# The IS-LM model with inflation

## The basic assumption

In Chapter 12, we developed the IS-LM model with constant wages and prices. We can now extend this model to allow for inflation. Instead of constant wages and prices, we must assume that n = nW = if. In the same that we dropped the assumption of constant P when we went on to the AS-AD model to allow for changes in real wages, we will drop the assumption that n = nW in section 1.4 to allow for inflation and changing real wages.

Let us briefly justify the assumption n = nW = if. nW = if may be explained by realizing that if workers expect 6% inflation, they will demand 6% wage increases to maintain the same real wage (they usually require more than 6% and an increase in real wages, but this is because the growth of the economy will allow for this - always think of these models as if there is no growth).

The assumption n = nW means that we have a balanced inflation. As in the IS-LM model, the real wage is then constant. This is a reasonable assumption if the economy is in a state where aggregate demand is insufficient and L is lower than the profit-maximizing level.

## Results

If n„, = n and if = n, both the IS- and the LM-curve will be fixed.

Fig. 14.4:The money market with inflation and constant money supply growth.

It is then possible to determine R* and Y * exactly as we did in chapter 12. We can also determine the real interest rate as r = R - if and if is given. All variables are now determined. Since n and nW are exogenous, P and W are given over time (as long as we know P and W at one point in time). L is determined exactly as chapter 12 and we do not allow L to exceed LOpT as this would require a drop in real wages n > nW at least for a while.

If, for example nM < n, the LM curve will glide upwards, R (and r) will increase while Y will fall. In a model with inflation, we typically consider changes in the growth of the money supply, nM, rather than changes in the in the money supply itself when we discuss monetary policy.

# The AS-AD model with inflation

In chapter 13 we removed the assumption of constant prices to allow varying real wages. The resulting model was called the AS-AD model. In the same way, we now remove the assumption that n = nW (but remember the discussion in 14.1.2 - n may only deviate from nW temporarily and they must be equal on the average).

## The AD-curve at a given point in time

The AD-curve, just like before, displays combinations of P and Y where both the money market and the goods market are in equilibrium. At any given time, even when we have inflation, aggregate demand will as before depend negatively on P. The explanation, as follows, is little more involved.

Say that the price level one year ago was 100 and that P is the price level today. Then n = (P - 100)/100 is the rate of inflation during the previous year and P = (1 + n)100 today. For example, if n is 10%, we have P = (1 + 0.1)100 = 110 today. Given the price level in the previous year, we have a positive relationship between P and i .

Given price level last year, there is a price level today which would make inflation exactly the same as the growth rate in money supply over the last year. For example, say that i M was 4% in the previous year and P was 100 a year ago, then if P = 104 today we have i = i M, the IS- and LM-curves are stable and we can find the level of GDP which gives the equilibrium in both markets by finding the point where they intersect.

Now, to show that the AD curve slopes downwards, we must show that if P > 104, a lower level of GDP will result in simultaneous equilibrium. To see this, simply note that for P > 104, the inflation has been a little higher and the LM curve will be a little higher up resulting in a lower level of GDP. A similar argument shows that GDP must be higher if P < 104 for both markets to remain in equilibrium.

Thus, at a given point in time, given the price level last year, aggregate demand will still depend negatively on P and the AD curve will slope downwards.