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Chapter 9: Perfect Competition

Chapter 9: Perfect Competition. Thus far we have examined how the consumer and firm attempt to optimize their decisions The results of this optimization depend on the set-up of the economy In this course we will examine the extreme set-ups: Perfect Competition and Monopoly.

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Chapter 9: Perfect Competition

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  1. Chapter 9: Perfect Competition • Thus far we have examined how the consumer and firm attempt to optimize their decisions • The results of this optimization depend on the set-up of the economy • In this course we will examine the extreme set-ups: Perfect Competition and Monopoly

  2. Chapter 9: Perfect Competition In this chapter we will cover: 9.1 Perfect Competition Characteristics 9.2 Economic and Accounting Profit 9.3 PC Profit Maximization 9.4 PC Short Run Supply and Equilibrium 9.5 PC Long Run Supply and Equilibrium 9.6 PC Costs 9.7 Economic Rent 9.8 Producer Surplus

  3. 9.1 Perfect Competition Characteristics • Fragmented Industry • -Many buyers and sellers • -No one buyer or seller has an effect on the industry • -Each firm and consumer is a price taker (uses market price) • 2) Homogeneous products • -All firms produce identical products • -No quality differences, no brand loyalty

  4. Perfect Competition Characteristics 3) Perfect Information -Buyers and sellers have full information, especially regarding prices 4) No barriers to entry or exit -No input is restricted to potential customers or firms -Any firm or customer can enter or exit the market in the long run

  5. Perfect Competition Characteristics • As a result, we have: • Many buyers and sellers • Buying and selling identical goods • At a given, set price. • Note: although we are examining a market for outputs, a similar analysis can apply to the market for inputs

  6. 9.2 Economic and Accounting Profit As seen before, Accounting Costs = Explicit Costs Economic Costs = Explicit Costs + Implicit Costs Furthermore, Accounting Profit = Revenue – Explicit Costs Economic Profit = Revenue – Explicit Costs - Implicit Costs

  7. Economic Profit Accounting Profit Implicit Costs Revenue Revenue Economic Costs Explicit Costs Explicit Costs Profit: Economists vs Accountants Economist’s View Accountant’s View

  8. Economic and Accounting Profit Implicit Costs are the BEST ALTERNATIVE return of ALL of an agent’s input (time, money, etc). Alternately, an agent’s time could earn a wage elsewhere. (ie: Work at Simtech for $3000 a month) An agent’s money both isn’t used currently and can be used elsewhere. (ie: Investing $5,000 @ 10% instead of using it to start a business gives an implicit cost of $500)

  9. Example • Mikey opens up a specialized mousepad company. Spending $5,000 a month on space and supplies, Mikey makes $8,000 a month. • Alternately, Mikey could work at Donald Duckpads Inc for $1,500 a month or at a reasearch lab for $1,000 a month. • Mikey could invest in bonds at 10% return or in stocks at 2% return. Calculate accounting and economic profit

  10. Example • Best alternatives: Donald Inc ($1,500) and Bonds ($500). (Since he can do both simultaneously.) • Accounting Profits = Revenue – Explicit Costs • =$8,000-$5,000 • =$3,000 • Economic Profit = Revenue – Explicit Costs • - Implicit Costs • =$8,000 - $5,000 - $1,500 - $500 • =$1,000

  11. 9.3 Profit Maximizing While previously we studied cost minimizing, in reality a firm is more concerned with maximizing its profits. Total Revenue: TR(Q)=PQ Total Cost: TC(Q) as found in previous chapters ie: TC(Q)=100+2Q Profit =Total Revenue – Total Cost: π(Q)=TR(Q)-TC(Q)

  12. Review: TC(Q) TC(Q) in general is derived as follows: Originally: TC=wL+rK (1) Tangency Condition: L=f(K) (2) Production Function: Q=f(L,K) (3) (2) + (3) Q=f(L) and L=f(Q) (4) (2) + (4) K=f(Q) (5) (1) + (4) + (5) TC=wf(Q)+rf(Q) TC=f(Q)

  13. Review: TC(Q) For Example: Originally: TC=wL+rK (1) Tangency Condition: L=K (2) Production Function: Q=2(LK)1/2 (3) (2) + (3) Q=2L and L=Q/2 (4) (2) + (4) K=Q/2 (5) (1) + (4) + (5) TC=wQ/2+rQ/2 TC=(w+r)Q/2

  14. Marginal Revenue • Definition: Marginal revenue is the change in revenue when output changes • Marginal revenue is the slope of the total revenue curve. • Since the PC firm is a price taker, the additional revenue gained from 1 additional output is equal to P.

