Assume the following model of the economy, with the price level fixed at 1.0: C=
ID: 1118711 • Letter: A
Question
Assume the following model of the economy, with the price level fixed at 1.0:
C= 0.8(Y–T)
T= 1,000
I= 800 –20r
G= 1,000
Y= C+ I+ G
Ms/P= Md/P= 0.4Y–40r
Ms= 1,200
a.Write a numerical formula for the IScurve, showing Yas a function of ralone.(Hint: Substitute out C, I, G, and T.)
b.Write a numerical formula for the LM curve, showing Y as a function of r alone.(Hint: Substitute out M/P.)
c.What are the short-run equilibrium values of Y, r, Y–T, C, I, private saving, public saving, and national saving? Check by ensuring that C+ I+ G= Y and national saving equals I.
d.Assume that G increases by 200. By how much will Yincrease in short-run equilibrium? What is the government-purchases multiplier (the change in Y divided by the change in G)?
Explanation / Answer
(a) In goods market equilibrium, Y = C + I + G
Y = 0.8(Y - 1,000) + 800 - 20r + 1,000
Y = 0.8Y - 800 + 800 - 20r + 1,000
(1 - 0.8)Y = 1,000 - 20r
0.2Y = 1,000 - 20r
Y = 5,000 - 100r [IS curve]
(b) In money market equilibrium, Md = Ms
0.4Y - 40r = 1,200
0.4Y = 1,200 + 40r
Y = 3,000 + 100r [LM Curve]
(c) In general equilibrium, IS = LM.
5,000 - 100r = 3,000 + 100r
200r = 2,000
r = 10
Y = 5,000 - (100 x 10) = 5,000 - 1,000 = 4,000
Y - T = 4,000 - 1,000 = 3,000
C = 0.8 x 3,000 = 2,400
I = 800 - (20 x 10) = 800 - 200 = 600
Private saving = Y - C = 4,000 - 2,400 = 1,600
Public saving = T - G = 1,000 - 1,000 = 0
National saving = Private saving + Public saving = 1,600
(d) G rises by 200. From IS equation,
0.2Y = 1,000 - 20r + 200 = 1,200 - 20r
Y = 6,000 - 100r [New IS curve]
Equating with LM curve,
6,000 - 100r = 3,000 + 100r
200r = 3,000
r = 15
Y = 6,000 - (100 x 15) = 6,000 - 1,500 = 4,500
Increase in Y = 4,500 - 4,000 = 500
Government purchase multiplier = 500 / 200 = 2.5
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