Question

Consider the following information on macroeconomic variables in a closed economy of Winterland (all figures are in billion $):

C=160 + 0.6 YD

I=150

G=150

T=100

1. Identify the exogenous and endogenous variables in this model.
2. Obtain the equilibrium level of GDP?
3. Using the equilibrium GDP in b, obtain the equilibrium level of consumption spending.
4. How much is the savinglevel at the equilibrium?
5. Calculate the multiplier?
6. If government purchase of goods and services (G) increase by $50 billion, how much the equilibrium level of GDP (Y) will change?
7. If government taxes (T) increase by $50 billion, how much the equilibrium level of GDP (Y) will change?

Answer 1

a) Exogenous variable = T & I

Endogenous variable = C & YD

b) C = 160 + 0.6YD = 160 + 0.6(Y - T) = 160 + 0.6(Y - 100)

Equilibrium level of GDP = Y

Y = C + I + G

Y = 160 + 0.6(Y - 100) + 150 + 150

Y = 160 + 0.6Y - 60 + 150 + 150

Y - 0.6Y = 400

0.4Y = 400

Y = 400 / 0.4

Y = $1,000

Thus, the equilibrium level of GDP is $1,000.

c) The equilibrium level of consumption spending (C) = 160 + 0.6(Y - T) = 160 + 0.6(1,000 - 100) = $700

d) Savings = YD - C = (Y - T) - C = (1,000 - 100) - 700 = $200

e) MPC = 0.6

Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.6) = 2.5

f) If government purchase of goods and services (G) increase by $50 billion, the new G = 200

Y = C + I + G

Y = 160 + 0.6(Y - 100) + 150 + 200

Y = 160 + 0.6Y - 60 + 150 + 200

Y - 0.6Y = 450

0.4Y = 450

Y = 450 / 0.4

Y = $1,125

Thus, the new equilibrium level of GDP is $1,125. The equilibrium level of GDP (Y) will change by $125.

g) If government taxes (T) increase by $50 billion, the new T = 150

Y = C + I + G

Y = 160 + 0.6(Y - 150) + 150 + 150

Y = 160 + 0.6Y - 90 + 150 + 150

Y - 0.6Y = 370

0.4Y = 370

Y = 370 / 0.4

Y = $925

Thus, the new equilibrium level of GDP is $925. The equilibrium level of GDP (Y) will change by $75.