Equilibrium in a two commodity market
Let us consider a two-commodity market model in which the two commodities are related to each other. Let us assume the functions for both commodities are linear. The two commodities are complementary commodities say (cars (c ) and petrol (P). The functions representing the commodities are as follows:
Qdc = 820 - 10 Pc - 4Pp Qdp = 590 - 2Pc - 6Pp
Qsc = -120 + 6Pc Qsp = - 240 + 4Pp
At equilibrium,
1) Qdc = Qsc
820 - 10Pc - 4Pp = - 120 + 6Pc
940 - 16Pc - 4Pp = 0
2) Qdp = Qsp
590 - 2Pc - 6Pp = -240 + 4Pp
830 - 2Pc - 10Pp = 0
There are now therefore two equations:
940 - 16Pc - 4Pp = 0. .....................(i)
830 - 2Pc - 10Pp = 0 ......................(ii)
Multiply (ii) by 8 which gives (iii). Subtract (i) from (iii) to eliminate Pc and solve for Pp.
6,640 - 16 Pc - 80Pp = 0..(iii)
- (940 - 16Pc - 4Pp = 0 ...................(i)
5,700 - 76Pp = 0
Pp = 75
Substituting Pp = 75 in (i) we obtain:
940 - 16Pc - 4(75) = 0
16pc = 640
Pc = 40
Substituting Pc = 40 and Pp = 75 into Qd or Qs for each market
1) Qdc = 820 - 10 (40) - 4 (75)
= 820 - 400 - 300
Qdc = 120 = Qsc
2) Qdp = 590 - 2 (40) - 6 ( 75)
= 590 - 80 - 450
Qdp = 60 = Qsp