# 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***In the same that we dropped the assumption of constant*

**if.***when we went on to the AS-AD model to allow for changes in real wages, we will drop the assumption that*

**P***=*

**n***in section 1.4 to allow for inflation and changing real wages.*

**nW**Let us briefly justify the assumption * n *=

*=*

**nW***=*

**if. nW***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).*

**if**The assumption * n *=

*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*

**nW***is lower than the profit-maximizing level.*

**L**## Results

If * n„, *=

*and*

**n***=*

**if***, both the IS- and the LM-curve will be fixed.*

**n****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***and*

**if***is given. All variables are now determined. Since*

**if***and*

**n***are exogenous,*

**nW***and*

**P***are given over time (as long as we know*

**W***and*

**P***at one point in time).*

**W***is determined exactly as chapter 12 and we do not allow*

**L***to exceed*

**L***as this would require a drop in real wages*

**LOpT***>*

**n***at least for a while.*

**nW**If, for example * nM *< n, the LM curve will glide upwards,

*(and r) will increase while*

**R***will fall. In a model with inflation, we typically consider changes in the*

**Y***of the money supply,*

**growth***rather than changes in the in the money supply itself when we discuss monetary policy.*

**nM,**# 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 *=

*(but remember the discussion in 14.1.2 -*

**nW***may only deviate from*

**n***temporarily and they must be equal on the average).*

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

The AD-curve, just like before, displays combinations of * P *and

*where both the money market and the goods market are in equilibrium.*

**Y***The explanation, as follows, is little more involved.*

**At any given time, even when we have inflation, aggregate demand will as before depend negatively on P.**Say that the price level one year ago was 100 and that * P *is the price level today. Then

*= (P - 100)/100 is the rate of inflation during the previous year and*

**n***= (1 + n)100 today. For example, if*

**P***is 10%, we have*

**n***= (1 + 0.1)100 = 110 today.*

**P***the price level in the previous year, we have a positive relationship between*

**Given***and*

**P***.*

**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

*was 100 a year ago, then if*

**P***= 104 today we have*

**P***=*

**i***, 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.*

**i M**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

*> 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.*

**P**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.