Answer to Question #221487 in Macroeconomics for oheneba joseph

Question

A.   Given that in an economy, , I , M_S =300, M_t = 0.4Y, and M_z=125-200r where, Y= income, C= consumption, I= investment, M_S= money supply, M_t= transactional-precautionary money demand, M_z= speculative money demand and r= interest rate. Calculate;   i. The equilibrium level of income and interest rate in this economy

   ii. The level of C, I, M_t, and M_z when the economy is in equilibrium     

Answer 1

Solution:

i.). The equilibrium level of income and interest rate in this economy:

Derive the IS and LM equations in order to find out the equilibrium level of income and interest rate in this economy.

First obtain IS equation:

Y = C + I

Y = 102 + 0.7Y + 150 – 100r

Y – 0.7Y = 102 + 150 – 100r

0.3Y = 252 – 100r

Y = 840 – 333r

IS equation: Y = 840 – 333r

 

Then obtain the LM equation:

Money market equilibrium: Md = Ms

Md = M₁ + M₂ = Mt + Mz

Md = 0.4Y + 125 – 200r

Ms = 300

Therefore, set Md equal to Ms to derive the LM equation:

Md = Ms

0.4Y + 125 – 200r = 300

0.4Y – 200r = 300 – 125

0.4Y – 200r = 175

0.4Y = 175 + 200r

Y = 438 + 500r

LM equation: Y = 438 + 500r

At equilibrium: IS = LM

840 – 333r = 438 + 500r

840 – 438 = 500r + 333r

402 = 833r

r = 0.483

The equilibrium rate of interest is = 0.483%

Substitute the value of r in the IS equation to derive the equilibrium income:

Y = 840 – 333r

Y = 840 – 333(0.483)

Y = 840 – 161

Y = 679

The equilibrium level of income is = 679

 

ii.). The level of C, I, Mt, and Mz when the economy is in equilibrium:

The level of C = 102 + 0.7Y = 102 + 0.7(679) = 102 + 475 = 577

The level of I = 150 – 100r = 150 – 100(0.483) = 150 – 48 = 102

The level of Mt = 0.4Y = 0.4(679) = 272

The level of Mz = 125 – 200r = 125 – 200(0.483) = 125 – 97 = 28