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Exercises · Q5

Q.Explain how price is determined in a perfectly competitive market with fixed number of firms.

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In a perfectly competitive market with a fixed number of firms, price is determined by the intersection of market demand and market supply, where each firm is a price taker and produces where price equals marginal cost.

In a perfectly competitive market, the key feature is that no single buyer or seller can influence the market price. Each firm is a price taker — it must accept the price determined by the market as a whole. When the number of firms is fixed (meaning no entry or exit in the short run), the market supply curve is simply the horizontal sum of the individual firms' supply curves. These individual supply curves are derived from each firm's marginal cost curve above its minimum average variable cost.

The determination of price happens through the interaction of total market demand and total market supply. Let’s walk through the logic step by step.

Market equilibrium condition:

Qd(P)=Qs(P)Q_d(P) = Q_s(P)

where QdQ_d is market demand and QsQ_s is market supply.

Step 1: Market demand — All consumers in the market collectively demand a certain quantity at each possible price. The demand curve slopes downward: as price falls, quantity demanded rises.

Step 2: Market supply — With a fixed number of firms, say NN firms, each firm has its own supply curve si(P)s_i(P) (which is its marginal cost curve above the shutdown point). The market supply is:

Qs(P)=∑i=1Nsi(P)Q_s(P) = \sum_{i=1}^{N} s_i(P)

This curve slopes upward: as price rises, each firm produces more, so total quantity supplied increases.

Step 3: Equilibrium price — The market reaches equilibrium at the price P∗P^* where the quantity demanded by all consumers exactly equals the quantity supplied by all firms. At this price, there is no excess demand or excess supply.

Watch out

A common mistake is to think that an individual firm "sets" its price. In perfect competition, the firm cannot set price — it can only choose how much to produce at the given market price. If it charges even slightly above P∗P^*, it sells nothing.

Step 4: Firm's decision — Once the market price P∗P^* is determined, each firm decides its output by equating price to its marginal cost:

P∗=MC(qi)P^* = MC(q_i)

This ensures profit maximization. The firm produces where the additional revenue from one more unit (the price) equals the additional cost of producing it. …

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