The IS Curve Derived & Explained
By Steve Bain
The IS curve adds more detail to the Keynesian economic model that I have been developing, but to understand it you first need to understand the more basic models on other pages.
In particular I would advise you to start with my page about the Consumption Function before reading this page because you will need the information on that page to make sense of what follows here.
If you already understand the necessary prerequisites, you find that this page is really easy to understand.
Before I get going, keep in mind that the IS curve is a continuation of Keynesian economic theory, and as such the usual assumptions apply i.e. that this is a short-run model of the economy in which production can be increased without any impact on the price level.
Okay, this diagram might look a little intimidating to some people but, if you read up on the consumption function as suggested, it will quickly become virtually self-explanatory.
The top half of the diagram should look familiar, it is a simple output expenditure model that shows how an increase in the consumption function leads to an increase in national income/output (with implied increase in employment).
The bottom half of the diagram is the new part that builds new depth to the model.
The IS curve introduces interest rates into the model where previously they had been absent. Investment had been held as one of the autonomous components of aggregate demand that fluctuated according to the level of business confidence, but here we add an extra dimension to show that investment levels are also higher when interest rates are lower.
The downward sloping IS curve illustrates this concept, with the interest rate plotted on the vertical axis against national income/output on the horizontal axis.
The reason why lower interest rates encourage more investment is because business can borrow money more cheaply when interest rates are lower, meaning that more investment projects become viable. In other words, at high interest rates some potential investment projects are ruled out because they are deemed unlikely to make enough profit to cover the expense of borrowing, but as that cost comes down those projects become profitable.
In the diagram, a reduction in the interest rate from R1 to R2 led to a boost in the consumption function from CF1 to CF2, and the economy expanded until a new equilibrium income/output level was achieved at Y2.
From the consumption function, the IS curve has been derived.
The slope of the IS Curve
Adding a little more complexity to the IS curve we can relate it to the Keynesian Multiplier, and as before I recommend that you click the link to get the background information on that concept in order to understand the next diagram.
The slope of the IS curve relates to the size of the multiplier. Starting with the top part of the diagram, imagine that for some reason consumer confidence rises in such a way that people start spending more of their money rather than saving it.
This is not uncommon, and sometimes signals the start of a bubble market e.g. in housing.
As people increase their spending, consumption increases and the consumption function gets steeper, as shown by the move from CF1 to the dashed line CF2.
This will cause an increase in national income as firms raise output and employment levels. Gradually, income rises from Y1 to Y2.
Now, since the increase in output was driven by an upturn in consumer confidence that led to an increase in spending (rather than a reduction in the interest rate spurring on extra investment), the interest rate is unchanged in the bottom half of the diagram at R1.
Of course, this sort of extra spending in the economy will lead to extra profits being earned by businesses, which may in turn lead to an increase in business confidence such that investment levels increase at the existing interest rate. This could lead to the same shift in the IS curve that an increase in government spending would cause - see the next diagram for an explanation.