Chapter 31, Problem 3P

Sub part (a):

To determine

Consumption schedule and marginal propensity to consume.

Explanation of Solution

Table -1 shows the consumption schedule:

Table -1

Gross domestic product	Consumption
100	120
200	200
300	280
400	360
500	440
600	520
700	600

Figure 1 illustrates the level of consumption at different level of gross domestic product (GDP).

In Figure 1, the horizontal axis measures the gross domestic output and the vertical axis measures the consumption level.

Size of marginal propensity to consume (MPC) can be calculated as follows.

$\begin{array}{c}\text{MPC}=\frac{{\text{Consumption}}_{\text{Present}}-{\text{Consumption}}_{\text{Previous}}}{{\text{Gross domestic product}}_{\text{Present}}-{\text{Gross domestic product}}_{\text{Previous}}}\\ =\frac{200-120}{200-100}\\ =\frac{80}{100}\\ =0.8\end{array}$

The size of marginal propensity to consume is 0.8.

Economics Concept Introduction

Concept introduction:

Consumption schedule: Consumption schedule refers to the quantity of consumption at different levels of income.

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

Sub part (b):

To determine

Disposable income, tax rate, consumption schedule, marginal propensity to consume and multiplier.

Explanation of Solution

Disposable income (DI) can be calculated by using the following formula.

$\text{DI}=\text{GDP}-\text{Tax}$ (1)

Substitute the respective values in Equation (1) to calculate the disposable income at the level of GDP $100.

$\begin{array}{c}\text{DI}=\text{100}-\text{10}\\ =\text{90}\end{array}$

Disposable income at the level of GDP $100 is $90.

Tax rate can be calculated by using the following formula.

$\text{Tax rate}=\frac{\text{Tax amount}}{\text{GDP}}$ (2)

Substitute the respective values in Equation (2) to calculate the tax rate at the level of GDP $100.

$\begin{array}{c}\text{Tax rate}=\frac{\text{10}}{\text{100}}\\ =0.1\end{array}$

Tax rate at the level of GDP is 10%.

New consumption level can be calculated by using the following formula.

${\text{New consumption}}_i={\text{Consumption}}_{\text{Present}}-\left({\text{Decreasing consummption}}_{\text{for \$10 tax}}\right)$ (3)

Substitute the respective values in Equation (3) to calculate the disposable income at the level of GDP $100. Since, the tax payment is equal amount of decrease in consumption for all the levels of GDP. The decreasing consumption for increasing $10 is assumed to be $8.

$\begin{array}{c}\text{New consumption}=120-8\\ =112\end{array}$

New consumption is $112.

Table -2 shows the values of disposable income, new consumption level after tax and the tax rate that are obtained by using Equations (1), (2) and (3).

Table -2

Gross domestic product	Tax	DI	New consumption	Tax rate
100	10	90	112	10%
200	10	190	192	5%
300	10	290	272	3.33%
400	10	390	352	2.5%
500	10	490	432	2%
600	10	590	512	1.67%
700	10	690	592	1.43%

Size of marginal propensity to consume (MPC) can be calculated as follows.

$\begin{array}{c}\text{MPC}=\frac{{\text{Consumption}}_{\text{Present}}-{\text{Consumption}}_{\text{Previous}}}{{\text{Gross domestic product}}_{\text{Present}}-{\text{Gross domestic product}}_{\text{Previous}}}\\ =\frac{192-112}{200-100}\\ =\frac{80}{100}\\ =0.8\end{array}$

The size of marginal propensity to consume is 0.8.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption, at a constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save. Multiplier can be evaluated using the following formula:

$\text{Multiplier}=\frac{1}{1-\text{Marginal propensity to consume}}$

Since the value of MPC remains the same for part (a) and part (b), there is no change in the value of multiplier. The value of multiplier is 5 $\left(\frac{1}{1-0.8}\right)$.

Figure -2 illustrates the level of consumption at different level of gross domestic product (GDP) for lump sum tax (Regressive tax).

In Figure -2, the horizontal axis measures the gross domestic output and the vertical axis measures the consumption level.

Economics Concept Introduction

Concept introduction:

Consumption schedule: Consumption schedule refers to the quantity of consumption at different levels of income.

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

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save.

Sub part (c):

To determine

Tax amount, consumption schedule, marginal propensity to consume and multiplier.

Explanation of Solution

Tax amount can be calculated by using the following formula.

