Question #50977

Consider the following aggregate expenditure model of the Canadian economy operating with given wages and other factor prices, price level, interest rates, exchange rates, and expectations:
C = 50 + 0.8YD I = 400 G = 500 T = 0.3Y X = 650 IM = 0.36Y
where C is consumption (the 0.8 term represents the marginal propensity to consume) YD is disposable income, I is investment, G is government spending on goods and services, T is the total value of taxes net of transfers (the 0.3 term represents the net tax rate on national income), X is exports, and IM is imports (the 0.36 term represents the marginal propensity to import).
-Calculate the level of disposable income, consumption, private saving, government budget balance, and net exports at the equilibrium. Express the components of aggregate expenditure (C, I, G, and NX) as percentages of GDP (to one decimal place).

Expert's answer

C = 50 + 0.8YD

I = 400

G = 500

T = 0.3Y

X = 650

IM = 0.36Y

(b) Y = C + I + G + NX

C = 50 + 0.8YD = 50 + (c - im)*(Y - T) = 50 + 0.44*0.7Y = 50 + 0.308Y

Y = 50 + 0.308Y + 400 + 500 + 650 - 0.36Y

1.052Y = 1600

Y = $1520.9

Disposable income YD = 0.308*1520.9/0.8 = 585.5

Consumption C = 50 + 0.308*1520.9 = 518.4

Private saving Sp = Y - T - C = 0.7*1520.9 - 518.4 = 546.2

Government budget balance BS = T - G = 0.3*1520.9 - 500 = -43.7

Net exports NX = X - IM = 650 - 0.36*1520.9 = 102.5

The components of GDP are:

C = 518.4/1520.9*100% = 34.1%

I = 400/1520.9*100% = 26.3%

G = 500/1520.9 = 32.9%

NX = 6.7%

I = 400

G = 500

T = 0.3Y

X = 650

IM = 0.36Y

(b) Y = C + I + G + NX

C = 50 + 0.8YD = 50 + (c - im)*(Y - T) = 50 + 0.44*0.7Y = 50 + 0.308Y

Y = 50 + 0.308Y + 400 + 500 + 650 - 0.36Y

1.052Y = 1600

Y = $1520.9

Disposable income YD = 0.308*1520.9/0.8 = 585.5

Consumption C = 50 + 0.308*1520.9 = 518.4

Private saving Sp = Y - T - C = 0.7*1520.9 - 518.4 = 546.2

Government budget balance BS = T - G = 0.3*1520.9 - 500 = -43.7

Net exports NX = X - IM = 650 - 0.36*1520.9 = 102.5

The components of GDP are:

C = 518.4/1520.9*100% = 34.1%

I = 400/1520.9*100% = 26.3%

G = 500/1520.9 = 32.9%

NX = 6.7%

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