   Chapter 12, Problem 44RE ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# National consumption Suppose that the marginal propensity to save is d S d y = 0.2 − 0.1 e − 2 y and consumption is $7.8 billion when disposable income is$0. Find the national consumption function.

To determine

To calculate: The national consumption function If consumption is $7.8 billion when disposable income is$0 billion and if the marginal propensity to save is dSdy=0.20.1e2y.

Explanation

Given Information:

The consumption is $7.8 billion when disposable income is$0 billion and if the marginal propensity to save is dSdy=0.20.1e2y.

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=0.20.1e2y

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

dSdy=1dCdydCdy=1dSdy=1(0.20.1e2y)=0.8+0.1e2y

And the consumption is $7.8 billion when disposable income is$0 so;

dCdy=0.8+0.1e2ydC=(0

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