Chapter 12.4, Problem 26E

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

Chapter
Section

### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# If consumption is $3 trillion when disposable income is$0 and if the marginal propensity to save is d S d y = 0.2 + e − 1.5 y find the national consumption function.

To determine

To calculate: The national consumption function If consumption is $3 trillion when disposable income is$0 trillion and if the marginal propensity to save is dSdy=0.2+e1.5y.

Explanation

Given Information:

The consumption is $3 trillion when disposable income is$0 trillion and if the marginal propensity to save is dSdy=0.2+e1.5y.

Formula used:

The power rule of integration is;

The integration of function f(x)=xn is given by;

xndx=xn+1n+1+c n1

The integration of function f(x)=eax is given by;

eaxdx=eaxa+c

Here c is any arbitrary constant.

The sum rule is;

f(x)±g(x)dx=f(x)dx±g(x)dx

Calculation:

Consider the marginal propensity to save is;

dSdy=0.2+e1.5y

And the marginal propensity to save is 1 minus the marginal propensity to consume,

dSdy=1dCdydCdy=1dSdy=1(0.2+e1.5y)=0.8e1.5y

And the consumption is $3 trillion when disposable income is$0 so;

dCdy=0.8e1.5ydC=(0.8e1

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