  15. Marginal Revenue & Marginal Cost • As seen previously, marginal cost changes as production increases. • If for the next unit, MR>MC, that unit should be produced, as it yields profit. • If for the last unit, MC>MR, that unit should not have been produced, as it decreases profit. • Therefore profit is maximized where MC=MR=P

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

  17. The previous curves are expressed by: TC(q) = 242q - .9q2 + (.05/3)q3 MC(q) = 242 - 1.8q + .05q2 P = 15 At profit maximizing point: 1) P = MC But this occurs twice. At one point, profit is maximized, at another minimized. Therefore, in order to MAXIMIZE profit: 2) MC must be rising

  18. Example • In the paper industry, MC=20+2Q (which is always rising), where Q=100 reams of paper. Find the cost-maximizing quantity if P=30 or P=40 • Solution: P=MC • 30=20+2Q • 5=Q • P=MC • 40=20+2Q • 10=Q

  19. Short Run Equilibrium In the short run, the firm either produces or temporarily shuts down, thus facing costs: STC(Q) = SFC + NSFC + TVC(q) when q > 0 SFC when q = 0 SFC: Sunk Fixed costs – unavoidable sunk costs NSFC: Non-sunk Fixed costs – fixed costs that are avoidable if the firm temporarily shuts down TVC: Total Variable Costs; depends on output

  20. 9.4 Short Run Supply Definition: The firm’s Short run supply curve tells us how the profit maximizing output changes as the market price changes. 3 Cases: Case 1: all fixed costs are sunk Case 2: all fixed costs are non-sunk Case 3: some fixed costs are sunk

  21. Case 1 : All Fixed Costs Sunk • Case 1: all fixed costs are sunk • NSFC=0 • STC=TVC(q) + SFC • If the firm chooses to produce a positive output, P = SMC defines the short run supply curve of the firm. But…

  22. The firm will choose to produce a positive output only if: • (q) > (0) …or… • Pq – TVC(q) – SFC > -SFC  • Pq – TVC(q) > 0  • P > AVC(q) • Definition: The price below which the firm would opt to produce zero is called the shut down price, Ps. In this case, Ps is the minimum point on the AVC curve.

  23. Therefore, the firm’s short run supply function is defined by: • 1. P=SMC, where SMC slopes upward as long as P > Ps • 2. 0 where P < Ps • This means that a perfectly competitive firm may choose to operate in the short run even if economic profit is negative.

  24. $/yr Example: Short Run Supply Curve of the Firm, NSFC = 0 SMC SAC AVC Ps Quantity (units/yr)

  25. 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. • Example: • STC(q) = 100 + 20q + q2 • SFC = 100 (nb: this is sunk) • TVC(q) = 20q + q2 • AVC(q) = 20 + q • SMC(q) = 20 + 2q

  26. a.The minimum level of AVC is the point where AVC = SMC or… • 20+q = 20+2q • q = 0 • AVC minimized at p=20 • b.The firm’s short run supply curve is, then: • P < Ps = 20: qs = 0 • P > Ps = 20: P = SMC  • P = 20+2q  • qs = ½P - 10

  27. Case 2: All Costs are non-Sunk • Case 2: all fixed costs are non-sunk • SFC=0 • STC=TVC(Q)+NSFC • If the firm chooses to produce a positive output, • P = SMC defines the short run supply curve of the firm. But…

  28. The firm will choose to produce a positive output only if: • (q) >(0) …or… • Pq – TVC(q) - NSFC > 0  • P > AVC(q) + AFC(q) = SAC(q) • Now, the shut down price, Ps is the minimum of the SAC curve

  29. $/yr Example: Short Run Supply Curve of the Firm, All Fixed Costs Non-Sunk SMC SAC Ps AVC Quantity (units/yr)

  30. Case 3: Some costs are sunk • Case 3: Short Run Supply Curve • (Some costs are sunk): • NSFC≠0, SFC ≠0 • Average Nonsunk Cost = Average Variable Cost + Average Nonsunk Fixed Cost • ANSC=AVC + NSFC/Q

  31. The firm will choose to produce a positive output only if: • (q) > (0) • Pq – TVC – SFC - NSFC > -SFC  • Pq – TVC - NSFC > 0  • P > AVC + NSFC/Q = ANSC • Definition: The price below which the firm would opt to produce zero is called the shut down price, Ps. In this case, Ps is the minimum point on the ANSC curve.

