Answer to Question #282505 in Macroeconomics for ABEX

Question

5. Consider an economy with levels of aggregates as follows:

Consumption function: C = 0:8 (1 − t) Y

Tax rate: t = 0:25

Investment: I = 900 − 50r

Government expenditure: G¯ = 800

Demand for money: L = 0:25Y − 62:5r

Money supply: M = 1000

Price level: P = 2

(a) Derive the IS and LM equations.

(b) Determine the equilibrium levels of income and interest rate.

(c) Calculate the full government spending multiplier, αG.

(d) By how much income and interest change for a unit change in

government spending allowing the money and goods market to

interact?

(e) How do you account for the difference between the value of the

government spending multiplier in (b) and the change in income

in (d)? (Hint: What happens to investment?)

Answer 1

Solution:

a.). Derive the IS and LM equations:

IS equation: Y = C + I + G

Y = 0.8(1 – 0.25) Y + 900 – 50r + 800

Y = 0.6Y + 1700 – 50r

Y – 0.6Y = 1700 – 50r

0.4Y = 1700 – 50r

Y = 4250 – 125r

IS equation: Y = 4250 – 125r

 

LM equation: M_D = M_S

$(\frac{M}{P})^{d} =(\frac{M}{P})^{s} = (\frac{M}{P})$

$\frac{1000}{2}$ = 0.25Y – 62.5r

500 = 0.25Y – 62.5r

Y = 2000 + 250r

LM equation: Y = 2000 + 250r

 

b.). At equilibrium: IS = LM

4250 – 125r = 2000 + 250r

4250 – 2000 = 250r + 125r

2250 = 375r

r = 6

Equilibrium interest rate = 6%

Substitute to derive the equilibrium income:

Y = 4250 – 125r = 4250 – 125(6) = 4250 – 750 = 3,500

Equilibrium income = 3,500

 

c.). The full government spending multiplier, αG = $\frac{1}{(1 - MPC)}$

MPC = 0.8

Government spending multiplier = $\frac{1}{(1 - 0.8)} = \frac{1}{0.2} = 5$

Government spending multiplier = 5