Chapter 1.6, Problem 16E

a.

To determine

To graph: the consumption function.

Answer to Problem 16E

  

Explanation of Solution

Given information:

The given equation for consumption function is as follows:

  $y=0.82x+24,\text{ where }x\ge 0$

Here, $x$ is nation’s disposable income, and $y$ is personal consumption expenditure.

Both $x$ and $y$ are in billions of dollars.

Calculation:

Put the values in the equation and make a table of values as shown below.

$x$	0	1	2	3	4	5	6
$y$	24	24.82	25.64	26.46	27.28	28.1	28.92

The graph for the given data is shown below.

  

b.

To determine

To find: the y -intercept.

Answer to Problem 16E

24

Explanation of Solution

Given information:

The given equation for consumption function is as follows:

  $y=0.82x+24,\text{ where }x\ge 0$

Here, $x$ is nation’s disposable income, and $y$ is personal consumption expenditure.

Both $x$ and $y$ are in billions of dollars.

Calculation:

Put $x=0$ in the equation and find y- intercept as follows:

  $\begin{array}{l}y=0.82x+24\\ y=0.82\left(0\right)+24\\ y=0+24\\ y=24\end{array}$

Thus, the y -intercept is 24.

c.

To determine

To explain: the significance of y- intercept and slope.

Answer to Problem 16E

Significance of y- intercept: If the disposable income is $0, the money spent on personal consumption expenditure is $24.

Significance of slope: For every billion dollars spent from disposable income, $0.82 billion is spent on personal consumption expenditures.

Explanation of Solution

Given information:

The given equation for consumption function is as follows:

  $y=0.82x+24,\text{ where }x\ge 0$

Here, $x$ is nation’s disposable income, and $y$ is personal consumption expenditure.

Both $x$ and $y$ are in billions of dollars.

Calculation:

Compare the equation with slope intercept formula to find m as follows:

  $\begin{array}{l}y=mx+b\\ y=0.82x+24\\ \therefore m=0.82\text{ and }b\left(y\text{-intercept}\right)=24\end{array}$

The significance of y- intercept is that, if the disposable income is $0, the money spent on personal consumption expenditure is $24.

The significance of slope is that, for every billion dollars spent from disposable income, $0.82 billion is spent on personal consumption expenditures.