# Perfectly Competitive Markets

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1 Characteristics: Fragmented: Many small firms, none of which have market power Undifferentiated Products: Products that consumers perceive as being identical. Perfect Pricing Information: Consumers have full awareness of the prices charged by all sellers in the market. Equal Resource Access: All firms have equal access to production technology and inputs How do work? Price takers: Due to industry fragmentation Law of One Price: From the 2nd and 3rd characteristic of perfectly competitive markets Free Entry (into the market): From the last characteristic of perfectly competitive markets Economic vs. Accounting Profit Economic Profit = Sales Revenue Economic Costs (including opportunity costs) Accounting Profit = Sales Revenue Accounting Costs 1

2 Query #1 Suppose Joe starts his own business. In the first year the business earns \$100,000 in revenue and incurs \$85,000 in explicit costs. In addition, Joe has a standing offer to come work for his brother for \$40,000 per year. Joe s accounting profit is and Joe s economic profit is. a) \$25,000 and \$15,000 b) \$15,000 and \$65,000 c) \$15,000 and \$60,000 d) \$15,000 and \$25,000 Query #1 - Answer Answer D Accounting Profit is the difference between a firm s sales revenue and its explicit costs. Accounting π = \$100,000 \$85,000 = \$15,000 Economic Profit is the difference between a firm s sales revenue and the totality of its economic costs, including all relevant opportunity costs. Economic π = \$100,000 \$85,000 \$40,000 = \$25,000 Page 308 Every firm in the perfectly competitive industry faces the following profit maximization problem: where the price p is taken as given (price taking assumption in perfectly competitive markets). Taking first order conditions with respect to output q, yields and rearranging yields p=mc(q). From our above profit maximization problem of firms operating in a perfectly competitive industry, we concluded that each of them increases their output q until p=mc(q). that is, every firm increases q until the point at which: the marginal revenue it obtains for every additional unit, i.e., the prevailing market price p, coincides with the marginal cost of producing that additional unit, MC(q). 2

3 We can also check if second order conditions are satisfied, so we confirm that the condition we found above p=mc(q), is a condition to maximize, rather than minimize, profits. Differentiating p MC(q)=0, with respect to q yields TR TC MC( q) MC( q) S.O.C: 0 0 since 0 q q Thus, a price taking firm maximizes π when p=mc(q). What happens if, rather than setting output at the point in which P = MC(Q), the firm sets it at a different price? If MR > MC (P > MC), we have Q π If MR < MC (P < MC), we have Q π Market Price in the Short Run Short run: Capital level K is fixed for all firms. Number of firms is also fixed in the market. Sunk fixed costs: A fixed cost that the firm cannot avoid if it shuts down and produces zero output. Example: lease that cannot be sublet Nonsunk fixed costs: A fixed cost that a firm does not need to incur if it produces no output. Example: heating 3

4 Short-Run when all fixed costs are sunk Supply The profit maximizing condition P = MC makes the supply decisions of the firm (Supply Curve) to coincide with the SMC curve (red line). Sunk Costs If P < AVC, then we have that, apart from the Sunk Fixed Cost, the firm is making losses for TFC+[Q(AVC P)], the shaded rectangle. This explains why the Supply Curve is Q=0 for all prices P < min(avc), i.e., the supply curve is a vertical spike for all P < min(avc) Note, finally, that there are points where p AVC, SAC the firm is not compensated for its fixed costs since P < SAC, although it is for its variable costs, since P> AVC. Short Run supply curve: The supply curve that shows how the firm s profit maximizing output decision changes as the market price changes, assuming that the firm cannot adjust all of its inputs. Short-Run Supply Curve, Example STC = Q + Q 2, then MC = Q VC What is the AVC curve? A) AVC = VC/Q = (20Q + Q 2 )/Q = 20 + Q What about the supply curve? Remember we need two conditions: (1) P=MC(Q), and (2) two segments: above/below the min of AVC Let us first find the Min of the AVC curve: We know that this minimum occurs where MC = AVC. Then, Q = 20 + Q 2Q = Q Q = 0 Then min AVC = = 20. Height Plug Q=0 at AVC 4

