Table 36-1 Suppose the economy of Macroland is described by the following: C = 200 + 0.8 DI (DI = disposable income)
I = 300 + 0.2 Y − 50 r ( Y = GDP)
( r , the interest rate, is measured in percentage points. For example, a 9 percent interest rate is r = 9). For this economy, assume that the Federal Reserve uses its monetary policy to peg the interest rate at
R = 5
G = 750
T = 0.25 Y
X = 200
M = 150 + 0.2 Y
Hint: DI = Y − T
From Table 36-1, find the budget deficit or surplus for Macroland.

Question

Quizplus · Accepted Answer

To find the budget deficit or surplus, we need to calculate the total government revenue and total government spending. Total government revenue is given by T = 0.25Y, and total government spending is given by G + X – M = 750 + 200 – (150 + 0.2Y) = 800 – 0.2Y.

Disposable income is given by DI = Y – T = Y – 0.25Y = 0.75Y. We can use the consumption function to find that consumption is C = 200 + 0.8DI = 200 + 0.8(0.75Y) = 170 + 0.6Y. Investment is given by I = 300 + 0.2Y – 50r = 300 + 0.2Y – 50(5) = 50 + 0.2Y.

Now we can use the national income identity to find that Y = C + I + G + X – M. Plugging in our expressions for consumption, investment, government spending, and net exports, we get:

Y = 170 + 0.6Y + 50 + 0.2Y + 750 + 200 – (150 + 0.2Y)

Simplifying:

Y = 1020 – 0.4Y

1.4Y = 1020

Y = 728.57

Now we can plug this back into our expressions for government revenue and spending:

T = 0.25Y = 0.25(728.57) = 182.14

G + X – M = 800 – 0.2Y = 800 – 0.2(728.57) = 664.29

The budget deficit is:

D = G + X – M – T = 664.29 – 182.14 = 482.15

However, this is not the final answer, because the question asks for the deficit or surplus when the interest rate is pegged at 5 percent. To find the new equilibrium level of income, we can use the equation for investment:

I = 50 + 0.2Y – 50r

Plugging in r = 5, we get:

I = 50 + 0.2Y – 50(5) = -200 + 0.2Y

Now we can use the national income identity again to find:

Y = C + I + G + X – M

Y = 170 + 0.6Y – 200 + 750 + 200 – (150 + 0.2Y)

1.2Y = 820

Y = 683.33

Plugging this back into our expressions for government revenue and spending, we get:

T = 0.25Y = 0.25(683.33) = 170.83

G + X – M = 800 – 0.2Y = 800 – 0.2(683.33) = 666.67

Now we can calculate the budget deficit:

D = G + X – M – T = 666.67 – 170.83 = 495.84

So the budget deficit when the interest rate is pegged at 5 percent is $495.84 billion. Since this is a negative number, it means that Macroland has a budget surplus of $495.84 billion. The answer is therefore B.

Table 36-1 Suppose the Economy of Macroland Is Described by the Following