Question

2. Consider the market demand and supply functions are: QD-2,000-500P and Os = 100 P +800. Calculate the consumer and producer surplus.

Answer 1

As a first step we need to find the equilibrium price P_e and quantity Q_e

Q_e = 2,000 - 500P_e = 100P_e + 800

Hence, 600P_e = 1,200

Hence, P_e = 2 and Q_e = 2,000 - 500P_e = 2,000 - 500 x 2 = 1,000

Let's plot the demand and supply curve on a graph.

Demand Curve is: P = (2,000 - Q) / 500

Supply Curve is: P = (Q - 800) / 100

Quantity	Demand	Supply
800	2.4	0
1100	1.8	3
1400	1.2	6
1700	0.6	9
2000	0	12

Producer's surplus = area of triangle ADE = 1 / 2 x AD x DE = 1 / 2 x (1,000 - 800) x 2 = 200

Demand & Supply Equations 14 12 10 4 2 B 2,000 0 1500 2000 2500 500 A 800 1000 DemandSupply

Consumer's surplus = area of triangle BDE = 1 / 2 x BD x DE = 1 / 2 x (2,000 - 1,000) x 2 = 1,000