Answer to Question #254158 in Macroeconomics for alex

Question

. Assume that the equations below describe the expenditures within a particular macroeconomy and that these equations conform to the assumptions we've made in lecture regarding the fixed price level Aggregate Expenditure model. All values for expenditure and income are dollar amounts, but for simplicity, we've dropped the $ below. 

C = 0.8(DI) + 4000C = Consumption expenditure, DI = Disposable IncomeI = 4000I = Investment expenditureG = 8000G = government expenditureX = 2600X = spending on exportsM = 3600M = spending on importsDI = Y - TY = real GDP, T = tax revenues/>T = 5000 

a. The equilibrium real GDP in this economy is 

b. The value of the government expenditure multiplier within this economy is 

c. The value of the tax multiplier within this economy is

Answer 1

a.

$C=0.8(DI) + 4000 \\ I = 4000 \\ G = 8000 \\ X = 2600 \\ M = 3600 \\ DI = Y-T \\ T = 5000$

Real GDP(Y) $= C+I+G+(X-M)$

$Y = 0.8(DI) + 4000 + 4000 + 8000 + (2600-3600) \\ Y = 0.8(Y-5000) + 15000 \\ Y = 0.8Y -4000 -15000 \\ Y -0.8 Y = 11000 \\ 0.2Y = 11000 \\ Y= \frac{11000}{0.2} = 55000$

The equilibrium real GDP in this economy = Y = $55000

b.

Marginal propensity to consume (MPC) in this economy = 0.8

Expenditure multiplier $= \frac{1}{1-MPC}$

$= \frac{1}{1-0.8} \\ = \frac{1}{0.2} \\ = 5$

c.

$MPC=0.8 \\ Tax \; multiplier = \frac{1}{1-MPC} \times (-MPC) \\ = \frac{1}{1-0.8} \times (-0.8) \\ = \frac{1}{0.2} \times (-0.8) \\ = \frac{-0.8}{0.2} \\ = -4$

Hence, the value of the tax multiplier within this economy = -4