# The economy is in crisis! How are we going to fix it? Should we cut taxes or increase government spending? Let’s find out. Suppose the economy can be modeled as follows.

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Problem Set #3
Principles of Macroeconomics Fall 2017

1) The economy is in crisis! How are we going to fix it? Should we cut taxes or increase government spending? Let’s find out.
Suppose the economy can be modeled as follows.
C=200+.75YD I=200
G=200 T=200
Graph the economy and solve for equilibrium income. (10 pts)

AE= C+I+G. substituting the values gives the equation
AE= 200+0.75(Y-200) +200+200
AE= 0.75Y+750
To find the equilibrium point graphically the figure ,Y, was substituted with numbers to find the values for the y and x axis. The point where the lines met including the 45 degree line is the point of the equilibrium for the economy

Figure 1 Equilibrium point
The graph indicates that the equilibrium point is 3000 where the 45degree line passes
What is the size of the government’s budget? (5 pts)
The size of the government’s budget is determined using the equation Y=C+I+G where Y=3000, while C=200+0.75(Y-200). Therefore C= 200+0.75 (3000) giving C as 2100. The budget therefore is 2100+400 giving a total 2500
What is the level of private saving at equilibrium? (5 pts)
Private savings is calculated by subtracting tax and consumption from the equilibrium using the equation: Ps=Y-T-C. Plugging in the figures into the equation, the private savings at equilibrium point is 3000-200-2100 giving private saving of 700
What is the level of aggregate saving at equilibrium? Is this what you expected? (5 pts)
At equilibrium aggregate saving should be equal to the investment. Using the equation S=Y-C aggregate savings can be determined. Aggregate savings for the government will be 3000-2100= 900. The expectation was that at the equilibrium, the savings could have been equal to the income hence nothing to save

Suppose full employment income is 2,000. By how much would the government have to change government spending to reach full employment? Graph it! (7 pts)
Government derives its income from employment tax. As a result when the full employment income is 2000, it denotes that tax income changed from 200 to 2000. It also indicates that the government spending will reduce. Represented in a form of an equation, the data appears as
AE =C+I+G where C= 200+0.75(Y-2000) and I=200 while government spending will be 200. Therefore AE= 200+0.75y-1500+400 simplified as
AE=0.75Y-900

Figure 2. Graph showing equilibrium point when tax income rises to 2000.
From the chart above, the government will have to change government spending by 3600 to so as to reach the expected employment levels
What is the spending multiplier in this case? (3 pts)

The spending multiplier in the scenario explained above is gotten by the formula 1/MPS where it is 1/(1-0.75) giving a multiplier of 4
What is the government’s budget at equilibrium? (3 pts)
The government’s budget at equilibrium is found by using the equation Y=C+1+G where Y=3600 while C is 200+ 0.75(3600-2000)+200+200. As a result, the government budget is equal to 1800

What is the level of private saving at equilibrium? (3 pts)

At equilibrium, the private saving is calculated by removing the amount of taxes (T) and consumption (C) from the income (Y). Consequently the private saving is equal to 3600- 200- 1200 giving private savings of 2200
What is the level of aggregate saving at equilibrium? Is this what you expected? (5 pts)

At equilibrium, it is assumed that all income are invested therefore the aggregate saving at equilibrium is equal to Zero. The aggregate saving at equilibrium is found by using the formula S=Y- C . Plugging in the numbers at the equation S=3600-1200= 2400. The amount of aggregate savings has more than doubled after an increase in employment income. It was expected because an amount can only be saved when the spending is less than income and in the scenario there was a high amount of earnings meaning the savings increased.
Again, suppose full employment income is 2,000. By how much would the government have to change taxes to reach full employment? (7 pts)

When the full employment income is 2000, the government will change taxes in the following manner
AE=C+I+G
Assuming that income Y= C+I then C = 200+0.75(3600-200x)+ 200
Therefore 2000= 3100-150x
150x= 3100-2000 giving 900 as a result the change will be x=900/150 or 6. Therefore the government will be forced to increase taxes by a factor of six for to arrive at full employment
What is the tax multiplier in this case? Graph it! (2 pts)
The tax multiplier does not change. Since the MPC is still 0.75 the multiplier is will obtained by 1/(1-0.75) giving 1/0.25 =4
What is the government’s budget now? (5pts)
The government’s budget will be Y=C+I+G where C= 200+0.75(3600-1200) investment will be 200 while government spending 200. Therefore the budget will be 2200
What is the level of private saving at equilibrium? (5 pts)
Private savings is calculated by Y-T-C where Y is 3600 T-1200 and consumption is 200+ 0.75(3600-1200)= 2000. Therefore the value of private savings are 3600-1200-2000= 400
What is the level of aggregate saving at equilibrium? Is this what you expected? (5 pts)

Aggregate saving is calculated by Y-C where Y=3600 and C= 200+0.75(3600-1200). Therefore, the aggregate savings are 3600-2000 = 2600
2. Income taxes
Suppose that the government decides to impose an income tax as opposed to a “lump sum” tax. We can now model the economy as follows.
C=200+.75YD I=200
G=200
Where and .2 represents a 20% income tax. Solve for equilibrium income in this case. Graph this economy and the economy we modeled in question 1. Why do they differ? (10 pts)

Aggregate income is calculated using the equation Y=C+I+G

What is the size of the government’s surplus or deficit at equilibrium? (5 pts)

What is the level of private saving? (5 pts)

What is the level of aggregate saving? Is this what you expected? (5 pts)

What is the multiplier in this case? Why is it different than in the first question? (5 pts)