I would like to know if these 3 questions which are related are correct. it is w
ID: 1201366 • Letter: I
Question
I would like to know if these 3 questions which are related are correct. it is worth 4 points to my final grade
PROBLEM NO. 3
1. Assume the following values of an economy.
Planned Investment (Ip) = $20
Autonomous Consumption (C ) = $30
Marginal Propensity to consume (MPC) = .9
What is the equilibrium income?
Y* = aggregate demand at the equilibrium level. (Consumption + investment)
Consumption function = autonomous consumption + mpc * Y.
C=30 + .9Y
AD = 30 + .9Y + 20 = 50 + .9Y
Y= 50 + .9Y
.1Y = 50
Y = $500 is the equilibrium level of income.
What is the value of saving at equilibrium?
Savings = income – consumption at the equilibrium level of Y=500,
Consumption = 30 +.9 * 500 = $480
Savings = 500 - 480= 20
c. Does the saving and Investment Identity hold true at equilibrium income OR GDP?
Since planned investment = $20 which is equal to savings calculated, the saving investment identity holds true at equilibrium income.
.
2. In addition to the values given in question (1) above, assume the government increases its spending by $30 without raising taxes. The government can do this by borrowing from the private sector.
a. Based on this information calculate the new level of equilibrium income.
If Government expenditures = $30, Y = C + I + G
Y = 1/1-.09 * (30+20+30) Y = 800
b. Calculate the total value of consumption at equilibrium.
C = 30 + .9(800) = 750
c. Calculate the total value of saving at equilibrium.
Savings = I – C 800 – 750 = 50
3. In addition to questions in (1 & 2) above, assume the government decides to raise autonomous taxes by $30 to balance its budget.
What is the new value of equilibrium income?
Y = 1/1-.9 (30-.9(30) +20+30) = 530
What is the value of the autonomous tax multiplier?
-.09/.01 = -9
c. What is the value of autonomous spending multiplier?
1/.1 = 10
Explanation / Answer
1. Y = C + I
a. C = a + b*Y
a = autonomous consumption
b = MPC.
Y = [30+0.9Y] + 20
Y-0.9Y = 50
0.1Y = 50
Y = $500.
b. Savings is the amount not spent.
Y - C = s
C + I - C = s
I = s = $20.
c. Indeed it does, as shown above.
d. Y = C + I + G
Y = 30 + 0.9Y + 20 + 30
Y-0.9Y = 80
Y = $800.
e. C = 30 + 0.9*800 = $750.
f. Savings = Y - C
s = 800 - 750 = $50.
g. Y = C + I + G
Now C = 30 + 0.9(Y-T)
or C = 30 + 0.9(Y-30)
Y = 30 + 0.9Y - 27 + 20 + 30
0.1Y = 53
Y = $530.
h. Multiplier = -MPC/1-MPC
Multiplier = -0.9/1-0.9 = -0.9/0.1 = -9
i. Multiplier = 1/1-MPC
Multiplier = 1/1-.0.9 = 10.