Homework Assignment 5

Fall 2014

Due Thursday November 20

Name:

Section:

1. Use the Keynesian cross to predict the impact on equilibrium GDP of the following. In each case,

state the direction of the change and give a formula for the size of the impact.

a. An increase in government purchases.

b. An increase in taxes.

c. Equal-sized increases in both government purchases and taxes.2. In the Keynesian cross, assume that the consumption function is given by C = 200 + 0.75 ( Y – T),

planned investment is 100, and government purchases and taxes are both 100.

a. Graph planned expenditure as a function of income.

b. What is the equilibrium level of income?

c. If government purchases increase to 125, what is the new equilibrium income?

d. What level of government purchases is needed to achieve an increase in income of 1,600?3. In the development of the Keynesian cross in the textbook, we assumed that taxes are a fixed

amount. Most countries, however, levy some taxes that rise automatically with national income.

(Examples in the United States include the income tax and the payroll tax.) Let’s represent the

tax system by writing tax revenues as

???? =????? +????????,

where????? and t are parameters of the tax code. The parameter t is the marginal tax rate: if

income rises by $1, taxes rise by t × $1.

a. How does this tax system change the way consumption responds to changes in GDP?

b. In the Keynesian cross, how does this tax system alter the government-purchases

multiplier?

c. In the IS – LM model, how does this tax system alter the slope of the IS curve?4. The following equations describe an economy.

???? =???? +???? +????.

???? = 120 + 0.5(???? ?????).

???? = 100 ? 10????.

???? = 50.

???? = 40.

(

????

????

)

????

=???? ? 20????.

???? = 600.

???? = 2.

a. Identify each of the variables and briefly explain their meaning.b. From the above list, use the relevant set of equations to derive the IS curve. Graph the IS curve

on an appropriately labeled graph.

c. From the above list, use the relevant set of equations to derive the LM curve. Graph the LM

curve on the same graph you used in part (b).

d. What are the equilibrium levels of income and interest rate?5. According to the IS-LM model, what happens in the short run to the interest rate, income,

consumption, and investment under the following circumstances? Be sure your answer includes

an appropriate graph.

a. The central bank increases the money supply.

b. The government increases government purchases.c. The government increases taxes.

d. The government increases government purchases and taxes by the same amount.