MACROECONOMICS+ACHIEVE 1-TERM AC (LL)
MACROECONOMICS+ACHIEVE 1-TERM AC (LL)
10th Edition
ISBN: 9781319467203
Author: Mankiw
Publisher: MAC HIGHER
Question
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Chapter 11, Problem 2PA

 (a)

To determine

The graphical representation of the planned expenditure as a function of income.

 (a)

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Explanation of Solution

The Keynesian cross model is a basic model of income determination, which describes that there is one level of national income that occurs at the point where the planned expenditure (PE) equals the actual expenditure (AE). The planned expenditure is the sum total of consumption expenditure (C), investment expenditure (I), and the government expenditure (G).

PE = C + I + G (1)

Now substitute the respective values in Equation (1) to get the value of planned expenditure.

PE = 120 +0.8(Y400)+ 200 + 400=120+0.80Y320+200+400 =0.80Y+400

Therefore, the planned expenditure as a function of income is PE=0.80Y+400.

Figure 1 illustrates the planned expenditure as a function of income.

MACROECONOMICS+ACHIEVE 1-TERM AC (LL), Chapter 11, Problem 2PA

In Figure 1, the vertical axis measures the planned expenditure (PE), and the horizontal axis measures the income and output levels where the interaction between the planned expenditure curve and the actual expenditure curve determines the equilibrium level of income and output.

Economics Concept Introduction

Planned expenditure: The planned expenditure is the amount households, firms, and the government would like to spend on goods and services.

Actual expenditure: The actual expenditure is the actual amount households, firms, and the government spend on goods and services.

 (b)

To determine

The equilibrium income.

 (b)

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Explanation of Solution

In Keynesian cross model, the level of equilibrium national income occurs at the point where the planned expenditure equals the actual expenditure.

Actual Expenditure = Planned Expenditure Y=PE (2)

Now, substitute the respective values in Equation (2) to solve the value of equilibrium level of income.

Y=PEY=0.80Y+400(1.80)Y=400Y=400.2=2,000

Therefore, the equilibrium level of income is $2,000, which is shown in Figure 1.

 (c)

To determine

The impact of an increase in the government purchases on equilibrium GDP.

 (c)

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Explanation of Solution

As described in part (a), the initial planned expenditure is PE=0.80Y+400. If the government purchase increases to 420, the new planned expenditure function will be PE=0.80Y+420, which means the government purchase increases by 20(420400).

Now, substitute the respective values in Equation (2) to solve the new equilibrium income.

Y=PEY=0.80Y+400(1.80)Y=400Y=400.2=2,000

Therefore, the new equilibrium level of income is $2,100, which indicates that an increase in government purchases of 20 increases income by 100. This is because of the multiplier effect of government purchase on national income.

This multiplier effect on income due to an increase in government purchase can be calculated using the following formula.

Government purchases mulitiplier=1(1MPC) (3)

Substitute the respective values into Equation (3).

Government purchases mulitiplier=1(10.8)=5

Therefore, the value of government purchases multiplier is 5.

Economics Concept Introduction

Government purchases multiplier: The government purchases multiplier indicates the ratio of change in equilibrium income to the change in government spending.

 (d)

To determine

Explain that the level of government purchases is needed to achieve an income of 2,400.

 (d)

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Explanation of Solution

As described in part (b), the original equilibrium income is 2,000 to achieve an income level of 2,400; there is a need for an increase of 400 (2,4002,000) over the original level of income, where the value of government purchases multiplier is 5 (described in part (c)).

Now, the increase in government purchase to achieve an income level of 2,400 can be calculated as follows:

Government purchase=Initial government purchaseMultiplier=4005=80

Therefore, the government purchases must increase by 80 to achieve a level of 480 for achieving an income of 2,400.

Now, substitute the respective values in Equation (2) to solve the new equilibrium income.

Y=PEY=0.80Y+480(1.80)Y=480Y=480.2=2,400

Therefore, an increase of government purchases of 80 increases income by 400.

Economics Concept Introduction

Government purchases multiplier: The government purchases multiplier indicates the ratio of change in equilibrium income to the change in government spending.

 (e)

To determine

Explain the level of government taxes needed to achieve an income of 2,400.

 (e)

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Explanation of Solution

As described in part (b), the original equilibrium income is 2,000 to achieve an income level of 2,400; there is a need for an increase of 400 (2,4002,000) over the original level of income.

Now the value of tax multiplier can be calculated as follows:

Tax mulitiplier=MPC(1MPC)=0.8(10.8)=4

Therefore, the value of tax multiplier is 4 .

Now, the value of government taxes can be calculated as follows:

Government purchase=Initial government purchaseMultiplier=4004=100

Therefore, the government taxes must decrease by 100 to achieve an income of 2,400, which means the government taxes must be 300.

Economics Concept Introduction

Tax multiplier: The tax multiplier indicates that the amount income changes in response to a $1 change in taxes.

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Students have asked these similar questions
Q4. In the Keynesian cross model, assume that the consumption function is given byC=120+0.8(Y-T).Planned investment is 200; government purchases and taxes are both 400.a. Graph planned expenditure as a function of income.b. What is the equilibrium level of income?c. If government purchases increase to 420, what is the new equilibrium income? What is the multiplier for government purchases?d. What level of government purchases is needed to achieve an income of 2,400? (Taxes remain at 400.)e. What level of taxes is needed to achieve an income of 2,400? (Government purchases remain at 400.)
11. In the Keynesian cross model, assume that the consumption function is given by: C = 140 +.75(Y-T); Planned investment is 300; government purchases are 400 and taxes are 500. (optional) a. Find the equation of planned expenditure as a function of income. Graph planned expenditure as a function of income. Make sure to label all curves and axes. b. What is the equilibrium level of income? Show your work. c. If government purchases increase to 450, what is the new equilibrium income? What is the multiplier for government purchases? Show your work. d. What level of government purchases is needed to achieve an income of 3,400? (Taxes remain at 500.) Show your work. e. What level of taxes is needed to achieve an income of 3,400? (Government purchases remain at 400.) Show your work.
Suppose in a simple Keynesian economy, planned consumption function is given by C=250+0.65(Y-T). Planned investment, government purchases, taxes are $100 million, $100 million and $150 million respectively.   3. If government purchases increase to $150 million, what is the new equilibrium level of income? 4. What level of government purchases is needed to achieve an income of $2000 million? 5. From question e) you get the newly government purchase. Now find out the multiplier value 6. What is the amount of shift in AD curve? [Use the multiplier value from (5)]
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