Question

Consider a hypothetical economy characterized by the following equations (all variables as defined in class).
Consumption: C = 700 + 0.95Y Investment: I=500− 30i Government spending: G=50 Money demand: L(i,Y )=0.75Y − 30i Money supply: Ms/P=400

(a) What is the equation of the IS curve?

(b) What is the equation for the LM curve? (c)

Solve for the equilibrium values of income (Y) and interest rates (i).

(d) Assume that the government engages in expansionary fiscal policy by increasing expenditure to G = 100. Solve for the new equilibrium values of income (Y) and interest rates (i). Illustrate your answer in a graph.

(e) Assume that instead of the expansionary fiscal policy in part (d) above, that the Monetary Authority (The Central Bank) engages in expansionary monetary policy by increasing the money supply by 100 to Ms/P = 500. Solve for the new equilibrium values of income (Y) and interest rates (i) in this case. Illustrate your answer in a graph.

(f) Which of the policies from parts (d) and (e) above would be the most effective expansionary policy ? Explain.

(g) Say that the government engaged in both of the policies of parts (d) and (e) simultaneously. Would this policy mix be more or less expansionary than the individual policies?

(h) Suppose that money demand in this economy was observed to be income insensitive so that it was now represented by L(i, Y ) = L(i) = 600 − 30i. In this case, which of the policies from parts (d) and (e) above would be the most effective expansionary policy? Explain your answer in terms of the concept of “crowding out”.

(i) Lastly, returning to the original model as in part (a), suppose that investment was now determined to be interest insensitive such that it could be represented by I = 600. In this case, which of the policies from parts (d) and (e) above would be the most effective expansionary policy? Explain this answer in terms of “crowding out ”.

Answer 1

A hypothetical economy is assumed to have the following variables:

Consumption is given as, C=700+0.95Y.

Investment expenditure is given as, I=500-30i.

Government spending is given as, 50.

The money demand function is given as, L(i,Y)=0.75Y-30i.

The money supply function is given as, Ms/P=400.

1. The IS shows all the different points where the goods market is in equilibrium. In other words, it represents different bundles of output and interest where the saving and investment are equal.

In the goods market at equilibrium,

So, the IS curve equation can be written as Y=25,000-600i.

b. The LM curve shows the different points where the money market is in equilibrium. It shows the different bundles of output and interest where the demand for money and the supply of money is equal.

In the money market at equilibrium,

So, the LM equation can be written as Y-533.33+40i.

c. At the point of intersection of IS and LM curves, the goods market, as well as the money market, will be in equilibrium. The output and interest rate will be in equilibrium as well.

So, we can say that the equilibrium interest rate is 38.23.

Putting the value of i in the LM equation,

So, the equilibrium income or output is 2062.53.

d. Now, if the government spending increases to 100, the goods market equilibrium will change while the money market equilibrium will remain the same.

So, the IS curve equation can be written as Y=26,000-600i.

The LM equation will remain the same.

At equilibrium,

So, we can say that the equilibrium interest rate is 39.79.

Putting the value of i in the LM equation,

So, the equilibrium income or output is 2,124.93.

The graph given above shows equilibrium in the IS-LM model and the effect of expansionary fiscal policy on interest and income. An increase in government spending causes income as well as interest rate to increase.