Handout 9-
1. Consumption Functions:
We are given the following equations from the Keynesian Model, find the autonomous consumption level, marginal propensity to consume (MPC) and marginal propensity to save (MPS). Find the savings function with respect to disposable income, and then use the given information about net taxes to find the consumption and savings function with respect to real output. If the consumption function with respect to disposable income is not given, find that first!
Note: Remember when we have the consumption function in the form C = a + b(Y - T) that autonomous consumption is a and the marginal propensity to consume is b.
To solve for the consumption and savings functions with respect to real output rather than disposable income we need to enter the value of net taxes.
The savings function with respect to disposable income is S = -a + (1 - b) (Y - T)
(a) C = 125 + 0.75(Y-T) Net Taxes = 100
Autonomous Consumption Level :
MPC :
MPS :
Savings Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to Y :
(b) C = 0.80(300-T+Y) Net Taxes = 50
Autonomous Consumption Level :
MPC :
MPS :
Savings Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to Y :
(c) 2T = 2Y - 3C + 300 Net Taxes = 90
Autonomous Consumption Level :
MPC :
MPS :
Savings Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to Y :
(d) 600 = 35(T - Y) + 50C Net Taxes = 0.2Y
Autonomous Consumption Level :
MPC :
MPS :
Savings Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to Y :
2. Equilibrium:
Solve for the short run equilibrium output using the Keynesian Model. Use the fact that Output = Y = C + I + G + X - M in equilibrium.
(a) C = Consumption function = 125 + 0.75(Y-T)
T = Net Taxes = 100
G = Government Spending = 100
I = Investment Spending = 120
Closed economy
(b) C = Consumption function = 20 + 0.75(Y - T)
T = 0.2Y
G = Government Spending = 50
I = Investment Spending = 20
X = M + 10
(c) S = Savings function w/ respect to output = -100 + 0.2Y
T = Net Taxes = 50
G = Government Spending = 100
I = Investment Spending = 175
M - X = 125
3. Tables, Functions, & Equilibrium (Challenging Problems):
Given the information in the following tables, fill the blanks (assuming that the consumption function is linear with respect to disposable income). Find the consumption function with respect to disposable income, the consumption function with respect to output, the savings function with respect to disposable income, and the savings function with respect to output. Then find the equilibrium output level in the closed economy if G + I = 100.
a) Flat Taxes: Taxes are a constant number
| Y |
T |
Y-T |
C |
S |
| 100 |
40 |
-40 |
20 |
|
| 100 |
|
760 |
95 |
40 |
Consumption Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to DI :
Savings Function w/ respect to Y :
Output :
b) Progressive Taxes: Taxes are a function of income (i.e. T = c + dY)
| T |
T |
Y-T |
C |
S |
| 0 |
-20 |
|
110 |
|
| 100 |
0 |
|
150 |
|
| 200 |
|
|
|
|
|
80 |
|
|
|
|
|
|
390 |
|
Tax Function :
Consumption Function w/ respect to DI :
Consumption Function w/ respect to Y :
Savings Function w/ respect to DI :
Savings Function w/ respect to Y :
Output :