Suppose that the consumption function is C=100+.8(y-t). Initially investment and government expendtures are I=75 and G=150 and taxes are T=50.
1.Depict this economy using the keynesian cross.
calulate the initial equilibrium income.
how much will income increas if government expendtures increase to g=200.
150
To depict this economy using the Keynesian cross, we need to first understand the components involved. The Keynesian cross graph shows the relationship between aggregate expenditure (AE) and national income (Y). In this case, the components are consumption (C), investment (I), government expenditure (G), and taxes (T).
The consumption function is given by C = 100 + 0.8(Y - T), where Y represents income. Initially, investment (I) is 75, government expenditure (G) is 150, and taxes (T) are 50.
To depict this on the Keynesian cross graph, we need to plot two lines:
1. The consumption function line: C = 100 + 0.8(Y - T)
2. The aggregate expenditure (AE) line: AE = C + I + G
Now, let's calculate the initial equilibrium income:
At equilibrium, AE = Y.
Substituting the given values into the equations:
AE = C + I + G
AE = (100 + 0.8(Y - T)) + 75 + 150
AE = 100 + 0.8Y - 0.8T + 75 + 150
AE = 325 + 0.8Y - 0.8T
Setting AE equal to Y:
Y = 325 + 0.8Y - 0.8T
We know that T = 50, so let's substitute that in:
Y = 325 + 0.8Y - 0.8(50)
Y = 325 + 0.8Y - 40
0.2Y = 360
Y = 360 / 0.2
Y = 1800
The initial equilibrium income is 1800.
To calculate the increase in income if government expenditure increases to G = 200:
We need to calculate the new equilibrium income.
Substituting the new value of G into the equation:
Y = 325 + 0.8Y - 0.8T
Since T remains at 50:
Y = 325 + 0.8Y - 0.8(50)
Y = 325 + 0.8Y - 40
0.2Y = 360
Y = 360 / 0.2
Y = 1800
The new equilibrium income remains the same, at 1800. There is no increase in income because the change in government expenditure is not large enough to impact the overall equilibrium level.