Lecture # 14 Perfectly Competitive Markets Lecturer: Martin Paredes

1. Lecture # 14 Perfectly Competitive Markets Lecturer: Martin Paredes

2. Outline • Perfect Competition Defined • Profit Maximisation • Short Run Equilibrium • Supply curve for the firm and market • Equilibrium • Producer surplus • Long Run Equilibrium • Equilibrium Conditions • Supply Curve

3. Perfectly Competitive Markets Definition: A perfectly competitive market consists of firms that produce identical products that sell at the same price. • Each firm’s volume of output is so small in comparison to the overall market demand that no single firm has an impact on the market price.

4. Perfectly Competitive Markets Assumptions: Firms produce undifferentiated products, in the sense that consumers perceive them to be identical. Consumers have perfect information about the prices all sellers in the market charge All firms (industry participants and new entrants) have equal access to resources (technology, inputs).

5. Perfectly Competitive Markets Assumptions (cont.): Each buyer’s purchases are so small that he/she has an imperceptible effect on market price. Each seller’s sales are so small that he/she has an imperceptible effect on market price. Each seller’s input purchases are so small that he/she perceives no effect on input prices

6. Perfectly Competitive Markets Implications of Assumptions: • The Law of One Price: Conditions (1) and (2) imply that there is a unique, single price at which all transactions occur.

7. Perfectly Competitive Markets Implications of Assumptions: • Price Takers: Conditions (3) and (4) imply that buyers and sellers take the price of the product as given when making their purchase and output decisions.

8. Perfectly Competitive Markets Implications of Assumptions: • Free Entry: Condition (5) and (6) implies that all firms have identical long run cost functions. • We need also need to assume that setup costs are easily achievable.

9. Profit Maximisation Definition: The Economic Profit is the difference between total sales revenues and the economic cost (including opportunity costs). • Then, the firm’s objective is to choose the amount of output to maximise profits: Max (q) = TR – TC = P· q – C(q) q

10. Profit Maximisation Example: Suppose: Total Revenues € 10 M Costs of supplies and labor € 9 M Owner’s opportunity cost € 2 M • Accounting Profit: € 10M – € 9M = € 1M • Economic Profit: € 10M – € 9M – € 2M = – € 1M • Business “destroys” € 1M of wealth of owner

11. Profit Maximisation • Since the firm’s objective is: Max (q) = TR – TC = P· q – C(q) q …then the first order condition is: d(q) = 0 …or… dTR = dTC dq dq dq • The last term states that marginal revenue equals marginal cost.

12. Profit Maximisation Notes: Recall that: • If MR > MC then profit rises if output is increased => Increase output. • If MR < MC then profit falls if output is increased => Decrease output. • Therefore, the profit maximization condition for any firm is MR = MC.

13. Profit Maximisation Definition: A firm’s marginal revenue is the rate at which total revenue changes with respect to output. MR = dTR(q) = d[P(q)· q] dq dq • In perfect competition, P(q) = P. As a result, MR = P.

14. Profit Maximisation Note: • Since MR = P under perfect competition, then the profit maximization condition for a price-taking firm is P = MC.

15. Profit Maximisation Example: Suppose: • The market price is P = 15 • Each firm has the cost function: TC(q) = 24q – 0.9q2 + 0.0167q3 => MC(q) = 24 – 1.8q + 0.05q2

16. €/yr Example: Profit Maximization Condition Total revenue = pq 15 q (units per year)

17. €/yr Example: Profit Maximization Condition Total cost Total revenue = pq q (units per year)

18. €/yr Example: Profit Maximization Condition Total cost Total revenue = pq Total profit q (units per year)

19. €/yr Example: Profit Maximization Condition Total cost Total revenue = pq Total profit 6 q (units per year) 30

20. €/yr Total revenue = pq Example: Profit Maximization Condition q (units per year) P, MR 15 q (units per year)

21. €/yr Total revenue = pq Total Cost Example: Profit Maximization Condition q (units per year) MC P, MR 15 q (units per year)

22. €/yr Total revenue = pq Total Cost Example: Profit Maximization Condition q (units per year) MC P, MR 15 q (units per year) 6 30

23. Profit Maximisation Notes: • At profit maximizing point: • P = MC • MC is non-decreasing

24. Profit Maximisation Notes: • What is the firm’s demand curve? • The firm can sell as much as it likes at price P, so the firm’s demand curve is a straight line at P • What is the firm’s supply curve? • It is defined by the MC curve, but not in its entirety.

