How is the equilibrium number of firms determined in a market where entry and exit is permitted?
In a market with free entry and exit, the equilibrium number of firms is determined by dividing the market equilibrium quantity by the quantity supplied by each individual firm. The formula is: n₀ = q₀/q₀f, where n₀ is the equilibrium number of firms, q₀ is the market equilibrium quantity, and q₀f is the quantity supplied by each firm.
With free entry and exit, the equilibrium price equals the minimum average cost of the firms. At this price, no firm earns supernormal profit or incurs loss. The market supplies exactly the quantity demanded by consumers, and each firm supplies its profit-maximising output at that price.
For example, if equilibrium price is Rs 20, market demand is 180 kg, and each firm supplies 30 kg at this price, then n₀ = 180/30 = 6 firms.
Explanation
The textbook explains that with free entry and exit, the equilibrium price equals minimum average cost. At this price, market supply equals market demand (q₀). Each firm supplies q₀f at this price. The equilibrium number of firms is calculated by dividing total market quantity by per-firm supply. The example in the text (Example 5.2) demonstrates this calculation: q₀ = 180, q₀f = 30, therefore n₀ = 6.
Solution Steps
Step 1: Determine equilibrium price (p₀) which equals minimum average cost under free entry and exit.
Step 2: Find market equilibrium quantity (q₀) from the demand curve at price p₀.
Step 3: Find quantity supplied by each firm (q₀f) at price p₀ from the firm's supply curve.
Step 4: Calculate equilibrium number of firms using n₀ = q₀/q₀f.