  32. Therefore, the firm’s short run supply function is defined by: • 1. P=SMC, where SMC slopes upward as long as P > Ps • 2. 0 where P < Ps • This means that a perfectly competitive firm may choose to operate in the short run even if economic profit is negative.

  33. $/yr Example: Short Run Supply Curve of the Firm SMC SAC ANSC AVC Ps Quantity (units/yr)

  34. Shut Down Rule Summary • If all fixed costs are sunk, • (AVC=ANSC) • Shut down if P<AVC (low) • If all fixed costs are nonsunk, • (ANSC=SAC) • Shut down if P<SAC (high) • If some fixed costs are sunk, some nonsunk, • Shut down if P<ANSC (middle)

  35. Shut Down Rule Summary • A firm will produce • If • It can cover its Non-Sunk Costs

  36. Short Run Market Supply Curve and Short Run Market Equilibrium Thus far we have seen that the individual firm’s short run supply curve comes from their marginal cost 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. (Just as market demand is the HORIZONTAL sum of individual demand curves)

  37. Example: From Short Run Firm Supply Curve to Short Run Market Supply Curve Typical firm:Market: Individual supply curves per firm. 1000 firms of each type SMC3 $/unit SMC2 $/unit SMC1 Market supply 30 24 22 20 0 1.2 mill 0 300 400 500 q (units/yr) Q (m units/yr)

  38. 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) • Qs(P)= Qd(P) • and qs(P) is determined by the firm's individual profit maximization condition.

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

  40. Example: Deriving a Short Run Market Equilibrium 300 identical firms Qd(P) = 60 – P STC(q) = 0.1 + 150q2 SMC(q) = 300q NSFC = 0 AVC(q) = 150q

  41. a. Short Run Equilibrium • Profit maximization condition: P = SMC • P = 300q • qs(P) = P/300 (for each firm) • Qs(P) = P (for industry) • Qs(P) = Qd(P)  P = 60 – P • P*= 30 • q* = 30/300=.1 • Q* = 30

  42. b.Do firms make positive profits at the market equilibrium? • SAC = STC/q = .1/q + 150q • When each firm produces .1, SAC per firm is: .1/.1 + 150(.1) = 16 • Therefore, P* > SAC so profits are positive.

  43. Comparative Statics in theShort Run • As seen in previous chapters, the entry or exit of firms or consumers, among other things, can shift the market demand and supply curves • Shifts in the market demand and supply curves will shift the equilibrium quantity as seen in chapters 1 and 2

  44. The Long Run In the short run, capital is fixed and firms may temporarily operate under an economic profit or loss. In the long run, capital can change and firms can enter and leave the market, resulting in zero economic profit. Remember that in the long run, all costs are nonsunk (they are all avoidable at zero output)

  45. Long Run MC Just as in the short run the firm operated at: P=SMC In the long run the firm operates at P=MC SMC≠MC (in general) since costs are reduced in the long run. Only at LR profit maximization is SMC=MC (because the short run is operating at the LR optimal capital point: Point A next slide)

  46. In the long run, this firm has an incentive to change plant size to level K1 from K0: $/unit MC AC A SMC0 • SAC0 P SAC1 SMC1 q (000 units/yr) 1.8 6

  47. 9.5 LR Supply Curve In the long run, a firms supply curve is The firm’s LR MC curve above AC. For if P>AC, Profits>0. Since Profits = (PxQ)-(ACxQ) As in the short run, market supply is the horizontal sum of individual firm supply.

  48. Long Run Supply Curve: $/unit MC S AC P SMC1 q (000 units/yr) 1.8 6

  49. LR PC Equilibrium • Long Run Perfectly Competitive Equilibrium occurs when: • Each firm maximizes profit with regards to output and capital (P=MC) • Each firm’s economic profit is zero (as firms keep entering until the price is pushed down to zero profits) (P=AC) • Market Demand=Market Supply

  50. Long Run Perfectly Competitive Equilibrium Typical FirmMarket $/unit $/unit MC Market demand SAC AC P* SMC q*=50,000 Q*=10M. q Q

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