Question

The market for bauxite is perfectly competitive. Market inverse demand is given by P^D(Q)=500-Q, where price is measured in dollars per ton and Q is measured in million of tons. Market inverse supply of bauxite is P^S(Q)=100+Q, where price is measured in dollars per ton and Q is measured in millions of tons.

-Calculate the equilibrium price and quantity in this market. Represent your solution using a graph.

-Calculate producer and consumer surplus. Identify consumer and producer surplus on a graph that illustrates equilibrium in this market.

Answer 1

Price($ per ton)	Quantity demanded	Quantity supplied
0	500	-100
100	400	0
200	300	100
300	200	200
400	100	300
500	0	400

PD(Q) = 500 - Q

PS(Q) = 100 + Q

At equilibrium,  PD(Q) = PS(Q)

=> 500 - Q = 100 + Q

=> 500 - 100 = Q + Q

=> 400 = 2Q

=> Q = 400/2 = 200

Therefore, equilibrium quantity = 200 million tons

Equilibrium price = PD(200) = 500 - 200 = $300 per ton

Consumer Surplus = Area of the shaded triangle in the above graph = 0.5 * base * height = 0.5 * 200 * ($500-$300) = 0.5 * 200 * $200 = $20,000

Producer Surplus = Area of the shaded triangle in the above graph = 0.5 * base * height = 0.5 * 200 * ($300-$100) = 0.5 * 200 * $200 = $20,000