Lecture 17: The IS/LM Model (1)

1. Lecture 17: The IS/LM Model (1) Based Primarily on Mankiw Chapter 10

2. Introduction & Learning Objectives • Today we will derive an IS curve and examine what determines the slope and position of the IS curve. • There are two ways to do this: using either the Keynesian cross model (traditional way), or using the neoclassical model (simpler). We will consider both derivations in turn. • In the next lecture we will derive an LM curve and examine what determines its slope and position. • After this, we will put the two curves together and present the complete IS/LM model. • This model is the basis for the claim made earlier that in the short-run both the goods market and the money market simultaneously determine r and Y.

3. The Keynesian Cross (1) Planned Expenditure, E Actual Expenditure, Y=E Planned expenditure, E = C(Y-T*) + I* + G* Using the Keynesian cross diagram we can see that the economy’s equilibrium income level is Y*. Whenever the economy is away from equilibrium, firms experience unplanned stock accumulation which acts as a signal for them to change production. a + I* + G* 45 Income, Output Y*

4. The Keynesian Cross (2) • The Keynesian cross is useful because it shows how the spending plans of households, firms and the government determine the economy’s income. • We also noted in the last lecture how fiscal policy (changes in taxes and spending) can move the economy from a “bad” equilibrium (one with a low level of Y) to a good equilibrium (one with a level of Y closer to the natural rate of output). • In effect, the government can exploit the multiplier process and improve output and employment in the economy.

5. Theoretical Weakness • Although the Keynesian cross is useful, it makes the simplifying assumption that the level of planned investment in the economy, I, is fixed at I*. This is unrealistic. • As we saw in earlier lectures, an important macroeconomic relationship is that planned investment depends on the real interest rate, r. • I = I(r) and it is assumed that whenever r rises then I falls. dI/dr < 0.

6. Constructing The IS Curve • To determine how income changes when the interest rate changes, we can combine the investment function with the Keynesian cross diagram. • Because investment is inversely related to the interest rate, an increase in the interest rate from r1 to r2 reduces the quantity of investment from I(r1) to I(r2). • The reduction in planned investment, in turn, shifts the planned-expenditure function downward. The shift in the planned-expenditure function causes the level of income to fall from Y1 to Y2. • Hence, an increase in the interest rate lowers income. • The IS curve summarises the relationship between the interest rate and the level of income. • The IS curve is downward sloping in {r, Y} space.

8. The Slope Of The IS Curve • The causality involved in constructing an IS curve is as follows • r changes  I changes  planned expenditure changes  Y changes. • Thinking about this causality carefully, we can see that the slope of the IS curve will depend upon the interest elasticity of investment and the multiplier. • For any given value of the multiplier, an increase in the interest elasticity of investment will make the IS curve relatively flatter. • Similarly, if the interest elasticity of investment is held constant, a reduction in the multiplier will make the IS curve relatively steeper.

9. Second Derivation • An simpler derivation comes from the neoclassical model. • Y = C + I + G • C = C(Y - T) • I = I(r) • G = G* • T = T* • Previously we would be assuming Y = Y* = F(K*, L*). • However, in the short-run (Keynesian model) Y is a variable. • Y = C(Y - T*) + I(r) + G* • I(r) = Y - C(Y - T*) - G*

10. Second Derivation (continued) • RHS of equation is Y - C(Y - T*) - G* • As Y rises (by Y), the first term on the RHS gets larger as does the second term (C(Y - T*)). However, the second term only increases by MPC  Y < Y. • Given that G is fixed the whole RHS increases in value when Y rises. • To preserve the equality the LHS must rise in value too. This means that I must rise. The only way this can happen is if r falls. • This is easy to see when we recall our basic equilibrium diagram from the neoclassical model and remove the restriction that Y is fixed at Y*. Again, IS is downward sloping in {r, Y} space.

11. Fiscal Policy And The IS Curve • The IS curve is drawn under the assumption that fiscal policy is held constant. • When we draw the IS curve, G and T are held fixed. • The following slide uses the Keynesian cross to show how an increase in government spending from G1 to G2 shifts the IS curve. This figure is drawn for a given interest rate and thus for a given level of planned investment. The Keynesian cross shows that this change in fiscal policy raises planned expenditure and thereby increases equilibrium income from Y1 to Y2 . • Therefore, an increase in government spending shifts the IS curve outward (to the right). The same is true of a tax cut. • Reduced government spending and increased taxes will shift the IS curve inward (to the left).

13. Summary of IS Curve • The IS curve shows the combinations of r and Y that are consistent with equilibrium in the goods market. • The IS curve has a negative slope because reductions in r increase planned investment spending and thus, through the Keynesian cross, raise the level of income/output Y. • The multiplier and the interest elasticity of investment influence the slope of the IS curve. • Fiscal policy is one factor that influences the position of the IS curve.