# Derivation of an IS curve

Derive the IS curve with the aid of diagrams

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Plotting the second point

To derive the second point we assume that a decrease in the interest rate takes place from i2 to i1. According to our investment schedule the level of investment increases to I2.

In the goods market the increase in investment spending increases the demand for goods.  The demand for goods curve shifts upwards.  The shift in the demand for goods is equal to the increase in investment (which is the result of a decrease in the interest rate).  At the initial level of equilibrium income, an excess demand is created and the increase in investment has a multiplier effect on the level of income and output. Eventually goods market equilibrium is achieved at point 2 with a corresponding level of equilibrium income of  Y2.

From the information in diagrams (a) and (b), namely that at an interest rate of i1 a goods market equilibrium occurs at an income level of Y2 the second point of our IS curve is plotted. Note that point 2 in diagram (c) corresponds to  point 2 in diagram (b) and indicates a goods market equilibrium position.

By assuming different interest rates we can derive a number of corresponding goods market equilibrium positions which will eventually gives us the IS curve. We will take a short cut by drawing a straight line  through points 1 and 2. This then is our IS curve showing combinations of interest rates and income levels where the goods market equilibrium is in equilibrium, given that all autonomous variables are unchanged

Comparing point 1 with point 2 we see that at both points the goods market is in equilibrium, that is,  where Z = Y.  The demand for goods is however higher at point 2 than at point 1 due to the lower interest rate which causes an increase in investment spending as well as a higher consumption spending by households due to the higher level of income