1. (The IS-LM-PC model): Assume the following relations characterize the goods m

Question

1. (The IS-LM-PC model): Assume the following relations characterize the goods market: (i) CJ 100 + 0.5YD! (ii) 11-100 + 0.25Y !-200(r1+ x !) (iii) G ! = 100! = 20au, x != 0.1 or 1096 (a) Derive the IS curve (as a relation between Yt and t) (b) Assume the LM curve is given by = 0.1 (ie. in period t, the central bank sets the real interest rate at 10 %). what is the short-run equilibrium level of output (n? (c) Suppose that L 1000 and un 0.05 (where L: total population, un-natural rate of unemployment) Calculate the value of potential output (Yn). How does Yn compare to the short-run equilibrium level of output )? (d) Calculate the natural rate of interest (m). How does rn compare to rt? Label this example as one of the cases covered in lectures 0.05 Calculate (e) Consider that the Phillips Curve is given by: [T!-!! != 0.0005 (Yl-Y!with !!! the change in inflation in period t. (f) Draw the IS-LM-PC graph Assume neither the government nor the central bank intervene until period t+4. Calculate the inflation rates from period t+1 through period t+3 (i.e. !! !,T!!!,T!!!). Describe briefly the situation of the economy toward the end of period t+3, based on the output gap and the time-path of the inflation rate from period t+1 through period t+3 (g) Given the state of this economy toward the end of period t+3, what choice would you advise to policymakers for period t+4? (Choose among A, B, C and D). Explain why A. The central bank should conduct a contractionary monetary policy in period t+4, thus raising the real interest rate target. B. The central bank should conduct an expansionary monetary policy in period t+4, thus lowering the real interest rate target. C. The government should implement a fiscal consolidation in period t+4 D. The government should intervene by expanding government spending and/or reducing overall taxes in period t+4

Explanation / Answer

For simplicity, I am assuming C! = C, I! = I, G! = G, T! = T, x! = x, r! = r, YD! = Y

a

C = 100 + 0.5YD

I = 100 + 0.25Y – 200 (r+x)

G = 100

T = 200

x= 10% = 0.10

a) Derive the IS curve

In a closed economy, Y = C + I + G

Now, C = 100 + 0.5YD = 100 + 0.5 (Y – T)

Note YD is disposable income = income (Y) – Taxes (T)

C = 100 + 0.5(Y – 200)

I = 100 + 0.25Y – 200(r+0.10)

G = 100

So, Y = C + I +G

Y = 100 + 0.5(Y – 200) + 100 + 0.25Y – 200(r+0.10) +100

Solve this for Y and r,

Y = 100 +100 + 100 – 0.5*200 – 200*0.10 + 0.5Y + 0.25Y -200r

Y = 180 + 0.75Y – 200r

Y – 0.75Y = 180 -200r

Y = (180 – 200r)/ 0.25

Y = 720 – 800r

IS equation is: Yt = 720 – 800rt

b.

Assume LM curve is given by rt=0.1

It means Yt = 0.1

Put the value of rt=0.1 in IS equation above,

We get,

Yt = 720 – 800 (0.1) = 640

Short run equilibrium level of output = 640

c.

c. suppose L = 1000 and un = 0.05

L= total polulation and un = natural rate of unemployment

Suppose the Yn = X

(640 – X)/X = 0.05

Solve for X,

0.05X + X = 640

X= 609.5

Potential output = 609.5

Actual GDP is greater than potential GDP, the actual unemployment will be lower than the natural level of unemployment

d). The real interest rate r = 10% keeps the economy in equilibrium where natural rate of intrest rn is the rate consistent with maintaining real GDP and potential GDP in the absence of any transitory shocks to demand. It means real GDP is growing at its trend rae and inflation is stable.

rn = 10%

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