Chapter 8, Problem 4.3P

Subpart (a):

To determine

Aggregate saving, unplanned investment.

Explanation of Solution

The savings can be calculated by using the following formula:

$\text{Aggregate Savings (S)}=\text{Aggregate Income (Y)}-\text{Aggregate Consumption (C)}$ (1)

Substitute the respective values in Equation (1) to calculate the aggregate saving (S).

$\begin{array}{c}\text{S=Y}-\text{C}\\ \text{S}=1,000-1,500\\ =-500\end{array}$

Thus, the aggregate saving is -$500 at the aggregate income is $1,000 and consumption is $1,500.

The unplanned investment can be calculated by using the following formula:

$\text{Unplanned investment (UI)}=\left[\begin{array}{l}\text{Aggregate Income (Y)}-\\ \left(\begin{array}{l}\text{Aggregate Consumption (C)}\\ \text{+ Planned investment (I)}\end{array}\right)\end{array}\right]$ (2)

Substitute the respective values in Equation (2) to calculate the unplanned investment.

$\begin{array}{c}\text{UI=Y}-\left(\text{C+I}\right)\\ =1,000-\left(1,500+250\right)\\ =1,000-1,750\\ =750\end{array}$

Thus, the unplanned investment is -$750 at the aggregate income is $1,000 and consumption is $1,500.

Table -1 shows the value of the aggregate saving and unplanned investment obtained by using Equation (1) and (2).

Table – 1

Aggregate Income (Y) (in $)	Aggregate Consumption (C) (in $)	Planned investment (I) (in $)	Aggregate Saving (S) (in $)	Unplanned investment (UI) (in $)
1,000	1,500	250	-500	-750
1,500	1,875	250	-375	-625
2,000	2,250	250	-250	-500
2,500	2,625	250	-125	-375
3,000	3,000	250	0	-250
3,500	3,375	250	+125	-125
4,000	3,750	250	+250	0
4,500	4,125	250	+375	+125

The economy will be in equilibrium when $\text{C+I=Y}$ and this happens at the point when the aggregate output is $4,000. At this point, the unplanned inventory is 0.

When the aggregate output is lower than the equilibrium point, the unplanned investment is negative, this implies the inventories are lower than desired. So the firm will expand production to increase inventories thereby increasing the aggregate output.

When the aggregate output is above the equilibrium point, the unplanned investment is positive, this implies the inventories are higher than desired. So the firm will reduce production to decrease inventories thereby decreasing the aggregate output.

Economics Concept Introduction

Concept introduction:

Aggregate output: Aggregate output refers to the total quantity of goods and services produced over a given period of time in an economy.

Consumption function: The consumption function is the relationship between consumption and disposable income.

Saving: The saving is an income that is used by a consumer to spend for future consumption.

Subpart (b):

To determine

MPC, MPS and Multiplier.

Explanation of Solution

Marginal propensity to consume (MPC):

The marginal propensity to consume can be calculated by using the following formula:

$\text{MPC}=\frac{{\text{Consumption}}_{\text{Present}}-{\text{Consumption}}_{\text{Previous}}}{{\text{Income}}_{\text{Present}}-{\text{Income}}_{\text{Previous}}}$ (3)

Substitute the respective values in Equation (3) to calculate the marginal propensity to consume.

$\begin{array}{c}\text{MPC}=\frac{\text{1,875}-1,500}{1,500-1,000}\\ =\frac{375}{500}\\ =0.75\end{array}$

Thus, the marginal propensity to consume is 0.75, which is applicable for all ranges since the change in consumption and change in income is same throughout.

Marginal propensity to save (MPS):

The marginal propensity to save can be calculated by using the following formula:

$\text{MPS}=\frac{{\text{Saving}}_{\text{Present}}-{\text{Saving}}_{\text{Previous}}}{{\text{Income}}_{\text{Present}}-{\text{Income}}_{\text{Previous}}}$ (4)

Substitute the respective values in Equation (4) to calculate the marginal propensity to save.

$\begin{array}{c}\text{MPS}=\frac{-\text{375}-\left(-\text{500}\right)}{1,500-1,000}\\ =\frac{125}{500}\\ =0.25\end{array}$

Thus, the marginal propensity to save is 0.25 which is applicable for all ranges since the change in saving and change in income is same throughout.

Multiplier:

The multiplier is calculated as follows:

$\begin{array}{c}\text{Mutliplier =}\frac{1}{\text{MPS}}\\ =\frac{1}{0.25}\\ =4\end{array}$

The multiplier is 4.

Economics Concept Introduction

Concept introduction:

Marginal propensity to consume (MPC): Marginal propensity to consume refers to the sensitivity of change in the consumption level due to the changes occurred in the income level.

Marginal propensity to save (MPS): The ratio of change in saving when there is a change in disposable income.

Multiplier: Multiplier is defined as the number which denotes the proportionate increase in income due to increase in investment.

Subpart (c):

To determine

Aggregate saving, unplanned investment.

Explanation of Solution

The new planned investment is $375$\left(125+250\right)$

Substitute the values in Equation (1) to calculate the aggregate saving (S).

$\begin{array}{c}\text{S=Y}-\text{C}\\ \text{S}=1,000-1,500\\ =-500\end{array}$

Thus, the aggregate saving is -$500 at the aggregate income is $1,000 and consumption is $1,500.

Substituting the respective values in Equation (2) the new unplanned investment is calculated as follows.

$\begin{array}{c}\text{UI=Y}-\left(\text{C+I}\right)\\ =1,000-\left(1,500+375\right)\\ =1,000-1,875\\ =-875\end{array}$

Thus, the unplanned investment is -$875 at the aggregate income is $1,000 and consumption is $1,500.

Table -2 shows the value of the aggregate saving and the new unplanned investment obtained by using Equation (1) and (2).

Table – 2

Aggregate Income (Y) (in $)	Aggregate Consumption (C) (in $)	Planned investment (I) (in $)	Aggregate Saving (S) (in $)	Unplanned investment (UI) (in $)
1,000	1,500	375	-500	-875
1,500	1,875	375	-375	-750
2,000	2,250	375	-250	-625
2,500	2,625	375	-125	-500
3,000	3,000	375	0	-375
3,500	3,375	375	+125	-250
4,000	3,750	375	+250	-125
4,500	4,125	375	+375	0

The economy will be in equilibrium when $\text{C+I=Y}$ and this happens at the point when the aggregate output is $4,500. At this point, the unplanned inventory is 0.

If the planned investment (I) increases by $125 (250 to 375), then the income rises by $500 $\left(4\times 125\right)$ which is 4 times the increase in I. This implies the computation is consistent with the value obtained by multiplier.

Economics Concept Introduction

Concept introduction:

Aggregate output: Aggregate output refers to the total quantity of goods and services produced over a given period of time in an economy.

Consumption function: The consumption function is the relationship between consumption and disposable income.

Saving: The saving is an income that is used by a consumer to spend for future consumption.

Planned investment: It includes additions to the capital stock and inventories and all those investments firms plan to make.