Assume that an economy is characterized by the following equations: C = 100 + (2
ID: 1205336 • Letter: A
Question
Assume that an economy is characterized by the following equations: C = 100 + (2/3)(Y – T) T = 600 G = 500 I = 800 – (50/3)r Ms/P = Md/P = 0.5Y – 50r
a. Write the numerical IS curve for the economy, expressing Y as a numerical function of G, T, and r.
b. Write the numerical LM curve for this economy, expressing r as a function of Y and M/P.
c. Solve for the equilibrium values of Y and r, assuming P = 2.0 and M = 1,200. How do they change when P = 1.0? Check by computing C, I, and G.
d. Write the numerical aggregate demand curve for this economy, expressing Y as a function of G, T, and M/P.
Explanation / Answer
(a) Equation of IS:
Y = C + I + G
= 100 + (2/3) x (Y - 600) + 800 - (50/3) x r + 500
= 1400 + (2/3)Y - 400 - (50/3)r
[1 - (2/3)]Y = 1000 - (50/3)r
Y / 3 = 1000 - (50/3)r
Multiplying by 3,
Y = 3000 - 50r
(b) LM equation:
Ms/P = 0.5Y - 50r
50r = 0.5Y - (Ms / P)
(c)
(i) P = 2, M = 1200
From LM,
0.5Y = 50r + (Ms / P) = 50r + (1200 / 2) = 50r + 600
Y = 100r + 1200
In equilibrium, IS = LM
3000 - 50r = 100r + 1200
150r = 1800
r = 12
Y = (100 x 28) + 1200 = 2800 + 1200 = 4000
(ii) If P = 1,
Ms / P = 1200
0.5Y = 50r + 1200
Y = 100r + 2400
Equating with IS,
3000 - 50r = 100r + 2400
150r = 600
r = 4
Y = (100 x 4) + 2400 = 400 + 2400 = 2800
Note: First 4 subparts are answered.