Answer to Question #286185 in Microeconomics for lisisia

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

Md = L_P + L_T = 1000 + 0.15Y + 2000 + 0.25Y – 15r = 3000 + 0.4Y – 15r

Md = 3000 + 0.4Y – 15r

Ms = 40,000

3000 + 0.4Y – 15r = 40,000/2 = 20,000

3000 + 0.4Y – 15r = 20,000

Y = 42,500 + 37.5r

LM equation: Y = 42,500 + 37.5r

 

At equilibrium: IS = LM

28,000 – 250r = 42,500 + 37.5r

r = 341.18

Interest = 341.18

Y = 42,500 + 37.5(341.18) = 55,294.25

Equilibrium income = 55,294.25

 

b.). Disposable income = Yd = Y – T = Y – (1000 + 0.3Y) = 55,294.25 – (1000 + 0.3(55,294.25)

Yd = 55,294.25 – 17,588.28 = 37,705.97

 

Total transaction demand for money = L_P + L_T = 1000 + 0.15Y + 2000 + 0.25Y – 15r = 3000 + 0.4Y – 15r = 3000 + 0.4(55,294.25) – 15(341.18) = 30,235.4

 

Investment demand =  4000 + 0.24Y – 100r = 4000 + 0.24(55294.25) – 100(341.18) = 4000 + 13270.62 – 3411.8 = 13,858.82

 

Nex exports = X – M = 2000 – 3000 + 0.2Y = 2000 – 3000 + 0.2(55292.25) = 2000 – 14058.85 = (12,058.85)