Question

Assume the following for a closed economy in period t: labor income is 70, taxes are 30, consumption is 60% of disposable income, i.e., C = 0.6(Y − T ), I = 40, and the production function is Cobb-Douglas: Y = AK0.5L0.5. (a) How much is capital income? (b) Is the government running a surplus, a deficit, or neither? Support your answer. (c) How much are public saving and private saving?

Answer 1

a) Given that labor income is 70, T = 30, C = 0.6(Y − T ), I = 40, Y = AK0.5L0.5. Since we have alpha = 0.5, 1 -

alpha is also 0.5 so that labor income = capital income = 70.

b) Now total income is 140 or Y = 140. This gives C = 0.6*(140 - 30) = 66 and I = 40. This implies AE = C + I + G =

66 + 40 + G = 140. Hence G is 140 - 106 = 34. This suggests that the government runs a deficit and it is worth T -

G = 30 - 34 = -4.

c) Public saving = -4 and private saving = Y - T - C = 140 - 30 - 66 = 44. National savings = 44 - 4 = 40 =

Investment