5 Short Run Example (cont.) Short run Supply Curve For p< 20, we have Q = 0 (vertical spike) For p 20, we have 0 if p 20 Supply (P) = p 10 if p 20 2 Query #2 The short run supply curve for a firm operating in perfect competition is a) the firm s marginal cost curve. b) the firm s average variable cost curve. c) the firm s average variable cost curve above marginal cost. d) the firm s marginal cost curve above the shut down price. Query #2 - Answer Answer D In the short run, a firm operating in perfect competition has a supply curve equal to the marginal cost curve above the shut down price, or the minimum average variable cost. For prices below the shut down price, the firm supplies zero output, and the supply curve is a vertical line at Q=0. 5

6 What if fixed costs are (1) sunk, and (2) nonsunk Supply with Sunk Costs Supply with Sunk Costs Supply New In this case you will never produce when P<ANSC Shut down price: The price below which a firm supplies zero output in the short run. Shutdown Price Explanation Generally, the shut down price is the minimum of the curve of average avoidable cost: ANSC If some fixed costs are sunk AVC If all fixed costs are sunk SAV If no fixed costs are sunk Example Consider again the following STC curve: STC = Q + Q 2 SMC = Q A) Assume that, out of the \$100 SFC = 36 and NSFC = 64. What is ANSC? We need to find the nonsunk costs. NSC = TC Sunk Costs = NSFC + Sunk Fixed Costs + VC Sunk Costs = NSFC + VC = Q + Then ANSC = 64 20Q Q2 Q Q Q Min ANSC It happens where ANSC = MC 64/Q Q = Q 64/Q = Q 64 = Q 2 Q = 64 8= min(ansc) then min ANSC = 64/ = \$36 Q=8 Height (P s ), which is the shut down price in this context 6

7 Example (cont.) B) We use the shutdown price, P S = \$36, to find the supply curve If p < 36 then Q = 0 If p 36 then Q is determined from p = MC, p p = Q. Hence, solving for Q yields Q = Supply curve from the previous example Supply (P) = 0 if p 36 p 10 if p 36 2 Query #3 For a particular perfectly competitive firm, costs are STC = q + q 2 and marginal costs are SMC = q. If the market price is equal to 40, what is the maximum profit the firm can earn? a) 400 b) 200 c) 100 d) 0 Query #3 - Answer Answer D At the profit maximizing point, P = SMC. We know that the price P = 40, and SMC = Q. Hence, setting them equal to each other, we can find the number of units this firm produces. P = SMC 40 = Q Q = 10 7

8 Since Q = 10 Total revenue is: Total cost is given by: TR = (P) (Q) TR = (40) (10) TR = 400 TC(Q) = Q + Q 2 TC(Q) = (10) + (10) 2 TC(Q) = 400 Short Run Market Supply How can we find the market supply curve if we know the supply curve for each individual firm? We horizontally sum the individual supply curves, as shown in the next slide. Therefore, profits are equal to: Page 315 π = TR(Q) TC (Q) π = π = 0 Short-run Market Supply Be careful: if we are adding up Supply 1, 2 for each price, we want Supply 1, 2 in terms of p. Secondly, we will divide our analysis for different price intervals. Don t worry: it is easier than you expect, but don t forget to multiply the number of types of firm per each supply curve. 8

9 Short run market supply curve The supply curve that shows the quantity supplied in the aggregate by all firms in the market for each possible market price when the number of firms in the industry is fixed. Equilibrium in the Short Run Given the short run supply curve SS, we can now find equilibrium prices and quantities by setting SS equal to market demand. Example Equilibrium in the Short Run Market demand is given by D(P) = 60 P VC STC = Q 2, N=300 firms Thus: SMC = 300Q and AVC = 150Q Example (cont.) Supply curve of each individual firm Min AVC occurs at AVC=SMC, 150Q=300Q so Q = 0, which implies min AVC = 0. Then, for any p > 0 we have p = MC, p = 300Q, or Q = p/300. Thus, every firm s supply curve is Q = p/300 for all p > 0. Don t forget solving for Q 9

