## The IS relation

The **IS relation** is the other building block of the ISLM model, along with the LM relation. The LM relation shows us how the interest rate depends on income in the economy through the relationship between supply and demand in the money market. At higher levels of income, the money market requires a higher rate of interest to bring the supply and demand for money into equilibrium, which is why the LM curve is upward sloping.

The IS relation now shows us how income in the economy depends on the interest rate, through the relationship between supply and demand in the goods market. The key channel here to think about, is investment, in the simplified Keynesian model of AD, Y=C+I+G. Investment depends **negatively** on the interest rate, firms are more willing to invest when interest rates are low, so high interest rates will mean investment is lower and low interest rates will mean investment is higher. If you increase or decrease I in the Keynesian model, you will increase or decrease Y. So you get a downward sloping relationship between interest rates and output, the IS relation:

What the IS curve is telling you, is that given a certain rate of interest, i, the goods market will come into equilibrium at a certain level of income, Y. The lower the rate of interest is, the more investment there will be in the economy, so the supply and demand comes into equilibrium at a higher level of output (or income).

You need to think about the Keynesian Cross model to understand the IS relation. Remember the effect of increasing I on the Keynesian Cross, means you shift the planned expenditure curve up, and you get a higher equilibrium level of Y. So higher I = higher Y. This is basically what happens when you **move down** the IS curve. The interest rate is getting lower so firms are investing more, higher I means higher income.

The Keynesian Cross also tells us about what to do on the IS curve if we get changes in autonomous consumption, government spending or taxation. Remember that an increase in a or an increase in G, or a decrease in T, shifts the planned expenditure curve up, so you get a higher equilibrium level of Y. This tells us that if we increase a or G, or decrease T, then we need to be at a higher level of Y on the IS relation – but those factors don’t depend on the interest rate, so they are not captured in the downward sloping line. So if you increase a or G, or decrease T, you have to **shift the whole IS curve** over to the right. The IS relation is basically telling us what level of Y will put the goods market into equilibrium at any given level of interest rate. So if we shift the curve over to the right, it means we have a higher level of Y at any given of interest rate – so if the interest rate stays constant, and I stays constant, but G for instance is higher, then we will get higher Y.

And what about if b, the marginal propensity to consume increases? Remember that b gives us the slope of the planned expenditure curve in the Keynesian Cross. If b increases, then this slope gets steeper. So if you start from the same point where the planned expenditure curve intersects the vertical axis, and draw a steeper line, it will intersect the 45 degree line, at a higher level of Y. So an increase in marginal propensity to consume also increases Y – another thing that we can capture in the IS relation by shifting the whole curve to the right (unless we take the mpc to be endogenous, ie dependent on the interest rate, which it may well be, but it is not treated as such in this model, just to keep it simple.)

So to sum up:

The IS curve is **downward sloping**, as the interest rate increases, income in the economy decreases

The IS curve **shifts out to the right** when there is an increase in government spending (a **fiscal expansion**) or an increase in consumer confidence that would increase autonomous consumer spending or increase the marginal propensity to consume.

The IS curve **shifts in to the left** when there is a decrease in government spending (a **fiscal contraction**) or an decrease in consumer confidence that would decrease autonomous consumer spending or decrease the marginal propensity to consume.