Econ303 Homework Assignment 5 Fall 2014

Econ303
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.