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Prove that b = the slope of the consumption function curve explain

Prove that b = the slope of the consumption function curve explain

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Answer #1

Consumption function is given by, C = C1 + bYd
where C1 is the autonomous consumption and thus it is constant, b is the marginal propensity to consume, and Yd is the disposable income.
We know that slope of any function is dY/dX. So, here, slope of the consumption function is dC/dYd as C lies on the Y-axis and Yd lies on the X-axis.
Now, dc from the consumption function as C1 is constant.
So, the slope of the consumption function is b.

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