Lecture 5. Perfectly Competitive Market (perfect competitive market)
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1. Perfect competition
2. Short-run supply by a single firm
3. Market equilibrium for short-run supply
4. Long-run supply by a single firm
5. Market equilibrium for long-run supply
1. Perfect Competition
⑴ Market: the set of all sellers and buyers that, through interaction, determine the price of a good.
⑵ Scope of a market
① Vertical scope: the scope of a market depending on the degree of integration across distribution stages.
② Spatial scope: e.g., a gold market vs. an agricultural products market.
③ Time scope: the more storable a good is, the longer the relevant time scope of the market.
④ Form of the product: e.g., an automobile market vs. a tractor market.
⑶ Perfectly competitive market: a market consisting only of price-takers.
① Requirement 1. There are very many producers and consumers participating in the market transaction.
○ No individual agent can affect the market price.
○ Everyone takes the price as given.
② Requirement 2. The product is homogeneous.
○ A particular producer’s product cannot receive a higher price than other producers’ products within the same industry.
○ Price-taker: a firm that can sell as much as it wants up to P*, but cannot sell at all at any price higher than P*.
③ Requirement 2-1. Law of One Price: the market price P can be treated as a constant.
○ One way to evaluate market performance is to check whether the law of one price holds.
○ Even if the law of one price holds, transport costs by distance prevent prices from becoming perfectly identical.
○ In pre-modern societies, information gaps made markets inefficient, so price differences often exceeded the range explainable by transport costs.
○ In England, the creation of the penny post (Paypost) system—an efficient postal system—contributed substantially to reducing such price differences.
④ Requirement 3. No barriers to entry.
○ New producers can enter and existing producers can exit freely.
⑤ Requirement 4. All economic agents have perfect information.
⑥ In reality, perfectly competitive markets do not exist: the concept serves as a benchmark for evaluating real-world market structures.
2. Short-run Supply by a Single Firm
⑴ Terminology
① SC (short-run total cost function): the cost incurred to produce quantity q when there is at least one fixed factor of production.
② SAC (short-run average cost function): SC divided by q.
③ SMC (short-run marginal cost function): the derivative of SC with respect to q.
④ SAFC (short-run average fixed cost function)
⑤ SAVC (short-run average variable cost function)
⑵ A firm’s short-run supply curve
Figure 1. A firm’s short-run supply curve
① The marginal cost curve always intersects the average cost (AC) curve or the average variable cost (AVC) curve at their extrema.
② When the market price is sufficiently high, the firm chooses output Q such that that price equals marginal cost.
③ If the market price is lower than the minimum point of the AVC curve, the firm stops producing.○ The highest market price at which the firm is indifferent to producing or not is called the shutdown price.
○ (Note) If you think carefully, shutdown is relevant only when the cost curve is discontinuous at the origin.
④ Short-run supply curve: the portion of the marginal cost curve above the shutdown point.
⑤ Example
○ P = P* = 2
○ TC = Q² + 10 if Q > 0, 6 if Q = 0
○ FC = 6, VC = Q² + 4
○ π = PQ − TC
○ (Note) At the shutdown price P* = 4, π(0) = π(q*) holds.
3. Market Equilibrium for Short-run Supply
⑴ Short-run market supply function: for each firm i’s supply function qᵢ.
Figure 2. The industry’s short-run supply curve
⑵ Market demand function
① Each individual firm faces a horizontal demand curve.
② The market demand curve slopes downward.
⑶ Market equilibrium
① Unknowns: kᶜ, ℓᶜ, P*, q*
○ Because this is a short-run supply equilibrium, the number of firms n is given as a constant, not an unknown.
○ In a long-run supply equilibrium, n is an unknown.
② Condition 1. Cost minimization problem: under this condition, express kᶜ and ℓᶜ as functions/relations in terms of q, v, w.
③ Condition 2. Profit maximization problem
④ Condition 3. Market demand equals market supply○ If Qᴰ > Qˢ, consumers try to buy more even at a higher price.
○ If Qᴰ < Qˢ, suppliers try to sell more by lowering the price.
○ If Qᴰ = Qˢ, the market price P does not change.
⑤ Combine Condition 2 and Condition 3 to determine P* and q*.
Figure 3. Short-run market equilibrium in a perfectly competitive market
⑷ Short-run producer surplus
4. Long-run Supply by a Single Firm
⑴ Long-run profit maximization problem
① Setting: since we focus only on supply, assume the price P is a constant.
② If the market price is below the minimum of the AC curve, the firm stops producing.
⑵ Long-run supply function
① The firm should produce at the output level that maximizes profit.
② First-order condition: the optimal output q is generally where the derivative of π(q) is zero (when differentiable).
③ Second-order condition: π(q) must be concave (so the second derivative is negative). Equivalently, the marginal cost must be increasing.
④ Long-run supply curve: the set of profit-maximizing output levels as a function of price.
5. Market Equilibrium for Long-run Supply
⑴ Market demand curve
① Case 1. Constant-cost industry: a price change → economic profit increases → new firms enter → a horizontal market supply curve.
② Case 2. Increasing-cost industry: an upward-sloping market supply curve.
⑵ Market equilibrium
① Unknowns: kᶜ, ℓᶜ, P*, q*, n*
○ Because this is a long-run supply equilibrium, the number of firms n is not a constant but an unknown.
○ In a short-run supply equilibrium, n is given.
② Condition 1. Cost minimization problem: under this condition, express kᶜ and ℓᶜ as functions/relations in terms of q, v, w.
③ Condition 2. Firms’ profits are zero○ Profit here means economic profit: each firm earns no more than it could in other industries.
○ Thus, accounting profit can be positive.
○ If there are profits, new firms enter; if there are no profits, firms exit the market.
○ Because equilibrium occurs at the minimum of ATC, production is socially efficient overall.
⑤ Condition 3. Market demand equals market supply
⑥ Method 1. Use Condition 2-1 and Condition 2-2 to find P* and q*, then use Condition 3 to determine n*.
⑦ Method 2. Use one of Condition 2-1 or Condition 2-2 together with Condition 3 to determine P* and q* (with n* given).○ For f(k, ℓ) = k^α ℓ^(1−α), 0 < α < 1, no meaningful conclusion follows from MC = AC.
⑧ Because two unknowns are adjusted, the long-run marginal cost curve, the minimum point of the long-run average cost curve, and the marginal revenue curve meet at one point.
Figure 4. Long-run market equilibrium in a perfectly competitive market (constant-cost industry)
Figure 5. Long-run market equilibrium in a perfectly competitive market (increasing-cost industry)
⑵ Long-run producer surplus: by Condition 2, long-run producer surplus is always 0.
Entered: 2020.04.10 12:55