In the Keynesian cross, assume that the consumption function is given by C= 200+0.75(Y-T). Planned investment is 100 government. a. Graph planned expenditure as a function of income. b. What is the equilibrium level of income. c. If government purchases increase to 125, what is new equilibrium income? d. what level of government purchases is needed to achieve an income of 1600?

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Answer

Planned Expenditure and Equilibrium Income in the Keynesian Cross

Planned expenditure is the sum of consumption and investment, given by:
Planned Expenditure (E) = C + I + G

Graph of Planned Expenditure as a Function of Income

Planned expenditure can be graphed as a line with a slope of 0.75 and intercept of 200. The equation for planned expenditure can be written as: E = 200 + 0.75(Y - T) + 100

Equilibrium Level of Income

The equilibrium level of income occurs where planned expenditure equals actual output. Mathematically, this is represented by: Y = E

If Government Purchases Increase to 125

If government purchases increase to 125, the new equation for planned expenditure becomes: E = 200 + 0.75(Y - T) + 125. To find the new equilibrium income, set Y = E and solve for Y.

Level of Government Purchases Needed to Achieve an Income of 1600

To achieve an income of 1600, we need to set Y = 1600 and solve for G in the planned expenditure equation. The equation becomes: 1600 = 200 + 0.75(1600 - T) + G. By solving for G, we can find the level of government purchases needed to reach an income of 1600.

In summary, by graphing planned expenditure as a function of income, determining the equilibrium level of income, adjusting government purchases to find a new equilibrium income, and solving for the level of government purchases needed to achieve a target income, we can analyze the Keynesian cross model to understand the relationship between income and expenditures in an economy.

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