Question

An open economy presents the following data.
· The intercept of the consumption function is 4700.
· The marginal propensity to save (MPS) is 0.25.
· There are no tax collections in this economy (we are assuming this because we have not yet covered the details of tax calculations in this course).
· Government expenditure is 10,000.
· Autonomous investment is 6,000.
· The marginal propensity to invest is 0.15.
· Autonomous exports are 5,000.
· Autonomous imports are 3,000.
· The marginal propensity to import is 0.1.

Using this information, answer the following four parts of the Question
a. Calculate the equilibrium level of GDP.
b. Calculate the multiplier in this economy.
c. Now suppose that the MPS rises to 0.4. Calculate the new multiplier in this economy.
d. Given the change in the MPS to 0.4, calculate the new equilibrium level of GDP

Answer 1

(a)

At equilibrium Y = AE

Aggregate Expenditure(AE) = C + I + G +X - M

where C= consumption = Co + (1 - MPS)Y where Co = autonomous Consumption = intercept of consumption function = 4700  

G = government purchase = 10,000

I = Investment = 6000 + iY where i = Marginal propensity to invest

X = Exports = 5000

M = imports = 3000 + mY where m = Marginal Propensity to import

Hence At equilibrium

Y = Co + (1 - MPS)Y + 6000 + iY + 10,000 + 5000 - (3000 + mY)

=> Y(1 - (1 - MPS) - i + m) = 4700 + 6000 + 10,000 + 5000 - 3000 = 22700

This 22700 is also known as Autonomous expenditure

=> Y = [1/(1 - (1 - MPS) - i + m)]*22700 = [1/(1 - 0.75 - 0.15 + 0.1)]*22700 = 113500

Hence, Equilibrium level of GDP = $113500

(b)

Formula:

Multiplier = [1/(1 - (1 - MPS) - i + m)]

=> Multiplier = [1/(1 - (1 - 0.25) - 0.15 + 0.1)] = 5

Hence Multiplier = 5

(c)

Formula:

Multiplier = [1/(1 - (1 - MPS) - i + m)]

=> Multiplier = [1/(1 - (1 - 0.4) - 0.15 + 0.1)] = 5

Hence New Multiplier = 1/0.35 = 2.86

(d)

New equilibrium GDP = multiplier * Autonomous expenditure = (1/0.35)*22700

Hecne New equilibrium GDP = $64857.1429