Question

Assume the following model of the expenditure sector:
C = 1000 +.7 (Y-T) Consumption Function
T = 300+ .2985 Y Tax Function
I = 500 – 50 r Investment Function
G = 2000 Government Expenditures
NX = - 1500 Net Exports
Md/P = .5 Y -50 r Demand for Money
Ms/P = 1000 Money Supply
a- Calculate the multiplier for this economy. (Use two decimal points)
b- Drive the “IS” and “LM” equations for this economy.
c- Fiscal policy authorities decided to use the expansionary Fiscal Policy by increasing
the G by $500. As result of this action
i- What would be the new interest rate and real GDP equilibrium?
ii- What would be the amount of the crowding out as result of the policy?

Answer 1

a. Multiplier = 1/(1-MPC) = 1/(1-0.7) = 1/0.3 = 3.33

b. IS curve is given by Y=C+I+G+NX

or, Y = 1000+0.7(Y-T)+500-50r+2000-1500

or, Y= 1000+0.7(Y-300-0.2985Y)+500-50r+2000-1500

or, Y= 1000+0.7Y-210-0.2Y+500-50r+2000-1500

or, Y-0.7Y+0.2Y = 1000-210+500+2000-1500 - 50r

or, 0.5Y = 1790 - 50r

or, Y + 100r = 3580 .....(i) is the required IS function

Now, LM curve is given by Money demand = Money supply

or, M_d/P = M_s/P

or, 0.5Y-50r = 1000

or, Y-100r = 2000 ....(ii) is the required LM function

Now, for equilibrium , solving equations (i) and (ii)

Y = 2,790

and r = 7.9%

c.i) Now if government increases G by 500,

the new IS curve becomes 0.5Y = 2290 - 50r

or, Y + 100r = 4580 ....(iii) is the new IS curve

Then, for equilibrium, solving equations (ii) and (iii),

new Y = 3290

and new r = 12.9%

ii) Now, initial IS curve is given by Y + 100r = 1790

At new interest rate of 12.9%, Y+100*12.9 = 1790

or, Y = 1790-1290 = 500

Thus, amount of crowding effect = equilibrium output at new interest rate on new IS curve - equilibrium output at new interest rate on initial IS curve = 3290 - 500 = 2790