10 Example (cont.) Market Supply is 300 (p/300) = p, that is, N supply function for every firm Competitive equilibrium occurs at the point where market supply equals market demand: p = 60 p 2p = 60 p*=30 Market Supply Market Demand Hence, p* = \$30, and Q* = 30 Figure (next Slide) Comparative Statics Roses and Valentines Day More Firms Increase in Demand N induces P and Q Elastic supply (small p) Inelastic Supply (large p) Hence, an increase in demand (e.g., a good becomes more fashionable) increases equilibrium prices, but this increase is particularly large when supply is inelastic. Low Demand months High Demand months An increase in demand for Mother s Day doesn t affect prices as supply is very elastic However, at Valentine s Day, supply is more inelastic, thus affecting prices 10

11 Using Changes in Demand to Estimate Supply We observe Q from 4.5 to 8.9 (see figure) P from 0.22 to 0.55 (also represented in the Figure) Hence, the slope of the supply curve is: Slope: We can use this slope to find the price elasticity of supply,, Interpretation: 1% in P 0.82% in Q S in Valentine s Day. Hence, supply is relatively inelastic to price changes, as suspected for Valentine s Day. Another Application of Inelastic Supply Nord Pool: Electric power exchange between Norway, Sweden, Finland, and Denmark Close to Perfectly Competitive Market: many suppliers, with rare disparities in the price of Mwh across the four countries, electricity is regarded as a homogenous good, etc. Yet prices are extremely high in unusually cold winters; why? Price that a local distributor of electricity pays to a generator. Because, for most firms, supply becomes really steep after exceeding its normal production level. Aggregate supply curve is very steep, and an increase in demand on cold days produces a very significant P. Long-Run Supply Long run supply Similar to short run, but now there are no fixed or sunk costs: Now all costs are avoidable, since the size of the plant, K, acts like variable, i.e., it can be varied. Long-run PC Markets Long run competitive equilibrium: The market price and quantity at which supply equals demand, established firms have no incentive to exit the industry, and prospective firms have no incentive to enter the industry. 1. No entry, no exit 2. Each firm maximizes long run profits, π, changing Q and K decisions 3. Economic profits are zero, since p = min AC 4. Market Demand = Market Supply (Note: These four properties hold in the long run, although properties 1 and 3 are equivalent) 11

12 Example Consider the following information: AC(Q) = 40 Q Q 2 MC(Q) = 40 2Q Q 2 D(p) = 25,000 1,000p Equilibrium in a P.C. market: N firms in the industry, each with: This is the aggregate demand We know that in a P.C. market the following 3 conditions must hold: p* = MC(Q*) = 40 2Q* (Q*) 2 (profit maximizing) p* = AC(Q*) = 40 Q* (Q*) 2 (zero profit) D(p*) = n* Q* 25,000 1,000p* = nq* (market demand = market supply) Example (cont.) From the first two equations, p=mc and p=ac, we obtain MC=AC: 1) 40 2Q* (Q*) 2 = 40 Q* (Q*) 2 Rearranging, 0.02 (Q*) 2 = 2Q* Q* 0.02 (Q*) 2 = Q* 0.02 Q* = 1 Q* = 1/0.02 = 50 units (The individual supply in equilibrium With this equality, we make MC=AC, finding the min of the AC, which occurs where MC and AC intersect Going back to the first equation (p=mc), and plugging Q*=50, we obtain 2) p* = 40 2Q* (Q*) 2 = (50) 2 = \$15 (This is the equilibrium price) Example (cont.) Now we know the equilibrium price, p*=\$15, as well as the individual supply for every firm, Q*=50 units Long-run equilibrium in a perfectly competitive market 3)Plugging p*=15 into the demand function, we obtain D(p*) = 25,000 1, = 10,000 4)Then, from condition D(p*) = n* Q*, i.e., market demand = market supply, we find that 10,000 = n 50 n = 10,000/50 = 200 firms in equilibrium Individual supply Let us depict these results on the next slide 12

