Question

Question 1 (42 p) Consider a closed economy where goods market and finalcial markets can be described by the following equations for period t С,-100 + 0.5yo- 2000.25Y- 200r G- 100: T-200 Suppose inflation escpectations in this economy is based on past period's inflation rate, ie. Let Yo- FIN)-No the labor force is given as constant at LF- 1000. (4p) Write down the IS equation for this economy (4p) Assume a horizontal LM function where the Central Bank announces the interest rate to be =-= 0.30 (in period t, the Central Bank sets the nominal interest rate a 30%, with r-0.1( 10% expected inflation rate for period t). What will be the short run equilibrium level of output, Yo for this economy? (4p) Suppose the natural unemployment rate for this economy is u.-5%, what would be the potential output level, Y How does Yo compare to the short-term equilibrium level of output, Yothat you have found? (3p) Based on your answer to part c), what can you suggest on the relationship between rand rn? Explain a. b. c. d. e) (4p) Suppose that the Phillips Curve (PC relationship for this economy is given by Express the PC relationship above as a function of output gap. Y,- f ) (4p) what is the current inflation rate, π for this economy? g) (8p) Draw the IS-LM-PC graph. Show the current short-run equilibrium of this economy h) (8p) How will the dynamics of this economy behave towards the medium run? Explain on your graph. i) What would happen if the CB does not intervene: and (i) if the CB intervenes, Show your answer on the graph that you have drawn in g). Make sure you also show the direction of movement(s) on your graph. j) (3p) Will the medium-run inflation rate in this economy be higher than lower thanequal to cument inflation rate π Explain. under cases (i) and (ii) that you have described in part hy?

Answer 1

a. IS equation is given as follows:

Y_t = C_t + I_t + G = 100 + 0.5Y^d + 200 + 0.25Y_t - 200r_t + 100 where, Y^d=(Y_t - T)= (Y_t - 200)

Y_t - 0.5Y_t - 0.25Y_t = 200 - 200r_t

Y_t = 800 - 800r_t IS equation

b. when central bank sets interest rate i_t = 30% with expected inflation for period t as $\pi$^e= 10%, then the real interest rate will be;

r_t = i_t - $\pi$^e = 0.30 - 0.10 = 0.20 = 20%

From horizontal LM curve we get the equilibrium real interest rate at 20%. Using this in IS equation to get the short run equilibrium level of output for this economy, as at equilibrium, IS=LM

Y_t= 800 - 800(0.20) = 640

c. Y_t=N=640, where N is workers employed,and LF= 1000

unemployed workforce = LF - N = 1000- 640 = 360

Unemployment rate,U_t = (unemployed workforce/ LF)* 100 =( 360/1000) * 100 = 36%

Natural rate of unemployment, U_n= 5%

using Okun's law,

(Y_n - Y_t)/Y_n = 2( U_t - U_n)

(Y_n - 640)/ Y_n =2( 0.36 - 0.05)

Y_n = 1684.21

Y_t (short run equilibrium level output) is very lower than the potential output (Y_n), this means economy is operating below the full employment level.

d. using Y_n in IS equation to find r_n

1684.21 = 800 - 800r_n

r_n = - 1.105 = -110%

Whereas r_t = 20% which is greater than the potential interest rate.

e. The Phillips curve equation for this economy is

$\pi$_t - $\pi$^e = -1(U_t - U_n)

from Okun's law,

(Y_n - Y_t)/Y_n = 2(U_t - U_n)

(U_t - U_n) = (Y_n - Y_t)/2Y_n , substituting this into phillips curve equation , we get:

($\pi$_t - $\pi$^e) = -1 { (Y_n - Y_t)/2Y_n}

f. $\pi$_t - $\pi$^e = -1(U_t - U_n)

$\pi$_t - 0.10 = -1(0.36 - 0.05)

$\pi$_t = -0.21 = -21%

g. Below is IS-LM-PC graph with current short-run equilibrium conditions.

Real interest rate LM 20% IS Output level Imflation rate A PC 0 Output level Y640 [],--2196

h. In the medium run , the dynamics of the economy would move towards full employment level output i.e. the economy will try to achieve its potential output. this will be achieved by some intervention either through fiscal policy or monetary policy. Due to intervention,the employment level will rise as more and more workers will be employed to reach the natural rate of unemployment and the potential level of output.

(i).when central bank doesn't intervene, this means that fiscal policy expansion is undertaken to achieve the potential output level. In fiscal policy expansion,either the government increases its expediture or reduces the tax rate. this shifts the IS curve to right to IS¹, while the LM curve remains constant. Thus, r remains same.

Real interest rate r= 20% LM IS IS Output level lmflation rate PC -t 0 Y 640 Output level -2196

(ii). If central bank intervenes, then it uses the monetary policy tool to move the economy towards potential output level.

central bank would use contractionary monetary policy by reducing the money supply, thus shifting the LM curve downwards to LM¹. This will reduce the interest rate , thus increasing the investment demand. This in turn will increase the output.

Real interest I rate LM n« 20% LM1 rt IS I Y Output level Inflation rate PC 0 ‰ Output level Yt-640 u--21%

j. The medium run inflation of the economy $\pi$¹ is greater than the current inflation rate $\pi$_t in both the cases whether central bank intervenes or not. This is because as we move towards full employment level, unemployment level reduces, output level increases and thus inflation will rise ( as can be seen from phillips curve).