Answer to Question #286285 in Macroeconomics for fred

Question

Consider the following equations for a small open economy for both the goods and money markets.

C = 3000 + 0.8Y^d; T = 1000 + 0.3Y; G = 6000; TR = 500; I = 4000 + 0.24Y – 100r; M = 3000 + 0.2Y; X = 2000; L_P = 1000 + 0.15Y; L_T = 2000 + 0.25Y – 15r; Ls = 1000 – 35r; MS = 40,000; P= 4

a.     Derive both the IS and LM equations for the economy and compute the Equilibrium level of Income and Interest Rate.

b.    At this equilibrium level of income and interest, compute the levels of disposal income, total transactions demand for money, investment demand and the value of net exports.

c.     Suppose the government raises govt. expenditure by 20% in order to increase aggregate demand. Show how this policy results in the crowding out effect.

Answer 1

Solution:

a.). IS equation: Y = C + I + G + X – M

C = 3000 + 0.8Yd = 3000 + 0.8(Y – T) = 3000 + 0.8(Y – (1000 + 0.3Y) = 3000 + 0.8Y – 800 – 0.24Y

C = 2200 + 0.56Y

Y = 2200 + 0.56Y + 4000 + 0.24Y – 100r + 6000 + 2000 – 3000 + 0.2Y

Y = 11,200 + 0.6Y – 100r

Y – 0.6Y = 11,200 – 100r

0.4Y = 11200 – 100r

Y = 28,000 – 250r

IS equation: Y = 28,000 – 250r

 

LM equation = Md = Ms

Total Real Md = L_P + L_T + L_S = 1000 + 0.15Y + 2000 + 0.25Y – 15r + 1000 – 35r

= 4000 + 0.4Y – 50r

Md = 4000 + 0.4Y – 50r

Ms = 40,000

4000 + 0.4Y – 50r = 40,000/2 = 20,000

4000 + 0.4Y – 50r = 20,000

Y = 40,000 + 125r

LM equation: Y = 40,000 + 125r

 

At equilibrium: IS = LM

28,000 – 250r = 40,000 + 125r

r = 32

Interest = 32

Y = 40,000 + 125(32) = 44,000

Equilibrium income = 44,000

 

b.). Disposable income = Yd = Y – T = Y – (1000 + 0.3Y) = 44,000 – (1000 + 0.3(44,000)

Yd = 44,000 – 14,200 = 29,800

 

Total transaction demand for money = L_T = 2000 + 0.25Y – 15r = 2000 + 0.25(44,000) – 15(32) = 2,000 + 11,000 – 480 = 12,520

 

Investment demand = 4000 + 0.24Y – 100r = 4000 + 0.24(44,000) – 100(32) = 4000 + 10,560 – 3,200 = 11,360

 

Net exports = X – M = 2000 – 3000 + 0.2Y = 2000 – 3000 + 0.2(44,000) = 2000 – 11,800 = (9,800)