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.      (2 marks)

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

Answer 1

The complete question is:

Given that in an economy, Given that in an economy, C = 102+0.7Y, I=150-100r, MS =300, Mt = 0.4Y, and Mz=125-200r where, Y= income, C= consumption, I= investment, MS= money supply, Mt= transactional-precautionary money demand, Mz= speculative money demand and r= interest rate. Calculate;

1. The equilibrium level of income and interest rate in this economy.

2. The level of C, I, Mt, and Mz when the economy is in equilibrium.00r

Solution

1)

$Y=C+I\\Y=102+0.7Y+150-100r\\Y-0.7Y=252-100r\\0.3Y=252-100r\\Y=840-333.3r\\$

$MS=Mt+Mz\\300=0.4Y+125-200\\0.4Y=300-125+200r\\0.4Y=175+200r\\Y=437.5+500r$

$437.5+500r=840-333.33r\\833.3r=402.5\\r=0.48\\Y=840-333.3(0.48)\\=840-160\\=680$

2)

$C=102+0.7(680)\\=102+476\\=578\\I=150-100(0.48)\\=150-48\\=102\\Mt=0.4(680)\\=272\\Mz=125-200(0.48)\\=125-96\\=29$