Econ 2123 Problem Set 2 Solution

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Private saving=Y-C-T=900-160-0.6(800)-100=160.

Public saving =T-G=-10. National saving equals private plus public saving, or 150. National saving equals investment. This statement is mathematically equivalent to the equilibrium condition, total demand equals production. In other words, there is an alternative (and equivalent) equilibrium condition: national saving equals investment.

2.

Real GDP

Consumption

Planned Investment

Government Purchases

Net Exports

$1000

$1000

$100

$150

$-50

$2000

$1900

$100

$150

$-50

$3000

$2800

$100

$150

$-50

$4000

$3700

$100

$150

$-50

Using the table above, answer the following questions. The numbers in the table are in billions of dollars.

(a) What is the equilibrium level of real GDP?

Equilibrium when Real GDP = Y = C+I+G+NX

Y= 2800+100+150-50

From the table we can see Real GDP = Y= $3000.

(b) What is MPC?

MPC= [pic 5]

From the table above, for every, we also see. [pic 6][pic 7]

Therefore, MPC=0.9

(c) If potential GDP is 4000, is the economy at full employment? If not, what is the condition of the economy?

The equilibrium GDP= $3000, yet potential GDP = $4000. This suggests the economy’s productive capacity is not fully utilized (in regards to the labor force). Therefore, we are in a recession.

(d) If the economy is not at full employment, by how much should government spending increase so that the economy can move to the full employment level of GDP?

In order to reach the potential GDP level of 4000, the government can increase spending to cover the gap of $1000 in real GDP.

[pic 8]

Since the multiplier is 10 given by and. Government spending must increase by 100.[pic 9][pic 10]

3. Automatic stabilizers

So far in this chapter, we have assumed that the fiscal policy variables G and T are independent of the level of income. In the real world, however, this is not the case. Taxes (T) typically depend on the level of income and so tend to be higher when income is higher. In this problem, we examine how this automatic response of taxes can help reduce the impact of changes in autonomous spending on output.

Consider the following behavioral equations:

C = c0 + c1YD

T = t0 + t1Y

YD = Y – T

G and I are both constant. Assume that t1 is between 0 and 1.

- Solve for equilibrium output.

Y=c0+c1YD+I+G implies

Y=[1/(1-c1+c1t1)][c0-c1t0+I+G]

- What is the multiplier? Dose the economy respond more to changes in autonomous spending when t1 is 0 or when t1 is positive? Explain.

The multiplier=1/(1-c1+c1t1)c1), so the economy responds less to changes in autonomous spending when t1 is positive. After a positive change in autonomous spending, the increase in total taxes (because of the increase in income) tends to lessen the increase in output. After a negative change in autonomous spending, the fall in total taxes tends to lessen the decrease in output.

- Why is fiscal policy in this case called an automatic stabilizer?

Because of the automatic effect of taxes on the economy, the economy responds less to changes in autonomous spending than in the case where taxes are independent of income. Since output tends to vary less (to be more stable), fiscal policy is called an automatic stabilizer.

4. Explain what types of policies a central bank can implement to reduce the interest rate.

Central banks have two options to reduce the interest rate: a central bank purchase of bonds or a reduction in the required reserve ratio. Both policies result in an increase in the money supply and a reduction in the interest rate.

5. Balanced budget versus automatic stabilizers

It is often argued that a balanced budget amendment would actually be destabilizing. To understand this argument, consider the economy of problem 1.

- Using your answer in problem 1 (a) to solve for taxes (T) in equilibrium.

T = t0 + t1[1/(1-c1+c1t1)][c0-c1t0+I+G]

Suppose that the government starts with a balanced budget and that there is a drop in c0.

- What happens to Y? What happens to taxes T?

Both Y and T decrease

- Suppose that the government cuts spending in order to keep the budget balanced. What will be the effect on Y? Does the cut in spending required to balance the budget counteract to reinforce the effect of the drop in c0 on output? (Don’t do the algebra. Use your intuition and give the answer in

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