Suppose the economy is represented by the following equations: M d /P = 6Y %u201

Question

Suppose the economy is represented by the following equations:

Md/P = 6Y %u2013 120r                               Ms/P = 5,400

C = 180 + 0.7(Y-T)                             I = 100 %u2013 18r + 0.1Y   T = 400                    G = 400  

Y = C + I + G

a. Write the numerical formula for the IS curve?

b. Write the numerical formula for the LM curve?

a.      What is the equilibrium level of r?

b.     What is the equilibrium Y?

c.      What is the value of consumption?

d.     What is the value of Investment?

e.      What is the level of real Money Demand?

Explanation / Answer

a)
Y = C+I+G
C = 0.8(Y-T)
T = 1000
C = 0.8(Y-1000) = 0.8Y-800
I = 800-20r
G = 1000
Y = 0.8Y-800+800-20r+1000 = 1000+0.8Y-20r
0.2Y = 1000-20r
Y = 5000-100r

b)
Ms/P = Md/P
1200 = 0.4Y-40r
0.4Y = 1200+40r
Y = 3000+100r

c)
[IS] = [LM]
5000-100r = 3000+100r
2000 = 200r
r = 10
Y = 5000-100%u202210 = 3000+100%u202210 = 4000
C = 0.8%u20224000-800 = 2400
I = 800-20%u202210 = 600
Y-T = 4000-1000 = 3000
Sp = Yd-C = (Y-T)-C = 3000-2400 = 600
Sg = T-G = 1000-1000 = 0 [Balanced budget]
S = Sp+Sg = 600+0 = 600 = I
Y=C+I+G = 2400+600+1000 = 4000

d)
[IS]
0.2Y = 1000-20r+%u0394G
Y = 5000-100r+5%u2022%u0394G
[LM]
100r = Y-3000
r = 0.01Y-30
LM%u2192IS
Y+%u0394Y = 5000-Y+3000+5%u2022%u0394G
2Y = 8000+5%u2022%u0394G
Y+%u0394Y = 4000+2.5%u0394G
%u0394G = +200
%u0394Y = 2.5%u2022%u0394G = 2.5%u2022200 = +500
Multiplier[G] = %u0394Y/%u0394G = 2.5

e)
[IS]
Y = 5000-100r
100r = 5000-Y
40r = 2000-0.4Y

[LM]
1200+%u0394M = 0.4Y-40r
0.4Y = 1200+%u0394M+40r = 1200+%u0394M+2000-0.4Y
0.8Y = 3200+%u0394M
Y+%u0394Y = 4000+1.25%u0394M
%u0394Y = 1.25%u0394M
%u0394M = +200
%u0394Y = 1.25%u2022200 = +250
Multiplier[M] = %u0394Y/%u0394M = 1.25

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