Question

. YOU ARE GIVEN THE FOLLOWING INFORMATION ABOUT THE ECONOMY OF ENGLAND. PLEASE ANSWER QUESTIONS A THROUGH C AND SHOW ALL WORK AND CALCULATIONS BELOVW DISPOSABLE INCOME CONSUMPTION (BILLIONS OF DOLLARS PER YEAR) $200 $100 S20 S30 $40 S360 $440 S520 A CALCULATE THE MARGINAL PROPENSITY TO CONSUME(MPC) AT EACH LEVEL OF DISPOSABLE INCOME AND CONSUMPTION LEVEL. INTERPET WHAT THE MPC NUMBER YO CALCULATED MEANS TO YO B. CALCULATE SAVINGS AT EACH LEVEL OF DISPOSABLE INCOME AND CONSUMPTION LEVEL. c. CALCULATE THE MARGINAL PROPENSITY TO SAVE(MPS) AT EACH LEVEL OF DISPOSABLE INCOME AND CONSUMPTION LEVEL. INTERPRET WHAT THE MPS NUMBER YO CALCULATED MEANS TO YO WHAT HAPPENS TO SAVINGS, THE MPC AND THE MPS WHEN CONSUMPTION AND DISPOSABLE INCOME INCREASES OR DECREASES? ALSO, DOES MPC +MPS-1 EXPLAIN WHY OR WHY NOT.

Answer 1

The following table is provided in the problem:

S. No.	Disposable Income (Billions of $ per year)	Consumption (Billions of $ per year)
1.	$ 0	$ 200
2.	$ 100	$ 280
3.	$ 200	$ 360
4.	$ 300	$ 440
5.	$ 400	$520

A. The marginal propensity to consume is the proportion of change in income that the consumer spends on consumption. It measures the ratio of change in consumption due to change in disposable income. It is denoted by 'c' and is calculated by the formula:

A. The marginal propensity to consume is the proportion of change in income that the consumer spends on consumption. It measures the ratio of change in consumption due to change in disposable income. It is denoted by 'c' and is calculated by the formula: MPC = c = delta C/delta Y Here, Delta C refers to the change in consumption and Delta Y refers to the chnage in income. The marginal propensity to consume for the provided disposable incomes (Y_1 = 0 Y_2 = 100 Y_3 = 200 Y_4 = 300 Y_5 = 400) and consumption (C_1 = 200 C_2 = 280 C_3 = 360 C_4 = 440 C_5 = 520) is: MPC = c = delta C/delta Y = C_2 - C_1/Y_2 - Y_1 = 280 - 200/100 - 0 = 80/100 = 0.8 MPC = c = delta C/delta Y = C_3 - C_2/Y_3 - Y_2 = 360 - 280/200 - 0 = 80/100 = 0.8 MPC = c = delta C/delta Y = C_4 - C_3/Y_4 - Y_3 = 440 - 360/300 - 0 = 80/100 = 0.8 MPC = c = delta C/delta Y = C_5 - C_4/Y_5 - Y_4 = 520 - 440/400 - 0 = 80/100 = 0.8 Hence, the marginal propensity to consume at each level of disposable income and consumption is 0.8. This means that for every dollar of income increase, the consumer spends 0.8 dollars for his consumption. B. The disposable income is used for either consumtion or saving. That is, Income = Consumption + Saving Saving = Income -Consumption

Here, $\Delta C$ refers to the change in consumption and $\Delta Y$ refers to the chnage in income.

The marginal propensity to consume for the provided disposable incomes and consumptions is:

$MPC=c=\frac{\Delta C}{\Delta Y}=\frac{C_{3}-C_{2}}{Y_{3}-Y_{2}}=\frac{360-280}{200-0}=\frac{80}{100}=0.8$
$MPC=c=\frac{\Delta C}{\Delta Y}=\frac{C_{4}-C_{3}}{Y_{4}-Y_{3}}=\frac{440-360}{300-0}=\frac{80}{100}=0.8$
$MPC=c=\frac{\Delta C}{\Delta Y}=\frac{C_{5}-C_{4}}{Y_{5}-Y_{4}}=\frac{520-440}{400-0}=\frac{80}{100}=0.8$
Hence, the marginal propensity to consume at each level of disposable income and consumption is 0.8. This means that for every dollar of income increase, the consumer spends 0.8 dollars for his consumption.

B. The disposable income is used for either consumtion or saving. That is,

Income = Consumption + Saving

Saving = Income -Consumption

The savings for the provided disposable incomes and consumptions are:

S. No.	Disposable Income (Billions of $ per year)	Consumption (Billions of $ per year)	Savings: S = Y - C
1.	$ 0	$ 200	$ -200
2.	$ 100	$ 280	$ -180
3.	$ 200	$ 360	$ -160
4.	$ 300	$ 440	$ -140
5.	$ 400	$520	$ - 120

C. The marginal propensity to save is the proportion of change in income that the consumer saves. It measures the ratio of change in saving due to change in disposable income. It is denoted by 's' and is calculated by the formula:

$MPS=s=\frac{\Delta S}{\Delta Y}$
Here, $\Delta S$ refers to the change in consumption and $\Delta Y$ refers to the chnage in income.
The marginal propensity to consume for the provided disposable incomes and savings $\left ( S_{1}=$ -200, S_{2}=$ -180, S_{3}=-160, S_{4}=-140, S_{5}=-120)$ is:

$MPS=s=\frac{\Delta S}{\Delta Y}=\frac{S_{2}-S_{1}}{Y_{2}-Y_{1}}=\frac{-180-\left ( -200 \right )}{100-0}=\frac{-180+200}{100}=\frac{20}{100}=0.2$
$MPS=s=\frac{\Delta S}{\Delta Y}=\frac{S_{3}-S_{2}}{Y_{3}-Y_{2}}=\frac{-160-\left ( -180 \right )}{100-0}=\frac{-160+180}{100}=\frac{20}{100}=0.2$
$MPS=s=\frac{\Delta S}{\Delta Y}=\frac{S_{4}-S_{3}}{Y_{4}-Y_{3}}=\frac{-140-\left ( -160 \right )}{100-0}=\frac{-160+140}{100}=\frac{20}{100}=0.2$

$MPS=s=\frac{\Delta S}{\Delta Y}=\frac{S_{5}-S_{4}}{Y_{5}-Y_{4}}=\frac{-120-\left ( -140 \right )}{100-0}=\frac{-140+120}{100}=\frac{20}{100}=0.2$

Hence, the marginal propensity to save at each level of disposable income, consumption and calculated savings is 0.2. This means that for every dollar of income increase, the consumer saves 0.2 dollars.