Question

17) Graphically derive the IS curve from the goods market equilibrium. What is the IS relation? Explain why IS curve is downward sloping.

18) Explain in detail and graph what effect a reduction in government spending will have on: (1) the LM curve; and (2) the IS curve.

Answer 1

17,

The real sector equilibrium and the derivation of IS curve

For simplicity we start our analysis with a closed economy in which there is no government. In the Keynesian model, the equilibrium level of employment and output is determined by the level of effective aggregate demand. Aggregate demand consists of connsumption and investment. E=C + I. The households dispose off their incomeeither by consuming or saving i.e, Y=C + S. For static flow equilibrium in the real sector, we must have aggregate supply equals aggregate demand for it or S = I.

Savings are assumed to depend positively on the level of income S=f(Y). The savings function is the counterpart of the consumption function C= -a+(+b)y. Investment is inversely dependent on the rate of interest. A crucial determinant of investment in the Keynesian model is expectations about the fututre (MEC) in the ISLM model expectations are given such that I=f( MEC,r).

The derivation of the IS curve is explained below,

The quadrant 1 of the diagram the income - savings relationship. At y1 level of income savings is s1.

It is transferred to the verical axis in quadrant 2, there shows the savings - investment equilibrium. The 450  line converts the distance into equal between horizontal and vertical axis.

The investment schedule in quadrant 3 shows that the rate of interest must be 'r1' to result in a level of investment I1.

The co-ordinate of 'y1' and 'r1' is then plotted in quadrant 4. Then we have one combination of income and rate of interest at which savings equals investment (S = I). The same process is repeated for income level y2 to obtain interest rate 'r2' which makes S =I. In this way we obtain a large number of interest rates and output levels at which S =I and by joining them we obtain the IS curve.

The slope of IS curve

The IS curve slopes downwards from left to right. It shows a high rate of interest and a low level of income or a low rate of interest and a high level of income. As the rate of interest falls, investment increases and so does income and savings. Conversely, a high rate of interest, which reduces investment , has to be balanced by a low income, which reduces savings. The slope of the IS curve depends on the interest elasticity of investment.

(If the investment demand functions is less interest elastic, the IS curve will be steeper. On the other hand, more the interest elasticity of investment, the IS curve will be flatter. In the limiting case where investment is perfectly interest inelastic, IS curve is vertical.)

18,

Reduction in government spending on IS and LM curves

  

LMs: P = P. LM: P= Po - -- /S Yf

A reduction in government spending or an increase in taxation would have the effects of shifting IS curve from IS1 to IS0. the price level would fall, shifting the LM schedule down from LM10: P=P1 to LM0 : P = P0 and the interest rate would fall.