Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Monopoly and Oligopoly ECON 212 Lecture 15 Tianyi Wang Queen’s Univeristy Winter 2013 Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 1 / 16 Introduction I Firm takes price as given in a perfectly competitive industry. I The opposite is monopoly, a market with only one …rm. I Note monopoly cannot chooses price and quantity independently. I Monopoly can choose price and let quantity determined by market demand. Or the other way around. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 2 / 16 Monopoly Problem I Monopoly faces market constraint in the form of market demand. I Let p (q ) be the inverse market demand curve. Let c (q ) be the cost function. Then monopolist’s problem is max p (q )q q c (q ) I Note monopoly must choose output level that MR=MC. I Solve by taking the FOC, p (q ) + qp 0 (q ) = c 0 (q ) I Marginal revenue consists of two parts: one from selling addtional unit and one from reduced price for all existing units. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 3 / 16 Markup I We can rewrite the FOC, p (q ) = I 1 MC (q ) (1 + e(1q ) ) where e(q ) is the price elasticity of demand and the term 1 (1 + e(1q ) ) is known as markup for the monopoly. I Note for perfect competition FOC is p (q ) = MC (q ). Thus it is a special case where demand elasticity is negative in…nity. I Also monopoly will never operate on inelastic part of demand curve ( 1 < e 0), for pro…t can be increased by reducting output. I See classnotes for graph. I See classnotes for linear demand. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 4 / 16 Extensions 1. E¢ ciency of monopoly. 2. Price Discriminations. 3. Natural monopoly. 4. Quality choices. 5. Group discount, bundling... Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 5 / 16 Oligopoly I Oligopoly lies between perfect competitive and monopoly. I There are a small number of …rms and entry is di¢ cult. I Strategic consideration: …rms recognize the interaction of decisions. I We consider a range of models. I I I sequential vs simultaneous quantity vs price Limit the number of …rms to two (duopoly) for simplicity. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 6 / 16 Simultaneous Quantity I Firms forcast each other’s decision when make decisions simultaneously. I Cournot model - quantity competition I Consider an industry with 2 identical …rms. Firm 1 expects …rm 2 to produce q2e . I Then if …rm 1 produces q1 , he expects the total output to be q = q1 + q2e . I Each …rm knows that equilibrium price depends on total output by inverse demand function p (q ). Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 7 / 16 Simultaneous Quantity I Firm 1’s problem is to choose q1 to max pro…t max p (q1 + q2e )q1 q1 I c ( q1 ) FOC gives q1 p 0 (q1 + q2e ) + p (q1 + q2e ) = c 0 (q1 ) I This implies …rm 1 set quantity as a function of …rm 2’s choice (in expectation). q1 = f1 (q2e ) I This equation is known as a reaction function; it describes how …rm 1 reacts to …rm 2’s choice. I Similarly …rm 2’s reaction function is q2 = f2 (q1e ) Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 8 / 16 Simultaneous Quantity I In equilibrium expectations are con…rmed so that no one has incentive to revise choices. I An equilibrium is two output levels q1 and q2 that solve the reaction functions simultaneously: q1 q2 = f1 ( q 2 ) = f2 ( q 1 ) I Note f 0 < 0. (strategic substitutes) I See class notes for graph. I See calss notes for …x-point theorem. I See class notes for example. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 9 / 16 Simultaneous Price I Alternatively …rm can set price and take as given the price it expects other …rm to set. I Bertrand competition - price competition. I We will get the same result as perfect competitive equilibrium. 1. Firm will not set a price below MC 2. If both set a price above MC, each has incentive to decrease by a bit. 3. So in equilibrium both set price at MC. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 10 / 16 Leadership - Quantity I One …rm makes quantity choice before the other. I Stakelberg model. I Assume …rm 1 is the leader and …rm 2 is the follower. I Equilibrium price determined by total output q = q1 + q2 according to inverse demand function p (q ). I In equilibrium, leader chooses output given expectation on follower’s output. I Follower produces the expected amount, so that no one has incentive to change. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 11 / 16 Leadership - Quantity I Start with follower’s problem, known as backward induction. I Given leader’s choice q1 , follower’s problem is max p (q1 + q2 )q2 q2 I c2 ( q 2 ) FOC is q2 p 0 (q1 + q2 ) + p (q1 + q2 ) = c20 (q2 ) I This implies follower’s reaction function q2 = f (q1 ). I Note f 0 < 0 Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 12 / 16 Leadership - Quantity I The Leader’s problem can be stated as follows max p (q1 + f (q1 ))q1 q1 I c1 ( q 1 ) Solve by taking FOC. q1 p 0 (q1 + q2 )(1 + f 0 (q1 )) + p (q1 + q2 ) = c10 (q1 ) I Output is higer than monopoly, since f 0 < 0 makes …rst term less negative. I In other words, competitiion increases output. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 13 / 16 Leadership - Price I Leader may set a price given his expection on follower’s choice. I Both will set the same price. Otherwise consumer buys from lower price. I Suppose leader set price p, and follower takes this as given, follower’s problem is max pq2 c2 (q2 ) q2 I FOC gives p = c 0 ( q2 ) I which is essentially a supply curve for follower S (p ). I Leader may calculate the residual demand RD (p ) = D (p ) which has an inverse residual demand curve of prd (q1 ). Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 S (p ), Winter 2013 14 / 16 Leadership - Price I The leader’s problem is max prd (q1 )q1 q1 c 1 ( q1 ) I Output can be found when MR=MC. I Price decreases and output increases compared with monopoly. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 15 / 16 Cartel I Firms can collude on production. I Cartel maximize total industry pro…t and allocate output to each …rm. max p (q1 + q2 )(q1 + q2 ) q 1 ,q 2 I c1 ( q 1 ) c2 ( q 2 ) FOCs are p (q1 + q2 ) + (q1 + q2 )p 0 (q1 + q2 ) = c10 (q1 ) p (q1 + q2 ) + (q1 + q2 )p 0 (q1 + q2 ) = c20 (q1 ) I Similar to monoply’s. Equate marginal cost. I However each member has incentive to cheat. I Punish cheating by reverting to competitive equilibrium. Game theory. Tianyi Wang (Queen’s Univeristy) ECON 212 Lecture 15 Winter 2013 16 / 16