**2.** Do the following problems in the Problems section of Chapter
12 in the text: 1,2,3

Disposable Income Consumption Spending
Saving

0
$ 1.0 million -$1.0 million

$ 1 million
$ 1.75 million -$0.75 million

$ 2 million
_____________ _____________

$ 3 million
_____________ _____________

$ 4 million
_____________ _____________

$ 5 million
_____________ _____________

$ 6 million
_____________ _____________

$ 7 million
_____________ _____________

$ 8 million
_____________ _____________

$ 9 million
_____________ _____________

$10 million
_____________ _____________

A. Define MPC. Assuming it is constant, calculate it and
use it to fill in the rest of the table. Define the multiplier.
What is its value for this example?

B. There are no taxes or transfer payments or depreciation in this model, for now. But, we have the following additional data:

Investment Spending = $ 2 million

Government Spending = $ 0.5 million {Only Federal, no State and

Local}

Exports = $ 3 million

Imports = $ 1 million

Given this information, what is the equilibrium level of GDP?

C. Economists working for the Department of Commerce predict that next year, imports will rise by $ 2 million, and exports will rise by only $0.5 million. Assuming that investment and government spending remain the same, and that the consumption function remains the same:

a. What will be the new equilibrium level of GDP next year
if these economists have forecasted correctly?

b. What will be the level of consumption spending
at this new equilibrium GDP? What will be the new level of savings?
Is it true that savings equal investment? Explain.

D. [To answer this question, we will begin with the data and the results in (B), and ignore what went on in (C).]

Most members of Congress agree that the Federal government has run a deficit for long enough, and that steps must be taken to eliminate it. Two plans have been discussed. One says to cut government spending from its current level of $0.5 million to zero. The other says taxes should be raised until the budget is balanced; assuming only autonomous taxes (sometimes called lump-sum taxes), this would mean that taxes must be raised from their current level of zero to $0.5 million.

a. Test each policy by finding the new equilibrium level of GDP each would bring about. Why do the equilibrium levels of GDP differ?

b. Discuss the implications of each policy
for the composition of equilibrium GDP, i.e., how does the proportion of
various goods produced and sold differ under each scheme, and who is buying
them?.

**4. **We are given the following
data for a simple economy.

[In millions of dollars]

Consumption Spending = C = a(r)+0.8*DI

a(r)= 100-5r where r - interest rate in percents

[a(r), autonomous consumption spending, is the component of consumption
spending that does not depend on DI, but depends on the rate
of interest.]

Investment = I(r) = 200 - 10r

Autonomous Government Spending = G = 100

Autonomous Taxes = Tx = 50

Autonomous Exports= X = 200

Autonomous Imports = IM = 175

r = 10 percent

A. For every one percentage point increase in the interest rate,
how much does consumption spending change?

In what direction? Give two examples of this type of consumption
spending.

B. Use the information given above to write total autonomous spending
as a function of the interest rate.

Give its value when r = 10.

C. Calculate the equilibrium level of GDP.

D. If interest rates rise from 10 percent to 12 percent, find
the new level of autonomous consumption, the new level

of investment, and the new value of autonomous spending?
What is the new equilibrium level of GDP?

E. If interest rates fall to 8 percent, find the new level of
autonomous consumption, the new level of investment, and

the new level of autonomous spending. What is the new equilibrium
level of GDP?

**5. **We are given the
following information about an economy:

[In millions of dollars]

Consumption Spending = C = a(r)+0.8*DI

a(r)= 200-10r where r - interest rate in percents

[a(r), autonomous consumption spending, is the component
of consumption spending that does not depend on DI, but depends on the
rate of interest.]

Investment Spending = I(r) = 300 - 15r

Autonomous Government Spending = G = 500

Autonomous Taxes = T_{0} = 50

Autonomous Exports= X = 200

Autonomous Imports = IM = 175

r = 10 percent

DI = Y - Taxes

Y = Real GDP

A. Find equilibrium real GDP for the data given above.

B. What is the state of the government budget? Calculate
the surplus or deficit.

C. The Congress decides to institute an income tax in this economy
to balance the government's budget.

Government spending will not change, but Instead of having only autonomous
taxes, the tax level will be

determined by the following equation:

Taxes = T_{0} + t*Y
Where T_{0} = 50, as above, and the tax rate, t = 0.25

a. Write down the equation
for the multiplier with an income tax.

b. For this particular problem,
what is the value of the expenditure multiplier once the income tax is
implemented?

c. Find the equilibrium
real GDP after the imposition of the income tax.

d. How did the imposition of the
income tax change the government's budget balance; did the income
tax meet

the policy
goal set by the Congress? Explain.

e. After the imposition
of the income tax, there is a surge in Autonomous Exports, which rise from
200 to 500.

Calculate the change
in equilibrium Y this will bring about.

f. After the surge in exports
and the change in equilibrium Y you calculated above, calculate the new
level of

tax revenue,
and the new state of the government's budget balance.