Chapter 26, Problem 13P

To determine

To determine: The aggregate consumer function, income-expenditure equilibrium and the value of the multiplier.

Concept Introduction:

Gross Domestic Product (GDP): It is defined as the value of output which is produced inside the border of a country in the given interval of time.

The formula to calculate change in GDP is:

Here,

• is autonomous spending.
• MPC is marginal propensity to consume.

Marginal Propensity to Consume (MPC): It is defined as the change which occurs in total consumption level due to a change in disposable income.

The formula to calculate MPC is:

Here,

• is change in disposable income.
• is change in consumption level.
• MPC is marginal propensity to consume.

Multiplier: It is defined as the ratio of total change in the gross domestic product due to a change in the autonomous spending.

The formula to calculate multiplier is:

Here,

• MPC is marginal propensity to consume.

Consumption Level (C): It is one of the largest components of GD .The individual consumption depends on the disposable income.

Consumption Function: It shows how the change in disposable income of an individual changes the consumption level.

The formula to calculate consumption function is:

Here,

• C is consumption level.
• is autonomous consumption.
• is disposable income.
• MPC is marginal propensity to consume.

Autonomous Consumption: This is defined as the consumption level when the income of an individual is zero.

Planned Aggregate Spending: It is the summation of consumption level in an economy and the planned investment.

The formula to calculate planned aggregate spending is:

Here,

• C is consumption level.
• is the planned investment spending.
• is the planned aggregate spending.

Unplanned Investment: All those investments that businesses do not intend to take in a given time. It is certain due to some external factors like fall in interest rate and increase in future profitability.

The formula to calculate unplanned investment is:

Here,

• Y_Dis disposable income.
• is unplanned investment spending.
• AE is the planned aggregate spending.

Explanation of Solution

a. Planned aggregate expenditure and unplanned investment.

GDP	YD(A)	C(B)	Iplanned(C)	AEplanned(D)	Iunplanned
(billions of dollars)
0	0	100	300	400
400	400	400	300	700
800	800	700	300	1,000
1,200	1,200	1,000	300	1,300
1,600	1,600	1,300	300	1,600	0
2,000	2,000	1,600	300	1,900	100
2,400	2,400	1,900	300	2,200	200
2,800	2,800	2,200	300	2,500	300
3,200	3,200	2,500	300	2,800	400

Conclusion:

Hence, the unplanned investment and the planned aggregate expenditure at specific income level have been stated in the table.

b. Aggregate consumption function.

Given,
Autonomous consumption is $100 billion.
Change in disposable income is $400 billion.
Change in aggregate consumer spending is $300 billion.

The formula to calculate MPC is:

Substitute $300 billion for and $400 billion for

Hence MPC is 0.75.

The formula to calculate consumption function is:

Substitute $100 billion for and 0.75 for MPC:

Conclusion:

Thus, the Consumption function is

c. Income-expenditure equilibrium GDP.

• Income expenditure equilibrium GDP is the point where planned aggregate spending is equal to the GDP.
• The table in part a highlights that the condition is satisfied at the level where GDP is equal to $1,600 billion.

Conclusion:

Hence, the equilibrium GDP (Y*) is $1,600 billion.

d. Value of the multiplier:

Given,
MPC is 0.75

The formula to calculate multiplier is:

Substitute 0.75 for MPC:

Conclusion;

Thus, multiplier is 4.

e. The new Y* when planned investment changes.

Given,
New investment is $200 billion
Initial investment is $300 billion

The formula to calculate change in planned investment is:

Substitute $200 billion for new investment and $200 billion for initial investment:

Given,

Change in investment is billion.
Real GDP is $1,600 billion.
Multiplier is 4.

The formula to calculate new Y* is:

Substitute $1,600 billion for real GDP, 4 for multiplier and billion for change in investment:

Conclusion:

Thus, new Y* is $1,200 billion.

f. The new Y* when autonomous consumption changes.

Given,
New autonomous consumption is $200 billion.
Initial autonomous consumption is $100 billion.

The formula to calculate change in autonomous consumption is:

Substitute $200 billion for new consumption and $100 billion for initial consumption:

Given,
Change in consumption is $100 billion.
Real GDP is $1,600 billion.
Multiplier is 4.

The formula to calculate new Y* is:

Substitute $1,600 billion for real GDP, 4 for multiplier and $100 billion for change in consumption:

Conclusion:

Thus, new Y* is $2,000 billion.