13 Empirical Application of n* For a given individual supply provided by individual firms, the larger the demand, the larger the number of firms (in this application, internet service providers, ISPs) in a local market. That is, n*=demand / Output by each firm Long-run Supply Curve P 1 Supply curve for this firm p 1 Entry Empirical evidence: (Pullman and Moscow) A) Market with less than 74,000 hab. 1-5 ISPs Min AC (Chicago) B) Market with more than 943,000 hab. 21 or more ISPs Typical Firm Market Explanation on the next slide Sequential Presentation of the Previous Figure Demand shifts from D 0 to D 1 Price increases from p 0 to p 1 (e.g. from \$15 to \$23) Large profits, since p 1 > SRAC in the left panel (shaded area) This induces the entry of new firms, from SS 0 to SS 1 in the right panel Equilibrium, in the long run, happens to be at p 0 = min AC No entry or exit of additional firms Long run supply curve is a flat line at p = min AC [This is the case of constant cost industry where Q from new firms doesn t affect input prices, i.e., doesn t affect firms cost curves] So far entry did not affect input prices, but What if it does? More firms in the industry can make inputs more expensive. Example: Scarce input, such a master grower in the rose industry, leads to an increase in the price of this input More firms can also make inputs cheaper. Example: Computer chips as inputs (smartphones); price drops when the smartphone industry expands. 13

14 Long-run supply with increasing costs Long-run supply curve with decreasing costs Entry SMC 0 SMC1 AC 0 E 1 where p=min AC 1 Min AC 1 AC 1 A B C P=min AC Example: Master grower (scarce inputs) [ in costs as a result of entry] Example: industry that uses a specific chip extensively [Entry induces the input providers to increase scale, lowering prices of chips.] Economic Rent Economic Rent: The economic return that is attributable to extraordinarily productive inputs whose supply is scarce. Alternative definition of Economic Rent: Maximum amount that a firm is willing to pay for services of an input, also referred to as the input s reservation rule Economic Rent (cont.) 0.25 Rose firm with an extraordinary master grower (lower AC curve) Rose firm with a run of the mill master grower Market for roses 14

15 Economic Rent (Cont.) Producer Surplus Firm 1 Firm 2 AC` and MC` in left hand side due to extraordinary master grower who receives a low salary as regular master grower MC and AC in right hand side since they use run of themill master grower who receives a low salary as regular master grower, their costs are higher. If P.C. p* = 0.25, then firm 1 profits are larger (shaded area) Competition for such a valuable (talented) master grower makes firm 2 offer him from 70,000 to 105,000. A similar argument applies to Firm 1. As a consequence, the economic rent will be 105,000 70,000=35,000, which is entirely captured by the extraordinary master grower. Producer Surplus: A measure of monetary benefit that producers derive from producing a good at a particular price. 25 PS = Supply Curve (in blue) Producer Surplus Difference between what a producer actually receives for selling one unit and the minimum price he must receive in order to be willing to supply that unit, i.e., its MC. This definition applies both in the case of individual firms and market supply. Note that with linear supply curves F.A.C.E. Producer surplus from the first 100 units when p=\$3.50 ABC Additional producer surplus from the last 25 units (from 100 to 125) PS = + 15

16 Producer Surplus (For each individual firm, and at the market level) Producer Surplus - Example Consider a linear market supply Q=60p (in thousands) Equilibrium price is \$2.50. What is producer surplus at this price? At p=\$2.50, equilibrium output is Q=60*(2.5)=150,000 Therefore, producer surplus is given by the area of triangle A in the following figure ,000 \$2.50 \$187,500 2 Producer Surplus - Example Q=60p Producer Surplus Example (Cont.) What if p increases to \$4.00; how does PS grow? Producer surplus grows in areas B + C, where Area B= (4 2.5) 150,000 = 225,000, and 1 Area C is (4 2.5) ( ) = 67,500, 2 where note that, at a price of p = \$4, output becomes Q = 60 4 = 240 Hence, when p increases from p=2.5 to p=4, Producer surplus grows in: (B) + (C) = 225, ,500 = 292,500 16

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