Question

9.15. A market contains a group of identical price-taking firms. Each firm has a marginal cost curve SMC(Q) 2Q, where Q is the annual output of each firm. A study reveals that each firm will produce if the price exceeds $20 per unit and will shut down if the price is less than $20 per unit.The market demand curve for the industry is D(P) 240 P/2,where P is the market price.At the equilibrium market price, each firm produces 20 units. What is the equilibrium market price, and how many firms are in this industry?

Answer 1

equilibrium market price = 40

Number of firms in the industry = 240

Step-by-step explanation:

Let we assume the number of firms be N

And, at equilibrium

Marginal cost = market price

2Q = P i.e market price .....................(i)

Also demand = supply at equilibrium point

which equals to

= 240 × (P ÷ 2) = N × Q.......(ii)

So,

from (i) and (ii)

N i.e Number of firms in the industry = 240

since Q i.e Quantity =20 units

So,

P = 2Q

= $40