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Perfect Competition & Welfare Outline Derive aggregate supply function Short and Long run equilibrium Practice problem Consumer and Producer Surplus Dead weight loss Practice problem Focus on profit maximizing behavior of firms Take as given the market demand curve $/unit Equation: P = A - B.Q linear demand Inverse demand function: willingness to pay Maximum willingness to pay A Constant slope P1 Demand Q1 A/B Quantity At price P1 a consumer will buy quantity Q1 Perfect Competition Firms and consumers are price-takers Firm can sell as much as it likes at the ruling market price do not need many firms do need the idea that firms believe that their actions will not affect the market price Therefore, marginal revenue equals price To maximize profit a firm of any type must equate marginal revenue with marginal cost So in perfect competition price equals marginal cost MR = MC Profit is p(q) = R(q) - C(q) Profit maximization: dp/dq = 0 This implies dR(q)/dq - dC(q)/dq = 0 But dR(q)/dq = marginal revenue dC(q)/dq = marginal cost So profit maximization implies MR = MC Perfect competition: an illustration With market price PC $/unit the firm maximizes profit by setting MR (= PC) = MC and producing quantity qc With market demand D2 • The supply curve moves to the right andmarket marketdemand supplyDS11 (a) The Firm (b)With The Industry • Price falls and market supply S1P1 equilibrium price is equilibrium price isis Q P1C $/unitprofits exist and quantity • Entry continues while and quantity is QCthat Now assume •Existing Long-run equilibrium is restored MC firms maximize demand atprofits price Pby supply curve S2 increasing C and S1 to increases D1 output AC to q1 D2 P1 S2 P1 Excess profits induce PC new firms to enter the market PC qc q1 Quantity D2 QC Q1 Q´C Quantity Perfect competition: additional points Derivation of the short-run supply curve this is the horizontal summation of the individual firms’ marginal cost curves $/unit Example 1: Three firms Firm 3 Firm 1 Firm 2 Firm 1: qMC = MC/4 = 4q +- 82 q1+q2+q3 Firm 2: qMC = MC/2 = 2q +- 84 Firm 3: qMC = MC/6 = 6q +- 84/3 Invert these 8 Aggregate: Q= q1+q2+q3 = 11MC/12 - 22/3 MC = 12Q/11 + 8 Quantity Example 2: Eighty firms $/unit Firm i Each firm: qMC = MC/4 = 4q +- 82 Invert these Aggregate: Q= 80q = 20MC - 160 MC = Q/20 + 8 Aggregate 8 Quantity Definition of normal profit not the same as zero profit implies that a firm is making the market return on the assets employed in the business Practice problem Demand : Q D 6000 50 P 9 Inverse Demand : P 120 TC q 100 q 2 10q Initial number of firms = 20 1) Find short run equilibrium 2) Find long run equilibrium 90 QD 50 Short run 6000 50 P 9 TC q 100 q 2 10q mc 2q 10 QD p 10 q 2 Q s 10 p 200 s D S 10 p 200 p 7800 55.7 140 6000 50 p 9 Long run P = min avg cost Point at which MC=AC mc 2q 10 100 ac q 10 q 100 mc ac 2q 10 q 10 q q 10 p 30 6000 50 p 4500 Q 500 9 9 nq Q n Q / q 500 / 10 50 Exercise Competitive Industry – 2 types of firms 1. Low cost firms: • Constant marginal cost 10 cents per unit – no fixed cost. • Total capacity of group = 1000 units 2. High cost firms: • marginal cost of 20 cents per unit • When producing at full capacity average cost = 30 cents • total group capacity of 2000 units a) Draw the long run supply curve of this industry and the short run supply curve assuming all firms are active. (b) After a fall in demand, there has been an initial price reduction in the short run, followed by a price increase in the long run. Draw demand curves before and after the fall in demand that would lead to this situation. Explain. (c) Consider again the initial situation and suppose the low cost firms discover extra capacity (e.g. new oil wells) at the same marginal cost of 10 cents per unit and that in the short run this lead to a reduction in price but in the long run the price returned to its previous level. Draw a picture for the supply function of this industry prior and after the change and the demand function that would explain this situation. Efficiency and Surplus Can we reallocate resources to make some individuals better off without making others worse off? Need a measure of well-being consumer surplus: difference between the maximum amount a consumer is willing to pay for a unit of a good and the amount actually paid for that unit aggregate consumer surplus is the sum over all units consumed and all consumers producer surplus: difference between the amount a producer receives from the sale of a unit and the amount that unit costs to produce aggregate producer surplus is the sum over all units produced and all producers total surplus = consumer surplus + producer surplus Efficiency and surplus: illustration $/unit The demand curve measures the willingness to pay for each unit Consumer surplus is the area between the demand curve and the equilibrium price The supply curve measures the marginal cost of each unit Producer surplus is the area between the supply curve and the equilibrium price Competitive Supply PC Consumer surplus Equilibrium occurs where supply equals demand: price PC quantity QC Producer surplus Demand Aggregate surplus is the sum of consumer surplus and producer surplus The competitive equilibrium is efficient QC Quantity Illustration (cont.) Assume that a greater quantity QG is traded Price falls to PG $/unit The net effect is a reduction in total surplus Competitive Supply Producer surplus is now a positive part and a negative part PC Consumer surplus increases PG Part of this is a transfer from producers Part offsets the negative producer surplus Demand QC QG Quantity Output restricted to QM $/unit Suppose output is restricted to QM The market clearing price is PM Consumer surplus is given by this area And producer surplus is given by this area This is the deadweight loss of monopoly Competitive Supply PM PC There are mutually beneficial trades that do not take place: between QM and QC Demand QM QC MR Quantity Exercise Consider a competitive industry where all firms are identical with cost function: C = 200 +q2/2 + 10q. Market demand is given by: p = 55 -Q/20 Find the long run equilibrium (price, quantity and number of firms.) • • • • • Mc=q+10, AC=200/q+q/2+10 Equating get: q/2=200/q q2 = 400 q=20 p=mc=30 Substituting in demand function: 30=55-Q/20 Q=500 Number of firms nq=Q n=Q/q=500/20=25 Exercise (continued) Suppose now the government introduces a regulation that limits the size of firms to no more than 10 units. Will there be exit or entry of firms? Find the new long run equilibrium. AC=200/q+q/2+10 AC AC(10)=35 P=35=55-Q/20 35 30 Q=400 10 20 n=40 q Exercise (continued) Suppose now the government introduces a regulation that forces firms to produce no less than 40 units. Find the new long run equilibrium. AC=200/q+q/2+10 AC AC(40)=35 P=35=55-Q/20 35 30 Q=400 20 40 n=10 q Exercise (continued) Welfare loss: 5*400+100*5/2 Welfare cost: =2,250 Original Surplus: 55 500*25/2=6,250 % loss = 36% 35 30 Qs Welfare loss 400 500 Q