General Business 765 Student Name ______________________
Spring 2002 ID Number ________________________
Answers to Homework #4
1. (8 points ) Suppose you are using the Keynesian Model to model an economy. Suppose the MPS with respect to disposable income is .2 and that taxes are given by the equation T = 5 + .25Y (i.e., taxes are now a function of income and will vary as the level of income in the economy varies).
a. Since T = 5 + .25Y, this implies that the tax expenditure multiplier equals
(-b/(1 – b +bt))
where b = MPC and t = the marginal tax rate. The value of this expression equals (-2) numerically, so for a $500 increase in aggregate income taxes must be decreased by $250.
b. –2
c. The government expenditure multiplier equals 2.5. Thus, for a $500 increase in aggregate output, government spending must increase by $200.
d. 2.5
2. (14 points) Suppose you are told that when disposable income is $100, consumption is $80 and when disposable income is $250, consumption is $200. Furthermore, suppose that taxes are autonomous and equal to $10.
a. MPC = .8
b. a = 0
c. a’ with respect to aggregate income = -8
d. equilibrium aggregate output = 260
e. Leakages = Injections in equilibrium. When Y = 260, then S = 50 and the equation S + T + M = I + G + X.
f. Since the equilibrium level of output, Y, equals 260 then 52 people are employed.
g. If employment increases by 50% then you want total employment to be 78 people. This level of employment implies a level of output equal to $390. To get an increase of $130 in aggregate output would require a change in government spending of $26. Total government spending would therefore equal $46.
3. (20 points) Suppose you are told that the MPS is equal to .2 for this economy and that taxes, investment spending, government spending, and net export spending are all autonomously determined in this economy.
|
Y |
T |
Y – T |
C |
S |
I |
G |
X – M |
AE |
Direction of change in Y |
|
1000 |
100 |
900 |
820 |
80 |
100 |
100 |
200 |
1220 |
increase |
|
2000 |
100 |
1900 |
1620 |
280 |
100 |
100 |
200 |
2020 |
increase |
|
3000 |
100 |
2900 |
2420 |
480 |
100 |
100 |
200 |
2820 |
decrease |
|
4000 |
100 |
3900 |
3220 |
680 |
100 |
100 |
200 |
3620 |
decrease |
|
6000 |
100 |
5900 |
4820 |
1080 |
100 |
100 |
200 |
5220 |
decrease |
a. Fill in the above table.
b. C = 20 + .8Y
c. equilibrium level of output Y = $2100
d. employment = 210
e. Labor productivity = $10/person
f. 5
g. the change in Y = 500, so the new equilibrium level of output equals $2600
h. the new level of employment equals 350, so the change in the level of employment is 115 people
i. Labor productivity = $8/person
j. Two graphs: one of the Keynesian cross with two different AE functions, and the other of a aggregate production function showing an increase in the level of employment.
4. Answer the following question using the data for a financial system given in the table below (data are in millions of dollars).
Bank Reserves 10
Demand Deposits 100
Cash in the Hands of the Public 100
Savings-type accounts 200
Large Denomination Time Deposits 100
Small Denomination Time Deposits 50
Noninstitutional MMMF Balances 400
Other Checkable Deposits 150
Travelers Checks 10
a. M1 = $360 million
b. M2 = $1010 million
c. 4% or .04
d. the change in demand deposits is equal to the money multiplier times the change in reserves, or (25)(10 million) = $250 million