Perfect Competition & Welfare

Perfect Competition & Welfare

Outline Derive aggregate supply function Short and Long run euilibrium 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 Euation: P A --B.Q linear demand Inverse demand function: willingness to pay $/unit A P 1 Maximum willingness to to pay pay Constant slope Q 1 Demand A/B At At price price P 1 a 1 consumer will will buy buy uantity Q 1 1 Quantity

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 euals price To maximize profit a firm of any type must euate marginal revenue with marginal cost So in perfect competition price euals marginal cost

MR MC Profit is π() R() - C() Profit maximization: dπ/d 0 This implies dr()/d - dc()/d 0 But dr()/d marginal revenue dc()/d marginal cost So profit maximization implies MR MC

Perfect competition: an illustration The supply curve moves to the right With With market market demand demand D 2 (a) The Firm (b) With With The market Industry demand demand D 2 and and market market supply supply S 1 Price falls and and market market supply supply S 1 With With market price 1 1 $/unit price P euilibrium C price price is is P 1 C $/unit euilibrium price price is is P 1 the C the firm firm maximizes Entry continues while profits exist and and uantity uantity is is Q 1C and and uantity uantity is is Q 1 profit C by by setting Now MC Now assume assume C that Existing Long-run that firms euilibrium maximize is restored MR MR ( ( P C ) C ) MC MC and demand and at profits price P demand by C and by increasing supply curve S D 2 S 1 increases 1 producing uantity to to c c output AC to to 1 1 D 2 D 2 P 1 P 1 S 2 P C Excess Excess profits profits induce Pinduce C new new firms firms to to enter enter the the market market D 2 c 1 Quantity Q C Q 1 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 Example 1: Three firms Firm 1: MC MC/4 4 + - 82 Firm 2: MC MC/2 2 + - 84 $/unit Firm 3 Firm 1 Firm 2 1 + 2 + 3 Firm 3: MC MC/6 6 + - 84/3 Invert these 8 Aggregate: Q 1 + 2 + 3 11MC/12-22/3 MC 12Q/11 + 8 Quantity

Example 2: Eighty firms Each firm: MC MC/4 4 + - 82 Invert these Aggregate: Q 80 20MC - 160 MC Q/20 + 8 $/unit 8 Firm i Aggregate Definition of normal profit not the same as zero profit Quantity implies that a firm is making the market return on the assets employed in the business

Practice problem Demand : Q Inverse Demand : P 120 TC D 6000 50 9 2 ( ) 100 + + 10 P 90 50 Q D Initial number of firms 20 1) Find short run euilibrium 2) Find long run euilibrium

Short run ( ) 3. 49 140 6900 9 50 6000 100 10 100 10 2 10 10 2 10 100 9 50 6000 2 + + + p p p S D p Q p mc TC P Q s s D

Long run P min avg cost Point at which MCAC mc ac mc 2 100 ac + + 10 + 2 10 p 30 6000 50 Q 9 n Q n 10 + p Q 10 100 + + 4500 500 9 / 500 / 10 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 The demand curve measures the willingness to pay for each unit Consumer surplus is the area between the demand curve and the euilibrium price $/unit Competitive Supply The supply curve measures the marginal cost of each unit Producer surplus is the area between the supply curve and the euilibrium price P C Consumer surplus Producer surplus Euilibrium occurs occurs where where supply supply euals euals demand: price price P C C uantity uantity Q C C Demand Aggregate surplus is the sum of consumer surplus and producer surplus The competitive euilibrium is efficient Q C Quantity

Illustration (cont.) Assume that a greater uantity Q G is traded Price falls to P G $/unit The net effect is a reduction in total surplus Competitive Supply Producer surplus is now a positive part and a negative part P C Consumer surplus increases P G Part of this is a transfer from producers Part offsets the negative producer surplus Demand Q C Q G Quantity

Output restricted to Q M $/unit Suppose output is restricted to Q M The market clearing price is P M Competitive Supply This This is is the the deadweight loss loss Consumer surplus is given by this area And producer surplus is given by this area P M P C There are mutually beneficial trades that do not take place: between Q M and Q C Demand Q M Q C MR Quantity

Exercise Consider a competitive industry where all firms are identical with cost function: C 200 + 2 /2 + 10. Market demand is given by: p 55 -Q/20 Find the long run euilibrium (price, uantity and number of firms.) Mc+10, AC200/+/2+10 Euating get: /2200/ 2 400 20 pmc30 Substituting in demand function: 3055-Q/20 Q500 Number of firms nq nq/500/2025

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 euilibrium. AC 35 30 10 20 AC200/+/2+10 AC(10)35 P3555-Q/20 Q400 n40

Exercise (continued) Suppose now the government introduces a regulation that forces firms to produce no less than 40 units. Find the new long run euilibrium. AC AC200/+/2+10 AC(40)35 35 30 20 40 P3555-Q/20 Q400 n10

Exercise (continued) Welfare cost: 55 Welfare loss: 5*400+100*5/2 2,250 Original Surplus: 35 30 Welfare loss Q s 500*25/26,250 % loss 36% 400 500 Q