Concept Introduction:
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 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 gross domestic product due to 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 GDP .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 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,
- YDis disposable income.
is unplanned investment spending. - AE is the planned aggregate spending.
Answer to Problem 13P
a. Planned aggregate expenditure and unplanned investment.
| GDP | YD (A) | C (B) | Iplanned (C ) | AEplanned  | 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 |
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.
c. Income- expenditure equilibrium GDP.
The equilibrium GDP (Y*) is $1,600 billion.
Explanation of Solution
Income expenditure equilibrium GDP is the point where planned aggregate spending is equal to the GDP. The table drawn in part a highlights the condition is satisfied at the level where GDP is equal to $1,600 billion.
d. Value of the multiplier.
Given,
MPC is 0.75.
The formula to calculate multiplier is,
Substitute 0.75 for MPC.
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.
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.
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