Question

1. Assume that the macro economy is given by the following equations AE = C+I+G+X-M

AE=Y

C=100+0.75(Y-T)

T=0.4Y I=100

G=400

X=100

M=0.25(Y-T)

i. What is the equilibrium level of Y in this economy? ii. What are the taxes? iii. What is disposable income? iv. Now assume that consumers become nervous that the economy may enter a recession. Decrease autonomous spending to 70. What is the level of Y now?

2. Many politicians have argued that the government should always maintain a balanced budget. In other words, the government should only be able to spend the money it receives in taxes. Using the economy above let the government spend only what it receives in taxes. Or G=T. What is the equilibrium level of Y in the economy?

3. The problem with this idea is that if the economy enters a recession, the government will also spend less making the recession worse. Using the economy in part 3, let consumers become worried that the economy might go into a recession. Decrease autonomous consumption as we sis in part iv. What is the equilibrium level of Y? 4. Compare the Y from these parts. Which recession is going to be worse? Notice that when G=T, government spending is dependent on Y. therefore, anything that reduces Y will also reduce G now. Given this description of the economy, would you support a law that forced governments to maintain a balanced budget each year? 5. AE = C+I+G+X-M

AE=Y C=100+0.75(Y-T)

T=0.4Y

I=100 –r1000

G=400

X=100

M=0.25(Y-T) Notice, when r=0 we have the same economy that we had in part 1. Assume that the level of potential GDP in this economy in 900. What interest rate r should the Federal Reserve choose to get the economy to Y=900?

6. Assume that an economy has multibank system. If a person deposits $5,000 into a bank that is required to hold 5% of its deposits in reserves, how much money will the deposit create?

Answer 1

1.i

AE = C + I + G + (X – M)

Y = {100 + 0.75 (Y – T)} + 100 + 400 + {100 – 0.25(Y – T)}

Y = {100 + 0.75 (Y – 0.4Y)} + 100 + 400 + {100 – 0.25(Y – 0.4Y)}

Y = (100 + 0.75Y – 0.3Y) + 500 + (100 – 0.25Y + 0.1Y)

Y = 100 + 0.45Y + 500 + 100 – 0.15Y

Y = 700 + 0.3Y

Y – 0.3Y = 700

0.7Y = 700

Y = 700 ÷ 0.7

    = 1,000

Answer: Y = 1,000

1.ii

Taxes (T) = 0.4Y

                 = 0.4 × 1,000

                 = 400 (Answer)

1.iii

Disposable income = Y – T

                               = 1,000 – 400

                               = 600 (Answer)

1.iv

Autonomous spending becomes 70.

Therefore, C = 70 + 0.75 (Y – T)

AE = C + I + G + (X – M)

Y = {70 + 0.75 (Y – T)} + 100 + 400 + {100 – 0.25(Y – T)}

Y = {70 + 0.75 (Y – 0.4Y)} + 100 + 400 + {100 – 0.25(Y – 0.4Y)}

Y = (70 + 0.75Y – 0.3Y) + 500 + (100 – 0.25Y + 0.1Y)

Y = 70 + 0.45Y + 500 + 100 – 0.15Y

Y = 670 + 0.3Y

Y – 0.3Y = 670

0.7Y = 670

Y = 670 ÷ 0.7

    = 957.14

    = 957 (after rounding to whole number)

Answer: Y = 957