Select Any One Of the Following Options: 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?1300120012501350
Question
Select Any One Of the Following Options: 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?1300120012501350
Solution
To find the equilibrium level of income in the Keynesian cross model, we need to set planned aggregate spending equal to actual aggregate income (Y).
Planned aggregate spending is the sum of consumption (C), investment (I), and government purchases (G).
Given the consumption function C = 200 + 0.75(Y-T), planned investment I = 100, and government purchases G = T = 100, we can write the equation for planned aggregate spending as:
C + I + G = 200 + 0.75(Y - 100) + 100 + 100
Solving this equation for Y gives us the equilibrium level of income.
First, simplify the equation:
C + I + G = 200 + 0.75Y - 75 + 200
Combine like terms:
C + I + G = 0.75Y + 325
Since we're looking for the point where planned spending equals income, set C + I + G equal to Y:
Y = 0.75Y + 325
To solve for Y, first subtract 0.75Y from both sides of the equation:
0.25Y = 325
Finally, divide both sides by 0.25 to solve for Y:
Y = 325 / 0.25 = 1300
So, the equilibrium level of income is 1300.
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