Question

When the price is $30 per unit, buyers in a market are willing to buy 400 gadgets and when the price is $60 per unit, they are only willing to buy 100 gadgets. When the price is $30 per unit, sellers in a market are only willing to sell 150 gadgets and when the price is $60 per unit, they are willing to sell 225 gadgets. Assume (1) the economic environment of buyers (their income, tastes or preferences, other prices, and expectations) and sellers (technology, input prices, etc.) are constant and (2) the demand and supply curves are linear all along. Determine the market equilibrium price and quantity.

Answer 1

When P is 30 Qd = 400

When P is 60 Qd = 100

Demand is Q = a - bP

Here we have 400 = a - 30b and 100 = a - 60b

This gives 400 - 100 = -30b + 60b or b = 10

Then a = 700

Hence the demand is Q = 700 - 10P

When P is 30 Qs = 150

When P is 60 Qs = 225

Supply is Q = c + dP

Here we have 150 = c + 30d and 225 = c + 60d

This gives 75 = 30d or d = 2.5 and so c = 75

Hence the supply is Q = 75 + 2.5P

Now market equilibrium has

Qd = Qs

700 - 10P = 75 + 2.5P

P* = 50

Q* = 200

Hence price is $50 per unit and quantity is 200 units at the equilibrium.