Chapter 9, Problem 1SQP

(a):

To determine

Unplanned inventory in the economy.

Explanation of Solution

The unplanned inventory investment can be calculated by subtracting the consumption from the real GDP and subtracting the autonomous investment from this value. In the first case, where the level of employment is 40 millions, the consumption is $300, whereas the real GDP is $325. The autonomous investment is $100. Thus, the unplanned inventory can be calculated as follows:

$\begin{array}{c}\text{Unplanned inventory}=\left(\text{Real }\text{}\text{GDP}-\text{Consumption}\right)-\text{Autonomous investment}\\ =\left(325-300\right)-100\\ =25-100\\ =-75\end{array}$

Thus, the unplanned inventory in this case is -75. Similarly, the other case unplanned inventory can be calculated and the table can be completed as follows:

Possible levels of employment (millions of workers)	Real GDP (Output) equals disposable income (billions of dollars)	Consumption (billions of dollars)	Unplanned inventory (billions of dollars)
40	$325	$300	$-75
45	375	325	-50
50	425	350	-25
55	475	375	0
60	525	400	25
65	575	425	50
70	625	450	75

Economics Concept Introduction

Aggregate expenditure: Aggregate expenditure is the measure of the national income. Thus, it is the sum value of the final goods and services produced in the economy, which is measured by the summation of the expenditures made by the factors during the given period of time.

(b):

To determine

Marginal propensity to consume and save.

Explanation of Solution

The marginal propensity to consume can be calculated by dividing the change in the consumption by the change in the disposable income. In the first place, when the consumption increases from $300 to $325, the change in the consumption is $25 billion. The real GDP was $325 and it changes to $375, which denotes the change in the disposable income by $50 billion. Thus, MPC can be calculated as follows:

$\begin{array}{c}\text{Marginal Propensity to Consume}=\frac{\text{Change in consumption}}{\text{Change in disposable income}}\\ =\frac{\$25\text{billion}}{\$50\text{billion}}\\ =0.5\end{array}$

Thus, MPC is 0.5. The MPS can be calculated by subtracting the MPC from 1 as follows:

$\begin{array}{c}\text{MPS}=\text{1}-\text{MPC}\\ =1-0.5\\ =0.5\end{array}$

Thus, the MPS is also equal to 0.5.

(c):

To determine

Equilibrium level of output when the economy employs 40 million workers.

Explanation of Solution

The level of unplanned inventory in the economy when employing 40 million workers is $75 billion. Thus, it means that the businesses in the economy would invest more and expand their output in the economy. This leads to an increase in the real GDP and the equilibrium level of real GDP, which is at $475 billion, where the unplanned inventory is $0.