Oligopoly and Monopolistic Competition .


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Oligopoly and Monopolistic Rivalry . APEC 3001 Summer 2007 Readings: Part 13. Goals. Attributes of Oligopoly and Monopolistic Rivalry Cournot Duopoly Display Vital Conduct In Cournot Duopoly Show Response Capacities and Nash Harmony Bertrand Duopoly Demonstrate
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Oligopoly and Monopolistic Competition APEC 3001 Summer 2007 Readings: Chapter 13

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Objectives Characteristics of Oligopoly & Monopolistic Competition Cournot Duopoly Model Strategic Behavior In Cournot Duopoly Model Reaction Functions & Nash Equilibrium Bertrand Duopoly Model Stackelberg Duopoly Model Effect of Industrial Organization on Prices, Output, & Profit Monopolistic Competition Model Basic Concepts of Economic Games & Their Solutions

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Oligopoly & Monopolistic Competition Definitions Oligopoly: An industry in which there are just a couple of essential dealers of an indistinguishable item. Monopolistic Competition: An industry in which there are (1) various firms each giving distinctive yet fundamentally the same as items (close substitutes) and (2) free passage and exit. Imperative: One association\'s decisions influences the benefit capability of different firms, which brings about vital connections among firms!

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Cournot Duopoly Model Assumptions P = a – bQ where Q is industry yield. Two firms deliver indistinguishable item: Q = Q 1 + Q 2 . Negligible Costs: MC 1 = MC 2 = 0. Address: How does Firm 1\'s decision of yield influence the interest for the Firm 2\'s yield? P = a – bQ = a – b(Q 1 + Q 2 ) = (a – bQ 1 ) – bQ 2 Linear Equation: Intercept = (a – bQ 1 ) & incline = - b

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Demand For Firm 2\'s Output Given Firm 1\'s Output Q 1 =15 Q 1 =10 Q 1 =5

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Important Implications Demand for Firm 2 relies on upon Firm 1\'s yield! In like manner, interest for Firm 1 relies on upon Firm 2\'s yield!

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Short Run Conditions: MC = MR MC\' > MR\' P* > AVC Long Run Conditions: LMC = MR LMC\' > MR\' P* > LAC Profit Maximization for Duopolist Nothing new here! To keep things basic, we will expect MC\' > MR\' & P* > AVC in the short run & LMC\' > MR\' & P* > LAC over the long haul.

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Firm 1 TR 1 = P(Q)Q 1 = (a – bQ)Q 1 = aQ 1 – bQQ 1 = aQ 1 – b(Q 1 + Q 2 )Q 1 = aQ 1 – bQ 1 2 – bQ 1 Q 2 MR 1 = TR 1/Q 1 = TR 1 " = a – 2bQ 1 – bQ 2 Firm 2 TR 2 = P(Q)Q 2 = (a – bQ)Q 2 = aQ 2 – bQQ 2 = aQ 2 – b(Q 1 + Q 2 )Q 1 = aQ 1 – bQ 1 Q 2 – bQ 2 MR 2 = TR 2/Q 2 = TR 2 " = a – bQ 1 – 2bQ 2 What is minor income for a Cournot Duopolist?

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Firm 1 Firm 2 What is the benefit expanding yield for a Cournot Duopolist? Be that as it may, now what do we do?

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The two association\'s are indistinguishable, so lets expect they carry on indistinguishably: Q 1 * = Q 2 *! Industry Output: Price: Firm Output: What about firm & industry benefit?

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Firm & Industry Profit Firm Profit: Industry Profit: So, what does this mean?

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Question: What might happen if the two firms converged into a restraining infrastructure? TR = P(Q)Q = (a – bQ)Q = aQ – bQ 2 MR = TR\' = a – 2bQ* MC = MR  0 = a – 2bQ or Q* = a/2b P* = P(Q*) = a – b(a/2b) = a/2 * = P(Q*)Q* = (a/2)(a/2b) = a 2/4b Notice that Industry benefit with an imposing business model is higher! Anyway, why might a Cournot Duopoly ever exist?

