In the Keynesian cross , assume the Consumption Function is given by : C= 200 + 0.75 (Y-T). Planned investment is 100; government purchases and taxes are both 100. What is the equilibrium level of Income?
Question
In the Keynesian cross , assume the Consumption Function is given by : C= 200 + 0.75 (Y-T). Planned investment is 100; government purchases and taxes are both 100. What is the equilibrium level of Income?
Solution
To find the equilibrium level of income in the Keynesian cross model, we need to set planned aggregate spending equal to actual income and solve for Y (income).
The aggregate spending (AS) in an economy is the sum of Consumption (C), Investment (I), and Government spending (G). In this case, the Consumption function is given by C = 200 + 0.75(Y-T), Investment is 100, and Government spending is 100. Taxes (T) are also 100.
So, the aggregate spending is:
AS = C + I + G AS = [200 + 0.75(Y-100)] + 100 + 100
Simplify this to:
AS = 200 + 0.75Y - 75 + 200 AS = 325 + 0.75Y
In equilibrium, aggregate spending equals income (Y), so we set AS = Y and solve for Y:
325 + 0.75Y = Y 325 = 0.25Y Y = 325 / 0.25 Y = 1300
So, the equilibrium level of income in this Keynesian cross model is 1300.
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