Chapter 24, Problem 11PA

Subpart (a):

To determine

Equations describing the economy.

Explanation of Solution

$\text{Y=C+I+G}$: Output is the summation of consumption, investment, and government expenditure. The equation explains the equilibrium condition for GDP or output in a closed economy.

$\text{C=100+0}\text{.75}\left(\text{Y-T}\right)$: The equation implies the consumption as a function of disposable income.

$\text{I=500-50r}$: The equation represents the investment as a function of the interest rate.

$\text{G=125}$: The equation means that the government expenditure is fixed at 125.

$\text{T=100}$: The equation means that the taxes are fixed at 100.

Economics Concept Introduction

Concept introduction:

Consumption spending: Consumption spending refers to the amount of expenditure incurred for consuming goods and services at a particular tie period with the given level of income.

Investment: An investment is the money invested in terms of assets and buildings by the individual, for future consumption and profit making.

GDP (Gross domestic product): GDP refers to the market value of all final goods and services produced in an economy during an accounting year.

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

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

Subpart (b):

To determine

Equations describing the economy.

Explanation of Solution

The slope of the consumption function is the marginal propensity to consume (MPC). Since the consumption function is $\text{C=100+0}\text{.75}\left(\text{Y-T}\right)$, the MPC is 0.75.

Economics Concept Introduction

Concept introduction:

Consumption spending: Consumption spending refers to the amount of expenditure incurred for consuming goods and services at a particular tie period with the given level of income.

Investment: An investment is the money invested in terms of assets and buildings by the individual, for future consumption and profit making.

GDP (Gross domestic product): GDP refers to the market value of all final goods and services produced in an economy during an accounting year.

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

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

Subpart (c):

To determine

Equations describing the economy.

Explanation of Solution

Since the interest rate r is 4 percent, the GDP can be equated as follows:

$\begin{array}{c}\text{Y = C + I + G}\\ \text{Y = 100 + 0}\text{.75 (Y- 100) + 500 - (50}\times \text{4) + 125}\\ \text{Y = 450 + 0}\text{.75 Y}\\ \text{Y= }\frac{450}{0.25}\\ =1800\end{array}$

The GDP is 1800. The calculated GDP $(1800)$ is less than full employment level GDP $(2000)$.

Economics Concept Introduction

Concept introduction:

Consumption spending: Consumption spending refers to the amount of expenditure incurred for consuming goods and services at a particular tie period with the given level of income.

Investment: An investment is the money invested in terms of assets and buildings by the individual, for future consumption and profit making.

GDP (Gross domestic product): GDP refers to the market value of all final goods and services produced in an economy during an accounting year.

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

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

Subpart (d):

To determine

Equations describing the economy.

Explanation of Solution

Assuming no change in monetary policy, an increase in government spending would restore full employment. The amount at which government purchases need to be increased can be calculated as follows:

Since the MPC is 0.75, the multiplier can be calculated thus

$\begin{array}{c}\text{Multiplier}=\frac{1}{1-\text{MPC}}\\ =\frac{1}{1-0.75}\\ =\frac{1}{0.25}\\ =4\end{array}$

The multiplier is 4. Thus, to increase GDP by 200 $(2000-1800)$, the government spending needs to be increased by 50 $\left(\frac{200}{4}\right)$.

Economics Concept Introduction

Concept introduction:

Consumption spending: Consumption spending refers to the amount of expenditure incurred for consuming goods and services at a particular tie period with the given level of income.

Investment: An investment is the money invested in terms of assets and buildings by the individual, for future consumption and profit making.

GDP (Gross domestic product): GDP refers to the market value of all final goods and services produced in an economy during an accounting year.

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

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

Subpart (e):

To determine

Equations describing the economy.

Explanation of Solution

Assuming no change in fiscal policy, a decrease in interest rate would restore full employment. The amount at which the interest rate needs to be decreased can be calculated as follows:

$\begin{array}{c}2000=100+0.75\left(2000-100\right)+\text{ 500 - 50r + 125}\\ \text{50r = 100 + 1500 -75 +500 +125 - 2000}\\ \text{ r = }\frac{150}{50}\\ \text{ r = 3}\end{array}$

The interest rate needs to be 3 percent for full employment. Thus, a decrease of 1 percent $(4-3)$ in the interest rate is required.

Economics Concept Introduction

Concept introduction:

Consumption spending: Consumption spending refers to the amount of expenditure incurred for consuming goods and services at a particular tie period with the given level of income.

Investment: An investment is the money invested in terms of assets and buildings by the individual, for future consumption and profit making.

GDP (Gross domestic product): GDP refers to the market value of all final goods and services produced in an economy during an accounting year.

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

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