The Modified Keynesian Model Y = C + I + G + X – IM … equilibrium condition in a
ID: 1202629 • Letter: T
Question
The Modified Keynesian Model
Y = C + I + G + X – IM … equilibrium condition in a 4-sector model where:
C = 150 + 0.9DI … consumption function
I = 50 … autonomous investment
G = 100 … autonomous government spending
X = 200 … autonomous exports
IM = 100 … autonomous imports
And also:
DI = Y – T + Tr T = 0 … autonomous taxes
Tr = 0 … autonomous transfer payments
YF = 5000 … full-employment Y
1. Solve for the equilibrium level of real output/income (Y*) in this economy.
2. Given the model above, net exports equal $________. Does this represent a trade deficit or trade surplus?
3. Given the model above, the federal budget has a (deficit/surplus) equal to $________.
4. What is the value of the MPC? … the value of the MPS?
5. Calculate the “oversimplified” expenditure multiplier.
6. Suppose that full-employment (YF) equals $5000. Is there a recessionary or inflationary output gap?
7. (Refer to question “6”.) How much is the gap equal to?
8. Suppose the government chooses to eliminate the gap by using expansionary fiscal policy (i.e., increasing G). Given the numbers above, by how much would government spending (G) need to increase to achieve the goal of full-employment?
9. Suppose instead that the government decided to lower taxes to eliminate the output gap in question “6”. How much would taxes need to fall to achieve the goal of full-employment?
10. Which action (raising G or lowering T) has the largest effect on the federal budget deficit and the national debt?
11. Suppose the national debt equaled $6000 before the tax cut (refer to question “9”). What would be the value of the national debt after this policy action?
Explanation / Answer
Q1. Calculate equilibrium level of real output/income (Y*) -
Y = C + I + G + X - IM
Y = 150 + 0.9DI + 50 + 100 + 200 - 100
Y = 400 + 0.9DI
Y = 400 + 0.9(Y - T + Tr)
Y = 400 + 0.9(Y - 0 - 0)
Y = 400 + 0.9Y
Y - 0.9Y = 400
Y = 4,000
The equilibrium level of real output/income in this economy is $4,000.
Q2. Exports, X = $200
Imports, IM = $100
Net Exports = Exports - Imports = $200 - $100 = $100
The net exports equal $100.
Positive value of net exports represent trade surplus.
Negative value of net exports represent trade deficit.
In the given case, value of net exports is positive. This represents a trade surplus.
Q3. When sum of government spending and autonomous transfer payments is greater than autonomous taxes, federal budget is said to be in deficit.
When sum of government spending and autonomous transfer payments is less than autonomous taxes, federal budget is said to be in surplus.
In the given case, sum of government spending and autonomous transfer payments ($100 + $0) is greater than the autonomous taxes ($0), therefore, federal budget is in deficit.
The deficit is equal to $100.
Q4. Consumption function -
C = 150 + 0.9DI
The coefficient of DI is MPC.
So, the value of MPC is 0.9
MPS = 1 - MPC = 1 - 0.9 = 0.1
The value of MPS is 0.1
Q5. Calculate the "oversimplified" expenditure multiplier -
Multiplier = 1/1-MPC = 1/1-0.9 = 1/0.1 = 10
The "Oversimplified" expenditure multiplier is 10.