Answer to Question #151253 in Microeconomics for me;

Question

Consider a market made up of identical perfectly competitive firms. Market demand is
Qd=6000-3p and market supply is Qs=1200+9p.

a)Solve for the equilibrium levels of quantity and price in this market.
b)Calculate consumer surplus and producer surplus at this equilibrium.

Answer 1

Solution:

a.). The equilibrium levels of quantity and price in this market:

At equilibrium: Market demand = Market supply

6000 – 3p = 1200 + 9p

6000 – 1200 = 9p + 3p

4800 = 12p

p = 4800/12

p = 400

Equilibrium Price = 400

Equilibrium quantity = 6000 – 3(400) = 6000 – 1200 = 4800

 

b.). Consumer surplus and producer surplus at this equilibrium:

Consumer surplus = ½ * Q_d * (P_MAX – P_d)

Where: Q_d = Quantity demanded at equilibrium = 4800

            P_MAX = Maximum price the buyer is willing to pay = 6000

            P_d = Equilibrium price = 400

= ½ * 4800 * (1200 – 400) = 2400 * 800 = 1,920,000

Consumer Surplus = 1,920,000

 

Producer Surplus = ½ * PS * (OP – OQ)

Where: PS = Equilibrium quantity = 4800

            OP = Market price = 400

            OQ = Minimum price to sell = 200

= ½ * 4800* (400 – 200) = 2400 * 200 = 480,000

Producer Surplus = 480,000