$\text{Tax}=\text{GDP}\times \text{Tax rate}$ (4)

Substitute the respective values in Equation (4) to calculate the tax amount at $100 GDP.

$\begin{array}{c}\text{Tax}=\text{100}\times \text{0}\text{.1}\\ =10\end{array}$

Tax amount is $10.

Table -3 shows the values of disposable income, new consumption level after tax and the tax rate that are obtained by using Equations (1), (2), (3) and (4). The change in tax amount is differing for different levels of GDP. The decreasing consumption for increasing each $10 is assumed to be $8 (Thus, if the tax payment is $30, then the consumption decreases by $24 $\left(3\times 8\right)$).

Table -3

Gross domestic product	Tax	DI	New consumption	Tax rate
100	10	90	112	10%
200	20	180	184	10%
300	30	270	256	10%
400	40	360	328	10%
500	50	450	400	10%
600	60	540	472	10%
700	70	630	544	10%

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption, at a constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save. Multiplier can be evaluated using the following formula:

$\text{Multiplier}=\frac{1}{1-\text{Marginal propensity to consume}}$

Since the value of MPC different for part (a) and part (c), the value of multiplier for both the part is different. The value of multiplier is 3.57 $\left(\frac{1}{1-0.72}\right)$.

Figure -3 illustrates the level of consumption at different level of gross domestic product (GDP) for proportional tax.

In Figure -3, the horizontal axis measures the gross domestic output and the vertical axis measures the consumption level.

Economics Concept Introduction

Concept introduction:

Consumption schedule: Consumption schedule refers to the quantity of consumption at different levels of income.

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

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save.

Sub part (d):

To determine

consumption schedule, marginal propensity to consume and multiplier.

Explanation of Solution

Marginal propensity to consume can be calculated by using the following formula.

$\text{MPC}=\frac{{\text{Consumption}}_{\text{Present}}-{\text{Consumption}}_{\text{Previous}}}{{\text{Gross domestic product}}_{\text{Present}}-{\text{Gross domestic product}}_{\text{Previous}}}$ (5)

Substitute the respective values in Equation (5) to calculate the MPC at $100 GDP.

$\begin{array}{c}\text{MPC}=\frac{184-112}{200-100}\\ =\frac{72}{100}\\ =0.72\end{array}$

The value of MPC is 0.72.

Table -4 shows the values of disposable income, new consumption level after tax and the tax rate that are obtained by using Equations (1), (2), (3), (4) and (5). The change in tax amount is differing for different levels of GDP. The decreasing consumption for increasing each $10 is assumed to be $8 (Thus, if the tax payment is $20, then the consumption decreases by $16 $\left(2\times 8\right)$).

Table -3

Gross domestic product	Tax	DI	New consumption	Tax rate	MPC
100	0	100	120	0%
200	10	190	192	5%	0.8
300	30	270	256	10%	0.64
400	60	340	312	15%	0.56
500	100	400	360	20%	0.48
600	150	450	400	25%	0.4
700	210	490	432	30%	0.32

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption, at a constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save.

Multiplier value is differing for each level of GDP. When the tax rate increases, it reduces the value of MPC. Since the value of MPC decreases, the value of multiplier will also decrease.

Figure 4 illustrates the level of consumption at different level of gross domestic product (GDP) for progressive tax.

In Figure 4, the horizontal axis measures the gross domestic output and the vertical axis measures the consumption level.

Economics Concept Introduction

Concept introduction:

Consumption schedule: Consumption schedule refers to the quantity of consumption at different levels of income.

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

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save.

Sup part (e):

To determine

Marginal propensity to consume and multiplier.

Explanation of Solution

Figure 1, Figure 2, Figure 3 and Figure 4 reveals that the proportional and progressive tax system reduces the value of MPC, so that the value of multiplier also decreases. The regressive tax system (Lump sum tax) does not alter the MPC. Since there is no change in the MPC, the multiplier remains the same.

Economics Concept Introduction

Concept introduction:

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

Progressive tax: Progressive tax refers to the higher income people paying higher tax amount than the lower income people.

Proportional tax: Proportional tax rate refers to the fixed tax rate regardless of income and the tax rate and is the same for all levels of income.

Regressive tax: Regressive tax refers to the higher income people paying lower percentage of tax amount and lower income people paying higher percentage of tax amount.

Multiplier: Multiplier refers to the ratio of change in the real GDP to the change in initial consumption at constant price rate. Multiplier is positively related to the marginal propensity to consumer and negatively related with the marginal propensity to save.