Assume that demand for a commodity is represented by the equation P=90-2Qd Supply is represented by the equation P=-5 +3Qs where Qd and Qs are quantity demanded and quantity supplied, respectively, and P is price

• Step 1: Rewrite the demand and supply equations to make Q the subject.

Demand equation

P = 90-2Qd

-2Qd = P -90

Q d = 45 - 0.5p

Supply equation

P = -5+3Qs

3Qs = P +5

Qs = 1/3p + 5/3

Qs = 5/3 +1/3p

• Step 2: Use the equilibrium condition Qs = Qd to find the equilibrium price

Qs = 5/3 +1/3p

Q d = 45 - 0.5p

Hence,

5/3 +1/3p = 45 - 0.5p

1/3p + 0.5P = 45 - 5/3

5/6P = 130/3

P = (130/3) * (6/5)

P = 52

• Equilibrium price = $52

Step 4: substitute the price (52) in either the demand equation of supply equation to obtain equilibrium quantity.

Q d = 45 - 0.5p

But P = 52

Q d = 45 - 0.5(52)

Qd = 19 units

• Since Qs = Qd, our equilibrium quantity is 19 units.