Explain how the slope of the IS curve changes if investment does not respond to changes in the real
interest rate (i.e. instead of investment being a function of the interest rate, I(r), investment is fixed at some
level regardless of the interest rate).

The slope of the investment curve is determined by the interest sensitivity coefficient. High interest sensitivity results in a more gradual slope. In this case, there is a drastic increase in investment spending in reaction to a relatively small reduction in the interest rate, because of the higher sensitivity.

Step-by-step explanation

If the investment is very sensitive to the interest rate, then a small decline in the interest rate will increase investment significantly. Therefore, the IS curve will be close to flat this means a small decrease in interest rate will cause a large increase in investment level. Thus, the IS curve will be relatively flat.

The slope of the IS curve also depends on the saving function whose slope is MPS. The higher the MPS the steeper is the IS curve. For a given fall in the interest rate the amount by which income would have to be increased to restore equilibrium in the product market is smaller, the higher the MPS.