Assignment 4
Economics 102                                          Professor Gigliotti


1. Do the following problems in the Problems section of Chapter 11 in the text:  1,2,3,4

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

3.  We are given the following data on consumption spending in a simple economy.

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?.
 

4We 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 = T0 = 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 = T0 + t*Y                        Where T0 = 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.