Answer to Question #50765 in Macroeconomics for bob

Question

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?

Answer 1

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