Question #50766

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).
(b) Calculatethelevelofdisposableincome,consumption,privatesaving,governmentbudgetbalance, 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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