Economics 110

Prof. John Duffy

Spring 2000

 

Homework # 4

 

Answer the following questions on separate sheets of paper. Your answers to these questions are to be handed in at the beginning of your recitation section that meets the week of February 28.

 

1.      In Homework #3, you found an estimate of the marginal propensity to consume out of real GDP, (which we denote by b), by calculating , using data for consumption, C over two years, and data for real GDP, Y over two years.  This question asks you to repeat this same calculation, and to calculate the marginal propensity to purchase imported goods out of real GDP, (denoted by m), by calculating , where denotes the change in imports, and  is the change in real GDP. Your calculations should make use of the following data for the U.S. economy:

 


 


a.       Calculate the marginal propensity to consume out of real GDP,

b.      Calculate the marginal propensity to import out of real GDP,

c.       Find the value of g (b-m), and calculate the value of the multiplier for the U.S. economy.

d.      Provide the economic intuition for why the multiplier is greater than one.

e.       Explain what would happen to the value of the multiplier if

i.                     The marginal propensity to consume increases.

ii.                   The marginal propensity to import increases.

      Be sure to justify each of your answers.

 

2.      Consider an economy where the components of aggregate expenditure are given by the following equations, where all dollar values are in billions of dollars:

 


 


a.       Derive the aggregate expenditure curve.

b.      What is the value of the multiplier? What is the value of equilibrium real GDP?  Show all of the steps involved in deriving your answers.

 

c.       If government expenditures increase by $100 billion, what happens to the equilibrium value of real GDP?

d.      Illustrate your answer to part c graphically.

e.       Suppose that the equation describing imports, IM=$50, is changed to:

 


 


Redo parts a through d with this new imports equation in place of the old equation.

 

 

3.      Answer the following questions about fiscal policy multipliers.

 

a.       Explain why the government purchases multiplier is:

 

       

 

b.      What is the tax multiplier? Why is it smaller than the government purchases multiplier?

c.       Using the government purchases multiplier and the tax multiplier, derive the balanced budget multiplier.  Show all the steps in your derivation.

d.      Suppose the Clinton administration proposes to spend $25 billion more on social programs and to pay for these programs by raising taxes by $25 billion. By how much will real GDP change (according to the balanced budget multiplier)?

 

4.      In developing the AE-Y model, we have assumed that taxes, TX, are independent of income, Y.  Suppose instead that taxes are proportional to the level of income, as with an income tax.  In particular, let us consider a version of our model where consumption, C, disposable income, YD, and taxes, TX, are given as follows:

 

 

 


 


where 0 < a < 1 is the marginal propensity to consume out of disposable income and 0 < t < 1 is the income tax rate.  Y  is, as before, the level of gross income or GDP.

 

  1. Suppose that imports, IM, are described by IM = IMA , i.e. they do not depend on Y (are autonomous) as is also true for investment, I, government expenditures, G, and exports, EX.  Derive, algebraically, the multiplier in this version of the model.  Hint: the multiplier should involve both a and t.
  2. How does an increase in the income tax rate, t, affect the value of the multiplier: does an increase in t make the multiplier larger or smaller?  What is the economic explanation for your finding?