Question

a. You are given the following information about the commodity and Money markets of a closed economy without government intervention.

  The commodity market

    Consumption function:

    C = 50 + 2/5Y

    Investment function:

    I = 790 – 21r

  The Money Market

    Precautionary and Transactions demand for money

    M_DT = 1/6 Y

    Speculative demand for money

    M_DS = 1200 -18r

    Money supply

    M_S = 1250

Required i.           Determine the equilibrium levels of income and interest rate for this economy.                                                   (5 Marks)ii.           Using a well labelled diagram, illustrate the equilibrium condition in part (i) above. (5 marks)

 

Answer 1

IS curve

Y= C+I

Y= 50+ $\frac{2}{5}Y+ 790-21r$

$\frac{3}{5}Y= 840-21r$

Y= 1400- 35r

LM curve

Money demand = Money supply

Money demand = 1200-18r+$\frac{1}{6}Y$

$\therefore 1250= 1200-18r+\frac{1}{6}Y$

Y= 300+108r

At Equilibrium, IS= LM

300+108r= 1400- 35r

143r= 1100

r= 7.69%

Plug in the value of r in the above equations to obtain Y

Y= 300+ 108(7.69)

= 1130.77

This can be represented diagramatically as below