Question

The demand functions of the 3 commodities: A, B and C are given as QdA = 20 - 3PA + PB + pc, QdB = 30 + PA - 5PB and QdC = 15 + PA3PC and the corresponding supply functions also QsA= 9PA, QsB = 30PB- 3 and QsC = 3PC - 1, then find equilibrium price and quantity of each ?

Answer 1

For commodity A:
QdA = QsA
20 - 3PA + PB + PC = 9PA
12PA = PB + PC + 20
PA = (PB + PC + 20)/12

For commodity B:
QdB = QsB
30 + PA - 5PB = 30PB - 3
PA + 5PB = 33
PA = 33 - 5PB

For commodity C:
QdC = QsC
15 + PA = 3PC - 1
PA = 3PC - 16

Now we can substitute the expressions for PA in terms of PB and PC, and solve for PB and PC:
(PB + PC + 20)/12 = 33 - 5PB
PB + PC + 20 = 396 - 60PB
61PB + PC = 376
3PC - 16 = (PB + PC + 20)/12
36PC - 192 = PB + PC + 20
35PC + PB = 212

Solving these two equations simultaneously, we get:
PB = 4.25
PC = 62.75

Substituting these values into the equations for PA, we get:
PA = 10.25

Therefore, the equilibrium price and quantity for each commodity are:
Commodity A PA = 10.25, QA = QsA = 92.25
Commodity B PB = 4.25, QB = QsB = 12.75
Commodity C PC = 62.75, QC = QsC = 187.25