Macroeconomics – IS Curve – steepness and interest sensitivity

Dear Economics Community

Could you please answer me whether the following statement is true, false or uncertain and illustrate by graph please?

“Other things equal, an IS curve is steeper, the more sensitive consumption is to the rate of interest”. True, false or uncertain? Briefly explain your answer.

As I am stuck with some questions. I break them into topics. I hope you can respond to me quickly. Thanks, Katie
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Katie,

This is a commonly asked question regarding the IS curve since it examines the very basis of the IS curve. The IS curve shows the combination of interest rates and national income that result in equilibrium in the goods market. The IS curve slopes downward because increases in the interest rate cause investment to fall, and thus reduce income through the multiplier:

(IS)    Y = C(Y, t) + I(i) + G + X(R) -M(R, Y), where R is the real exchange rate (eP* /P)

The slope depends of the responsiveness of investment to changes in the interest rate, and the magnitude of the autonomous investment multiplier. You plot Interest Rates on the Y-axis and National Income on the X-axis. Steepness then increases as the impact of interest rates decreases.

 

IS Curve 

Curve IS is not as steep as curve IS1. IS shows more impact on national income due to changes in interest rate, so LESS steepenss means MORE sensistivity.