To answer the questions, we need to first understand the components and equations provided. Here's a brief overview:
C = Consumption function
Yd = Disposable Income
T = Taxes
Y = GDP
I = Investment
G = Government spending
X = Exports
M = Imports
Yf = Full Employment GDP
Ye = Equilibrium Income
Yd = Y - T
Now let's proceed with the calculations and interpretations:
The value of the autonomous component of the AE function:
The autonomous component of the AE function refers to the portion of aggregate expenditure that does not depend on the level of income. It includes autonomous consumption (C) and autonomous investment (I). From the information given, the autonomous component is:
Autonomous expenditure = C + I = (550 + 0.6Yd) + 600
The value of the slope of the AE function:
The slope of the AE function represents the marginal propensity to consume (MPC). In this case, the slope is determined by the consumption function. From the given information, the MPC is 0.6.
The value of Ye (Equilibrium Y):
To find the equilibrium level of income, we set aggregate expenditure (AE) equal to income (Y). So, AE = Y.
AE = C + I + G + X - M
AE = (550 + 0.6Yd) + 600 + 650 + 300 - (150 + 0.2Y)
Simplifying the equation and substituting Yd = Y - T:
AE = 550 + 0.6(Y - T) + 600 + 650 + 300 - (150 + 0.2Y)
AE = 550 + 0.6(Y - 90) + 600 + 650 + 300 - (150 + 0.2Y)
Now we can solve for Ye by setting AE = Y and solving for Y.
The value of the multiplier:
The multiplier represents the change in equilibrium income resulting from a change in autonomous expenditure. It is determined by the MPC (marginal propensity to consume). The formula for the multiplier is: Multiplier = 1 / (1 - MPC).
In this case, the MPC is 0.6. Thus, the multiplier is: Multiplier = 1 / (1 - 0.6).
The size of the GDP (output) gap:
The GDP gap represents the difference between actual GDP (Y) and full employment GDP (Yf). The formula for the GDP gap is: GDP gap = Yf - Y.
Given that Yf is 4,266 and we calculated Ye in question 3, we can now find the GDP gap.
The value of saving at Ye:
Saving at equilibrium (Ye) is determined by subtracting consumption (C) from disposable income (Yd). From the given information, Yd = Y - T and C = 550 + 0.6Yd. Now we can calculate saving at equilibrium (Ye).
Determining if the gap is inflationary or recessionary:
To determine if the gap is inflationary or recessionary, we need to consider the GDP gap. If the GDP gap is positive, it indicates inflationary pressure, meaning that the economy is producing above its potential. If the GDP gap is negative, it indicates recessionary conditions, meaning that the economy is producing below its potential. We can use the calculated GDP gap to determine whether it is inflationary or recessionary.
Please provide the values for taxes (T), disposable income (Yd), and full employment GDP (Yf) so that I can calculate the values and complete the exercise.