25. Short Run Equilibrium Definition: The short run is the period of time in which the firm’s plant size is fixed and the number of firms in the industry is also fixed. • Firms need to take into account their respective short run total cost.

26. Short Run Equilibrium • Recall that the short run total cost function can be decomposed into two elements: • Total variable cost: TVC(q) • Total fixed cost: TFC • In turn, the fixed cost can be divided into: • Sunk fixed costs SFC • Non-sunk fixed costs NSFC

27. Short Run Equilibrium • Then: TVC(q) + SFC + NSFC when q > 0 TC(q) = SFC when q = 0 • Obviously TFC = SFC + NSFC

28. Firm's Supply Curve in Short Run Definition: The short run supply curve for a firm tells us how the profit-maximizing output changes as the market price changes.

29. Firm's Supply Curve in Short Run General Idea: • If the firm chooses to produce q > 0, then condition P = SMC defines short run supply curve of the firm. • The firm produces q > 0 as long as: (q)  (0) • If (q) < (0), then the firm shuts down.

30. Firm's Supply Curve in Short Run Definition: The shut-down price, Ps, is the price below which the firm would opt to produce zero. • The firm’s short run supply function is defined by: SMC when P  PS s(P) = 0 when P < PS

31. Firm's Supply Curve in Short Run • The value of Ps depends on the structure of the fixed costs. In particular, whether there are sunk costs or not. • Let’s look at two cases: • All fixed costs are sunk NSFC = 0 and SFC > 0 ==> (0) = SFC • All fixed costs are non-sunk NSFC > 0 and SFC = 0 ==> (0) = 0

32. Firm's Supply Curve in Short Run Case 1: NSFC = 0 and SFC > 0 • Hence, TFC = SFC (fixed costs are all sunk) • The firm will choose to produce a positive output only if: (q) (0) …or… P· q – TVC(q) – TFC  – TFC = – SFC

33. Firm's Supply Curve in Short Run Case 1: NSFC = 0 and SFC > 0 • In other words: P· q – TVC(q)  0 …which can be re-written as: P  AVC(q) • Therefore, the shut-down price, Ps, is the minimum point on the AVC curve.

34. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 €/yr SMC SAC AVC Quantity (units/yr)

35. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 €/yr SMC SAC AVC Ps Quantity (units/yr)

36. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 €/yr SMC SAC AVC Ps Quantity (units/yr)

37. Firm's Supply Curve in Short Run Case 1: NSFC = 0 and SFC > 0 • A perfectly competitive firm may operate in short run even if economic profit is negative. • At prices below SAC but above AVC, profits are negative if the firm produces…but the firm loses less by producing than by shutting down because of sunk costs.

38. Firm's Supply Curve in Short Run Case 2: NSFC > 0 and SFC = 0 • The firm will choose to produce a positive output only if: (q) (0) …or… P· q – TVC(q) – TFC  0

39. Firm's Supply Curve in Short Run Case 2: NSFC = 0 and SFC > 0 • In other words: P  AVC(q) + AFC = SAC • Therefore, the shut-down price, Ps, is the minimum point on the SAC curve.

40. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 SMC SAC AVC Quantity (units/yr)

41. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 €/yr SMC SAC Ps AVC Quantity (units/yr)

42. Example: Short Run Supply Curve of the Firm NSFC = 0 and SFC > 0 €/yr SMC SAC Ps AVC Quantity (units/yr)

43. Short Run Market Supply Curve Definition: • The market supply at any price is the sum of the quantities each firm supplies at that price. • The short run market supply curve is the horizontal sum of the individual firm supply curves.

44. Example: From Short Run Firm Supply Curve to Short Run Market Supply Curve Firm Type 1 Firm Type 2 Market supply SMC1 SMC2 P P P 30 20 Q Q Q

45. Short Run Perfectly Competitive Equilibrium Definition: A short run perfectly competitive equilibrium occurs when the market quantity demanded equals the market quantity supplied: • ni=1 qs(P) = Qd(P) • where qs(P) is determined by the firm's individual profit maximization condition.

46. Example: Short Run Perfectly Competitive Equilibrium €/unit Market: Supply P* Demand Q* m. units/yr

47. Example: Short Run Perfectly Competitive Equilibrium €/unit €/unit Market:Typical firm: Supply SMC SAC P*=MR P* AVC Demand Ps q* Units/yr Q* m. units/yr

48. Producer Surplus Definition: The Producer Surplus is the area above the market supply curve and below the market price. It is a monetary measure of the benefit that producers derive from producing a good at a particular price.

49. Example: Producer Surplus P Market Supply Curve Q

50. Example: Producer Surplus P Market Supply Curve P* Q