Perfect Competition Definition

Perfect Competition Definition What is the essence of perfect competition? All agents in the market take the relevant price for this market as given. That is, all agents assume that their behaviour will not affect the market price. Moreover, they assume that they can buy or sell as much as they like at the market price. By agents we mean both Firms and Consumers. Notice that often a firm has market power: sometimes can affect the price (a large firm in a market) sometimes it is the only firm in the market (monopoly) But also a consumer sometimes has market power Think of the government as a consumer of weapons. () October 10, 2012 1 / 20

Perfect Competition Environment What makes a market behave perfectly competitive? Many atomistic buyers and producers Homogenous good Perfect information (consumers and firms). Free entry and exit. Perfectly divisible output. No transaction costs. () October 10, 2012 2 / 20

Demand Side We assume that the aggregate demand curve for a good is downward-sloping q = D(p), where D (p) < 0. Often it is more convenient to work with the inverse demand function: p = P(q) where P (q) < 0. How can we derive this function? () October 10, 2012 3 / 20

Derivation of Demand Curve DEMAND FOR PIZZA First slice what would be the maximum you would pay for one slice of pizza? Say, 3. How about the second slice? (this is after you had your first slice) Say, 1.5 (certainly less than for the first slice). And for the third slice? (this is after you had your second slice) Say, 0.2 (certainly less than for the second slice). () October 10, 2012 4 / 20

Derivation of Demand Curve DEMAND FOR PIZZA () October 10, 2012 5 / 20

Consumers Welfare From the demand function, we can first derive the total utility obtained from x units of pizza. More importantly, knowing the market price, we can obtain the consumer surplus This is the utility net of the monetary cost to buy the pizza Consumer surplus from x units of pizza. if buying one slice: 3 1 = 2 if buying two slices: (3 + 1.5) 2 1 = 2.5 if buying three slices: (3 + 1.5 + 0.2) 3 1 = 1.7 Demanded quantity of pizza if p = 1: 2 slices. What if p = 0.19? () October 10, 2012 6 / 20

Supply Side Cost Functions 1 Fixed cost (FC): The cost that does not depend on the amount of output produced 2 Variable cost (VC): The cost that rises with output (and equals zero if no output is produced) 3 Total cost (TC): TC (q) = FC + VC (q). TC (q) 4 Average or unit cost (AC): AC (q) =. q 5 Marginal cost (MC): the cost of one (infinitesimal) additional unit. MC (q) = TC (q). If working with discrete quantities: MC (q) = TC (q + 1) TC (q) () October 10, 2012 7 / 20

Supply Side Costs The MC function crosses the AC cost function at the minimum average cost level... Why? () October 10, 2012 8 / 20

Equality of minimum AC and MC mathematical proof Let q min denote the output that minimizes AC (q). Then: AC (q min ) = 0. (1) () October 10, 2012 9 / 20

Equality of minimum AC and MC mathematical proof Let q min denote the output that minimizes AC (q). Then: AC (q min ) = 0. (1) Recalling that AC (q) = TC (q)/q, then it follows that: AC (q) = TC (q) q TC (q) q 2. (2) Bearing in mind (1), the numerator in (2) must thus equal zero when q = q min. That is, TC (q min ) q min = TC (q min ). () October 10, 2012 9 / 20

Fixed and Variable Costs examples Consider a steel producer Fixed costs Rent Loan payments Maintenance Variable costs Intermediate inputs: water, electricity, fuel, iron... Labour cost Taxes () October 10, 2012 10 / 20

Fixed and Variable Costs time horizon Fixed costs are mostly related to the size of the plant () October 10, 2012 11 / 20

Fixed and Variable Costs time horizon Fixed costs are mostly related to the size of the plant by varying the size of the plant, we may change the rent, the level of maintenance, the size of the loan required to set up the plant... From that perspective fixed costs are only fixed in the short run () October 10, 2012 11 / 20

Firm s Optimisation Problem Producer solves max q : Π(q) = P(q)q VC (q) FC First Order Condition: Π(q) = 0 P(q) + P(q) MC (q) = 0 () October 10, 2012 12 / 20

Firm s Optimisation Problem Producer solves max q : Π(q) = P(q)q VC (q) FC First Order Condition: Π(q) = 0 P(q) + P(q) MC (q) = 0 under perfect competition: P(q) = p, then P(q) = 0 () October 10, 2012 12 / 20

Firm s Optimisation Problem Producer solves max q : Π(q) = P(q)q VC (q) FC First Order Condition: Π(q) = 0 P(q) + P(q) MC (q) = 0 under perfect competition: P(q) = p, then P(q) = 0 Competitive firm sets q such that: p = MC (q ) () October 10, 2012 12 / 20

Firm s Optimisation Problem Firm s supply curve But, is the condition p = MC (q ) enough? () October 10, 2012 13 / 20

Firm s Optimisation Problem Firm s supply curve But, is the condition p = MC (q ) enough? Actually, it may not be enough... () October 10, 2012 13 / 20

Firm s Optimisation Problem Firm s supply curve But, is the condition p = MC (q ) enough? Actually, it may not be enough... If p <, then the firm prefers to set q = 0... Why? VC (q) q () October 10, 2012 13 / 20

Firm s Optimisation Problem Firm s supply curve But, is the condition p = MC (q ) enough? Actually, it may not be enough... If p <, then the firm prefers to set q = 0... Why? VC (q) q So, the firm s supply curve can be plotted as () October 10, 2012 13 / 20

Aggregate supply curve Summing up horizontally across all firms in the industry, we obtain the aggregate supply curve. () October 10, 2012 14 / 20

Equilibrium The perfect competition equilibrium lies at the intersection of demand and supply curves: () October 10, 2012 15 / 20

Equilibrium: short vs. long run In the short run, the number of firms is fixed... () October 10, 2012 16 / 20

Equilibrium: short vs. long run In the short run, the number of firms is fixed... Hence, firms may make positive profits in the short run. () October 10, 2012 16 / 20

Equilibrium: short vs. long run In the short run, the number of firms is fixed... Hence, firms may make positive profits in the short run. But a feature of perfect competition is: free entry With free entry, positive profits must attract new firms to enter the market. In the long run new firms must enter so long as profits remain positive. () October 10, 2012 16 / 20

Equilibrium From the short to long run () October 10, 2012 17 / 20

Long-run Competitive Equilibrium Productive Effi ciency 1 Under perfect competition, firms set production to equalise: MC (q ) = p. 2 At the minimum level of the average cost function, we have: MC (q min ) = AC (q min ). 3 In the long run competitive firms must make zero profits, hence: AC (q ) = p 4 Therefore, in the long run: p = MC (q min ) = AC (q min ). In the long run, perfect competition ensures productive effi ciency Firms produce at a point in which they minimise their average costs. () October 10, 2012 18 / 20

Competitive Equilibrium Pareto Effi ciency We measure the social welfare as: consumer surplus + producer surplus. () October 10, 2012 19 / 20

Competitive Equilibrium Pareto Effi ciency We measure the social welfare as: consumer surplus + producer surplus. Consumer Surplus: red area below the demand curve minus the price paid by the consumers. () October 10, 2012 19 / 20