A. To graph planned expenditure as a function of income, we can use the following equation:
Planned Expenditure (E) = Consumption (C) + Investment (I) + Government Purchases (G)
E = 200 + 0.75(Y - T) + 100
B. To find the equilibrium level of income, we need to set planned expenditure equal to income:
Y = E
Y = 200 + 0.75(Y - 100) + 100
Y = 200 + 0.75Y - 75 + 100
Y = 225 + 0.75Y
0.25Y = 225
Y = 900
Therefore, the equilibrium level of income is 900.
C. If government purchases increase to 125, the new planned expenditure equation becomes:
E = 200 + 0.75(Y - 100) + 125
To find the new equilibrium income, set planned expenditure equal to income:
Y = E
Y = 200 + 0.75(Y - 100) + 125
Y = 200 + 0.75Y - 75 + 125
Y = 250 + 0.75Y
0.25Y = 250
Y = 1000
Therefore, the new equilibrium income is 1000.
D. To achieve an income of 1600, we need to find the level of government purchases that will make planned expenditure equal to 1600:
E = 200 + 0.75(Y - 100) + G
1600 = 200 + 0.75(1600 - 100) + G
1600 = 200 + 0.75(1500) + G
1600 = 200 + 1125 + G
1600 = 1325 + G
G = 275
Therefore, a level of government purchases of 275 is needed to achieve an income of 1600.
2. In the Keynesian cross, assume that the consumption function is given by
𝑪 = 𝟐𝟎𝟎 + 𝟎. 𝟕𝟓 (𝒀 − 𝑻) Planned investment is100; government purchases and taxes are both 100.
A. Graph planned expenditure as a function of income.
B. What is the equilibrium level of income?
C. If government purchases increase to125, what is the new equilibrium income?
D. What level of government purchases is needed to achieve an income of 1,600?
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