Chapter 12.4, Problem 21E

### 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

# Suppose that the marginal propensity to consume is d C d y = 0.7 − e − 2 y and that consumption is $5.65 trillion when disposable income is$0. Find the national consumption function.

To determine

To calculate: The national consumption function If consumption is $5.65 trillion when disposable income is$0 trillion and if the marginal propensity to consume is dCdy=0.7e2y.

Explanation

Given Information:

The consumption is $5.65 trillion when disposable income is$0 trillion and if the marginal propensity to consume is dCdy=0.7e2y.

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 n1

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 consume is;

dCdy=0.7e2y

Here, y is the national disposable national income

To find the National consumption function C, integrate the above expression with respect to y as;

C=(0

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