Question

1. This question is based on our lectures on the IS-LM framework. Consider the economy given by the following equations: C = 0:8(1 t)Y t = 0:25 I = 900 50r G = 800 L(r; Y ) = 0:25Y 62:5r M P = 500 (a) What is general deÖnition of the IS curve? Derive the IS curve from the above equations.

(b) What is general deÖnition of the LM curve? Derive the LM curve from the above equations.

(c) Describe in words the conditions that satisfy the deÖnition of an equilibrium. Find the equilibrium level of the endogenous variables.

(d) Determine the level of spending multiplier with and without money market. Explain the di§erence (if any).

(e) Explain in words what a§ects/determines the slope of IS and LM curves.

(f) Explain how the slope of IS curve determines the e§ectiveness of monetary policy and that of LM curve determines the e§ectiveness of Öscal policy?

(g) Under what circumstances might the LM curve be horizontal? Under such case what would be the spending multiplier? Explain the implications of increasing the government spending. (10 mar

Answer 1

IS-LM Framework

C = 0.8(1-t)Y

t = 0.25

I = 900-50r

G = 800

L(r, Y) = 0.25Y - 62.5r

M/P = 500

(a) IS curve is the locus of all the combinations of interest rates and output at wich the goods market is in equilibrium.

Now, Deriving the IS curve equation:-

Y = C + I + G

Y = {0.8(1 - 0.25)Y} + {900 - 50r} + 800

Y = 0.6Y + 1,700 - 50r

0.4Y = 1,700 - 50r

Y = 4,250 - 125r

(b) LM curve is the locus of all the combination of interest rates and output at which the money market is in equilibrium which means real money demand equals real money supply.

Now, Deriving the LM curve equation:-

L(r, Y) = M/P

0.25Y - 62.5r = 500

0.25Y = 500 + 62.5r

Y = 2,000 + 250r

Or r = 0.004Y - 8

(c) Equilibrium occurs where the IS curve intersects the LM curve. At the intersection, Both the markets, Goods market and the money market are in equilibrium and balanced. IS and LM curves changes due to many factors and economic policies. Fiscal policy shifts the IS curve and monetary policy shifts the LM curve.

Now, Deriving the equilibrium level of endogenous variables:-

Equating the IS curve equation and LM curve equation.......

4,250 - 125r = 2,000 + 250r

2,250 = 375r

Therefore, r = 6

Hence, Y = 3,500

(d) Spending multiplier without money market:-

Y = C + I + G

Y = 0.8(1 - 0.25)Y + 900 - 50r + 800

Y - 0.8(0.75)Y = 900 - 50r + 800

0.4Y = 1,700 - 50r

Y= 1/0.4 {1,700 - 50r}

Hence, The spending multiplier is 1/0.4 which is 2.5

Spending multiplier with money market:-

Y = 4,250 - 125r

Putting the value of r from LM equation in IS equation-

Y = 4,250 - 125(0.004Y - 8)

Y = 4,250 - 0.5Y + 1,000

1.5Y = 5,250

Y = 3,500

It means the spending multiplier is 1.5 in case of money market.

Yes, There is a divergence in spending multiplier in two cases because in absence of money market, spending in the economy multiplies the output by full amount but in presence of money market, spending crowds out some of the investment from the economy. Hence, it multiplies the output by less amount.

Note- It is strongly advisable that students refer to the diagrams of the IS-LM Framework to get clearer explanation of the algebraic equation.