Question #50765

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).

(a) Solve for aggregate expenditures (AE) as a function of Y, and calculate the equilibrium level of national income. Illustrate your equilibrium in a diagram with AE on the vertical and Y on the horizontal axis. What is the value of the multiplier?

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).

(a) Solve for aggregate expenditures (AE) as a function of Y, and calculate the equilibrium level of national income. Illustrate your equilibrium in a diagram with AE on the vertical and Y on the horizontal axis. What is the value of the multiplier?

Expert's answer

C = 50 + 0.8YD I = 400 G = 500 T = 0.3Y X = 650 IM = 0.36Y

(a) AE = Y = C + I + G + NX = 50 + 0.8(Y - 0.3Y) + 400 + 500 + 650 - 0.36Y = 0.2Y + 1600

Y = 0.2Y + 1600

Y = 1600/0.8 = 2000

So, the equilibrium level of national income is 2000.

The value of the multiplier is:

m = 1/(1 - c*(1 - t) + im) = 1/(1 - 0.8*(1 - 0.3) + 0.36) = 1/0.8 = 1.25

(a) AE = Y = C + I + G + NX = 50 + 0.8(Y - 0.3Y) + 400 + 500 + 650 - 0.36Y = 0.2Y + 1600

Y = 0.2Y + 1600

Y = 1600/0.8 = 2000

So, the equilibrium level of national income is 2000.

The value of the multiplier is:

m = 1/(1 - c*(1 - t) + im) = 1/(1 - 0.8*(1 - 0.3) + 0.36) = 1/0.8 = 1.25

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