Question

Qd1 = 90 – 2P1 + 3P2 – 5P3 ; Qs1 = P1 – 10

Qd2 = 36 + 3P1 – 3P2 + 2P3 ; Qs2 = –14 + P2

Qd3 = 45 – 3P1 + 3P2 – 3P3 ; Qs3 = P3 – 20

a. Determine the equilibrium prices and quantities for the three commodity Market

model.

Answer 1

At Equilibrium, Quantity demanded = Quantity supplied

$Q_{d1}=Q_{S2}$

$90-2P_1+ 3P_2-5P_3= P_1-10$

$=100-3P_1+ 3P_2-5P_3= 0$ ....................(i)

$Q_{d2}=Q_{s2}$

$36+ 3P_1-3P_2+2P_3=-14+P_2$

$=50+3P_1-4P_2+2P_3= 0$ .........................(ii)

$Q_{d3}=Q_{s3}$

$45-3P_1+ 3P_2-3P_3= P_3-20$

$=25-3P_1+ 3P_2-2P_3= 0$ ...........................(iii)

Solve Eqns (I) and (ii) simultaneously by elimination method by adding the two eqns

$100-3P_1+ 3P_2-5P_3= 0$

$50+3P_1-4P_2+2P_3= 0$

=$150-P_2-3P_3=0$ ..............................................(iv)

Solve Eqns (ii) and (iii) simultaneously by adding the two Eqns

$50+3P_1-4P_2+2P_3= 0$

$25-3P_1+ 3P_2-2P_3= 0$

=$75-P_2$

$P_2= 75$

From Eqn (iv),

$150-75-3P_3=0$

$3P_3=75$

$P_3= 25$

From Eqn (I)

$100-3P_1+ 3(75)-5(25)= 0$

$3P_1= 200$

$P_1= \frac{200}{3}= 66.7$

$Q_1= 66.7-10= 56.7$

$Q_2= -14+75= 61$

$Q_3= 25-20=5$