Question

19) Consider the following IS LM model: C= 300 + 25YD I = 150 + 25 Y - 1,000 i G = 350 T= 100 i*=.02 1. Derive the Irelation. Solve for equilibrium real output. 2. Solve for equilibrium values on C and I, and verify the value you obtained for Y by adding C, I, and G. 3. Now suppose that the central bank increases the interest rate to 8%. How does this change the LM curve? Solve for Y, I, and C, and describe in words the effect of an expansionary monetary policy and graph.

Answer 1

1) Use C + I + G + NX = Y for IS equation

300 + 0.25*(Y – 100) + 150 + 0.25Y – 1000i + 350 = Y

775 – 1000i = Y – 0.5Y

Y = 1550 – 2000i

This is the IS equation

Since i = 0.02 we have Y = 1550 - 2000*0.02 = 1510

Hence, equilibrium income is 1510

2) C = 300 + 0.25*(1510 - 100) = 652.50

I = 150 + 0.25*1510 - 1000*0.02 = 507.50

Since C + I + G = 652.50 + 507.50 + 350 = 1510, the equilibrium output found in 1) is correct

3) When rate of interest is increased to 8% LM curve shifts left. This is not an expansionary monetary policy but a contractionary monetary policy since rate of interest is increased.

We cannot find LM because we have not given any values for LM

For IS we can see that there is a movement up along the IS curve

Y = 1550 – 2000*0.08 = 1390

C = 300 + 0.25*(1390 - 100) = 622.50

I = 150 + 0.25*1390 - 1000*0.08 = 417.50

G = 350

An easy monetary policy (monetary expansion) is aimed at reducing the rate of interest which increases the access to credit by economic agents. If the central bank chooses to use a monetary expansion, it can decrease the reserve requirements or the discount rate. Or it can buy government securities in the market. In the money market, supply of real money balances will rise and money supply curve shifts to the right which reduces the interest rate. With a lower rate of interest, investment spending increases. This also increases net capital outflow and depreciates the currency which raises net exports. All of these changes shift the aggregate demand to the right, implying that the level of national income will rise in the short run. This shifts the LM curve to the right in the IS-LM model in the short run.

Real interest rate, r LM IS, Y Y Income, Output, Y