Question

Question 6 Consumption C = 50 +0.7Yd Income tax t = 0.3Y Investment |= 600 - 30r Government expenditure G = 300 Md = Y-50r, Ms = 1040, P = 2 Derive the IS and LM equations and find the equilibrium levels of income and rate of interest. E BI U A- A - IE * 1 1 1 XX, B. va G 1 12pt - Paragraph - Ⓡ

Answer 1

IS curve can be derived from, Y=C+I+G (where Y=level of output,C=consumption,I=investment,G=government expenditure)

or, Y=50+0.7Y_d+600-30r+300

or, Y=50+0.7(Y-t)+600-30r+300 (where Y_d=Y-t)

or, Y=50+0.7(Y-0.3Y)+600-30r+300

or, Y=50+(0.7*0.7Y)+600-30r+300

or, Y=50+0.49Y+600-30r+300

or, Y-0.49Y=950-30r

or, 0.51Y+30r=950....(i)

LM can be derived from, Money demand = Money supply/Price level

or, M_d = M_s/P

or, Y-50r = 1,040/2

or, Y-50r = 520 .....(ii)

Now, adding equation (i)*5 and equation (ii)*3, we get,

(2.55Y+150r) + (3Y-150r) = 4,750-1,560

or, 5.55Y = 3,190

or, Y = 580 is the required equilibrium level of output

Now, from (ii), Y-50r = 520

or, 50r=Y-520

or, 50r=580-520

or, 50r=60

or, r = 1.2% is the required rate of interest.