Question

Question 1: IS-LM-AD in a closed economy (35 Marks) The following represent the key equations for a closed economy: Md 18+0.5Y-450 Money demand C" = 6 + 0.8(Y-T)-250r 1 -33-200r u-u0.3 a) Write out the equations for the IS and LM curves for this economy, with the real Desired consumption Desired investment Initial budget position Okun's law Y-Y rate of interest (r) on the left-hand side. Next, use these relationships to find the AD curve, written with output (Y) on the left-hand side. Based on your model, describe briefly how, in the short run, output (Y) would respond to a rise in G and why? How would output respond in the short run to a cut in taxes and why? b) You are given the following information: G 15; the velocity of money () is 2; and the price level (P) is one. Use this information to find real output, the real interest rate and the nominal money supply (M). Verify that your values of Y and r will give values of C and I that are consistent with the national accounts identity. Assume that the level of output you found in part b) is the economy's long-run full-employment level, defined as Y c) Now suppose that the efficiency of the payments systems has improved. We can capture this by assuming that the constant term in the money demand equation falls from 18 to 10. At the same time, the central bank is unaware of this change and keeps the nominal money supply constant at the level you found in part b). Find the short-run effects of this change on Y and r. If the natural rate of unemployment, ii, is 690, what is the actual rate of unemployment, u, following the change in the efficiency of the payment system? Provide a brief explanation of your results. For simplicity, you can assume that wages remain constant in the short un

Answer 1

sIS curve represents the locus of equilibrium interest rate and output that equates demand and supply in the goods market

IS curve: Y= C+I+G ----eq1

From the question, C= 6+0.8(Y-T)-250r, I= 33-200r and G=T-----eq2

solving equation 1 and 2 we will get

Y= (39-450r+0.2T)/0.2= 195-2250r+T

IS Curve: r= (195-(Y-T))/2250-----------eq3

AD is the locus of the equilibrium price level and output that bring both goods and money market to equilibrium.

Equilibrium in the Money market occurs when the nominal money supply equals nominal money demand.

M^d=M^s

r= (18+0.5Y- M^s/P)/450-----eq4

Solve equation 3 and 4 to get the aggregate demand curve

AD curve: $\small Y= (30+\frac{2T}{7})+\frac{10}{7}.\frac{M^{s}}{P}$

where T and M^s are exogenous variables

Effect of increase in G:

Since G=T if G increases than T increase which increases the intercept component of the AD curve and consequently AD curve shifts upward leading to an increase in Y assuming AS curve is unaffected.

Effect of tax cut on Y:

This case no different than the previous one if T decreases it will decrease the intercept component of the AD curve and consequently AD curve shifts downward leading to a decrease in Y assuming AS curve is unaffected.

(b)

The quantity thoery states

MV=PY

V=2 and P=1

Therefore M=0.5Y

Put the above value in money market equation

we get r bar= 0.04

and put this value r into the IS equation to find the real output

Y bar= 120 and M^s=60

(c)

If the intercept of money demand is changed from 18 to 10 and G=T=15

New LM curve r= (10+0.5Y- M^s/P)/450

Since it will not affect the IS curve then

IS curve: r= (195-(Y-T))/2250

Solve these equations to get short-run equilibrium Y and r and M^s=60

Y= 920/7

Now, ubar= 0.06

u-ubar=-0.3((Y-Ybar)/Ybar)

u= 0.06-0.3(((920/7)-120)/120)

u= 0.0314