Question

Suppose that the marginal propensity to save is dS/dy=0.2-0.1e^-2y and the consumption is 7.8 trillion when disposable income is $0. Find the national consumption function: C(y)=?

Note:In my textbook, the answer is C(y)=0.8y-0.05e^-2y+7.85. I like to know why/how?

Answer 1

We have the following information:-

MPS	dS/dy=0.2-`
Consumption	7.8
Disposable inc	0

National consumption function c(y) is in trillions of dollars with y being the disposable income

We know that MPC = 1-MPS

so MPC = 1-0.2-0.1e^-2y

Now that we know dC/dy we can anti-differentiate to find C(y)

This will result in an unknown constant C which can be solved since we know C(0) = $7.8 trillion

anti-differential of (1-.2) =.8y

anti-differential of 0.1e^-2y =

This results in = (e^?2y^2)/20 + C =-.05e^-2y^2+7.8

hence c(y)=0.8y-0.05e^-2y^2+7.8

unfortunately, I am not able to get to the exact answer but I think the approach is correct