Homework 5-
Given the following model of a closed economy:
Y = C + S + T
C = a + b(Y - T) = 10 + 0.7(Y - T)
Where Y: GDP,
T: tax,
Y-T: disposable income,
C: aggregate consumption,
S: aggregate saving
a: autonomous consumption,
b: marginal propensity to consume
Also, assume there is no foreign sector and that government spending equals $0.
1) Given the information in the table, fill the blanks using the model described above, and solve for the consumption function.
|
Y
|
T
|
Y-T
|
C
|
S
|
|
0
|
0
|
0
|
10
|
|
|
100
|
20
|
80
|
|
14
|
|
200
|
30
|
|
129
|
41
|
|
|
41
|
259
|
191.3
|
67.7
|
|
800
|
|
750
|
|
|
2) Now assume that there is a shock in the economy that causes the level of autonomous consumption to increase by 2 units, fill in the blanks of the following table and solve for the new consumption function.
|
Y
|
T
|
Y-T
|
C
|
S
|
|
0
|
0
|
0
|
|
|
|
|
20
|
80
|
|
|
|
200
|
|
170
|
|
|
|
|
41
|
259
|
|
|
|
800
|
|
750
|
|
|
3) Show that mpc+mps=1, where the mpc is the marginal propensity to consume and the mps is the marginal propensity to save.
4) Derive a saving function with respect to disposable income based on the information in question 2. (That is, find an equation that expresses the relationship between saving and disposable income. Do not find a numerical solution.) Verify that the equation you find fits the results you found in question 2.
5) If there is a reduction in taxes, what will happen to the level of consumption and the level of saving in this economy, according to this model? Explain your answer.