 + 0)
(d)
= − ℎ = 1−1−1 (0 − 10 + 0 − 20 + 0) − ℎ
(e) Y=1000, C= 400, I=350.
= 1600. Y=C+I+G, where G=250
(f) Y=1300, C= 475, I=425.
= 2200. Y=C+I+G, where G=400
(g) Y=1000, C= 400, I=200.
= 400. Y=C+I+G, where G= 400
