9.14. A perfectly competitive industry consists of two types of firms: 100 firms of type A and 30 firms of type B. Each type A firm has a short-run supply curve sA (P) 2P. Each type B firm has a short-run supply curve sB (P) 10P. The market demand curve is D (P) 5000 500P. What is the short-run equilibrium price in this market? At this price, how much does each type A firm produce, and how much does each type B firm produce?

At P = 5, Firm A will produce 2P = 2 into 5 = 10 units

At P = 5, Firm B will produce 10P = 10 into 5 = 50 units

Explanation:

An equilibrium in Market occurs when Market Supply = Market Demand

At Price P Total Quantity supplied by Firms of Type A

= sum of quantity supplied at P by all firms of Type A = (2P) into 100 = 200P

At Price P Total Quantity supplied by Firms of Type B

= sum of quantity supplied at P by all firms of Type B = (10P) into 30 = 300P

Hence Market Supply is given by:

S (P) = 200P plus 300P = 500P

Market demand = D (P) = 5000 minus 500P

Hence, at equilibrium Market demand = Market Supply

=> At equilibrium

D (P) = 5000 minus 500P = S (P) = 500P

=> 1000P = 5000. Hence P = 5.

Hence Short Run equilibrium Price in the Market = 5

At P = 5, Firm A will produce 2P = 2 into 5 = 10 units

At P = 5, Firm B will produce 10P = 10 into 5 = 50 units