Question

The inverse market demand curve for a good is p = 120 – 0.25Q and the inverse market supply curve for the good is p = 50 + 0.45Q. Calculate the equilibrium price and quantity, consumer surplus and producer surplus.

Answer 1

Inverse market demand curve as follows -

p = 120 - 0.25Q

Inverse market supply curve is as follows -

p = 50 + 0.45Q

At equilibrium,

Demand = Supply

120 - 0.25Q = 50 + 0.45Q

0.45Q + 0.25Q = 120 - 50

0.70Q = 70

Q = 70/0.70

Q = 100

p = 120 - 0.25Q

p = 120 - [0.25 * 100] = 120 - 25 = 95

Thus,

The equilibrium price is $95 per unit.

The equilibrium quantity is 100 units.

Calculate the price when quantity demanded is zero -

p = 125 - 0.25Q

p = 125 - [0.25*0] = 125

The price when Qd is zero is $125

Calculate the consumer surplus -

CS = 1/2 * [Price when Qd is zero - Equilibrium price] * Equilibrium quantity

CS = 1/2 * [$125 - $95] * 100

CS = 1/2 * $30 * 100

CS = $1,500

The consumer surplus is $1,500.

Calculate the price when quantity supplied is zero -

p = 50 + 0.45Q

p = 50 + (0.45 * 0) = 50 + 0 = 50

The price when Qs is zero is $50.

Calculate the producer surplus -

PS = 1/2 * [Equilibrium price - Price at which QS is zero] * Equilibrium quantity

PS = 1/2 * [$95 - $50] * 100

PS = 1/2 * $45 * 100 = $2,250

The Producer Surplus is $2,250.