Final answer:
The quantity of output each firm will produce in the market is 10 units. There are 2 firms in the market. We solved this by setting the market demand equal to the market supply and then finding the equilibrium price and quantity.
Step-by-step explanation:
To find the quantity of output a firm will produce in this competitive market and the number of firms, we need to determine the market equilibrium where market demand equals market supply (Qd = Qs). However, there appears to be a typo in the question. But using the correct demand and supply equations, QD = 80 - 2P and QS = P - 10, we'll solve for the equilibrium price (P) and quantity (Q).
Setting Qd equal to Qs, we get 80 - 2P = P - 10. Solving for P, we find that P = 30. Substituting P back into the supply function, QS = 30 - 10 = 20, which means the market equilibrium quantity is 20 units.
Given that each identical firm has a marginal cost (MC) curve of MC = 3q, and in the long run, firms produce where price equals marginal cost (P = MC), we set P = MC to find the quantity per firm: 30 = 3q yields q = 10. This is the output per firm. To find the number of firms in the market, divide the total market quantity by the quantity per firm: 20 / 10 = 2 firms.