Question

Show the derivation of the IS curve. Clearly label your graphs.

Answer 1

Derivation and properties of IS explained with the help of suitable diagrams:

The goods market equilibrium schedule is the IS curve (schedule). It shows combination of interest rates and levels of output such that planned (desired) spending (expenditure) equals income. The goods-market equilib­rium schedule is a simple extension of income determination with a 45° line diagram (of the Keynesian type). Now, investment is no longer fully exogenous, but is also determined by the rate of interest (which is a policy variable).

Figure 3 shows a typical invest­ment (demand) schedule. It shows the planned level of investment (spending) at each rate of interest. Since higher rates of interest reduce the profitability of additions to the capital stock, higher interest rates of imply lower planned rates of invest­ment spending. (Changes in autonomous investment shift the investment schedule).

The investment function is expressed as: I = I̅ – cr, C<0, where r is the rate of inter­est and c measures the interest response of investment, I̅ de­notes autonomous investment, that is, investment spending which is independent of both income and the rate of interest. The investment function above states that the lower the interest rate, the higher is planned in­vestment, with the coefficient c measuring the responsiveness of investment spending to the in­terest rate.

The IS Curve:

Figure 4 shows how the IS curve is derived. At an interest rate, r1, equilibrium in the goods mar­ket is at point E in the upper part with an income level or Y1. In the lower part of the diagram this is recorded as point E’.

Now a fall in the interest rate to r2 raises aggregate demand increasing the level of spending at each income level. The new equilibrium level of income is Y2. In the lower part, point F shows the new equilibrium in the goods corresponding to an interest rate r2.

Definition:

The IS curve is a locus of points showing alternative combi­nations of interest rates and income (output) at which the goods market clears. That is why the IS curve is called the goods market equilibrium schedule.

Properties:

We can gain further insight into the IS curve by raising and answering the following questions:

1. What determines the slope of the IS curve?

2. What determines the position of the IS curve, given its slope, and what causes the curve to shift?

3. What happens when the interest rate and income are at levels such that we are off the IS curve?

The Slope of the IS Curve

The IS curve is negatively sloped, because a higher level of the interest rate reduces investment spending, thereby reduc­ing aggregate demand and thus the equilibrium level of income. The steep­ness of the curve depends on the interest elasticity of investment (i.e., how sensitive investment spending is to changes in the interest rate) as also on the (investment).

Position off the IS Curve:

Figure 5 is just a reproduction of Fig. 4(b), along with two additional points — the disequilibrium points G and H. At point G national income is the same as at E, but the rate of interest is lower (r2). Consequently, the demand for investment is higher than that at E, and the demand for goods is also higher than that at E.

This simply means that the demand for goods must exceed the level of output, and so there is an excess demand for goods. Likewise, at point H, the rate of interest is higher than at F, but the demand for goods is lower than at F, and there is excess supply of goods.

Thus, Fig. 5 clearly shows that points above and to the right of the IS curve- points like H—are points of excess supply of goods (ESG). By contrast points below and to the left of the IS curve are points of excess demand for goods (EDG). At a point like G, for instance, the interest rate is too low and aggregate demand too high relative to output.

Major Points:

The major points about the IS curve are the following:

1. The IS curve is the schedule of combinations of the interest rate and the level of income such that the goods market is in equilibrium.

2 The IS curve is negatively sloped because an increase in the interest rate reduces planned (desired) investment spending and therefore reduces aggregate demand, thereby lowering the equilibrium level of income.

3. The smaller the investment multiplier and the less sensitive investment spending is to interest rate changes, the steeper is the IS curve.

4. The IS curve is shifted by changes in autonomous spending. An increase in autonomous spending, such as investment spending or govern­ment expenditure shifts the IS curve to the right.

5. At points to the right of the IS curve, there is excess supply in the goods market, at points to the left of the curve, there is excess demand for goods.