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Here is a Game Suppose a = 100 & b = 5 Each firm can pick the ideal Cournot Output: a/3b = 20/3 or a large portion of the syndication yield: a/4b = 20/4. Each firm should pick its yield before knowing the other company\'s decision.

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The Profit Matrix Firm 1 gets the opportunity to pick the line, while Firm 2 gets the opportunity to pick the section. The benefits for the amusement are dictated by the line & section that is picked. Firm 1\'s benefit is in intense , Firm 2\'s benefit is in italics .

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What is a company\'s best technique, given the other association\'s decision? Firm 1 amplifies benefit by picking Q 1 = 20/3! In the event that Firm 2 picks Q 2 = 20/4, Firm 1\'s benefits are higher on the off chance that it picks Q 1 = 20/3 (277.7 > 250). On the off chance that Firm 2 picks Q 2 = 20/3, Firm 1\'s benefits are higher on the off chance that it picks Q 1 = 20/3 (222.2 > 208.3). Firm 2 boosts benefit by picking Q 2 = 20/3! In the event that Firm 1 picks Q 1 = 20/4, Firm 2\'s benefits are higher in the event that it picks Q 2 = 20/3 (277.7 > 250). On the off chance that Firm 1 picks Q 1 = 20/3, Firm 2\'s benefits are higher on the off chance that it picks Q 2 = 20/3 (222.2 > 208.3).

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The Prisoner\'s Dilemma Both Firm\'s eventual happier consenting to create a large portion of the imposing business model yield contrasted with the Cournot yield. However, both company\'s augment their own benefit by picking the Cournot yield paying little mind to what the other firm does. In this way, picking a large portion of the imposing business model yield appears to have neither rhyme nor reason.

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Reaction Functions & Nash Equilibrium An Asymmetric Cournot Duopoly Assumptions P = a – bQ where Q is industry yield. Two firms deliver indistinguishable item: Q = Q 1 + Q 2 . Peripheral Costs: MC 1 = c 1 & MC 2 = c 2 with the end goal that c 1  c 2 .

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Firm 1 Firm 2 What is the benefit expanding yield for unbalanced Cournot Duopolists? Be that as it may, now what do we do?

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Reaction Functions & Nash Equilibrium Definitions Reaction/Best Response Function: A bend that tells the benefit boosting level of yield for one oligopolist for every amount provided by others. Nash Equilibrium: A mix of yields with the end goal that each association\'s yield boosts its benefit given the yield picked by different firms.

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Example Asymmetric Duopoly Reaction Functions Assuming a = 100, b = 5, c 1 = 50, & c 2 = 45 R 2 (Q 1 ) A: Nash Equilibrium R 1 (Q 2 )

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General Solution to the Problem & Starting with substitution infers

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Or For a = 100, b = 5, c 1 = 50, & c 2 = 45,

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Bertrand Duopoly Model Firms pick cost at the same time, rather than amount. Question: Does this matter? Yes, or we most likely would not discuss it!

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Bertrand Duopolist Strategy Question: If I know my rival will pick some value P 0 , say $50, what cost would it be advisable for me to pick? Suspicions Two Firms Demand: P = a – bQ Marginal Costs: MC = MC 1 = MC 2 = 0 Question: What does Firm 2\'s request look like given Firm 1\'s decision of cost?

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Firm 2\'s Demand Given Firm 1\'s Price P 1 =75 P 1 =75 P 1 =50 P 1 =50 & 75 P 1 =25 P 1 =25, 50, & 75

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Implications Firms have a motivator to undermine their rival\'s cost the length of they can make a benefit. This conduct will drive the cost down to the minor cost: P* = MC  0 = a – bQ*  Q* = a/b * = P*Q* = ( a – b(a/b))(a/b) = ( a – a)(a/b) = 0 Bertrand result is same as impeccable rivalry!

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Stackelberg Duopoly Model Firms pick amounts consecutively instead of at the same time. Question: Does this matter? Yes, or we most likely would not discuss it! Suppositions Two Firms Demand: P = a – bQ Marginal Costs: MC = MC 1 = MC 2 = 0 Firm 1 picks yield Q 1 first. Firm 2 picks yield Q 2 second subsequent to seeing Firm 1\'s decision. Q = Q 1 + Q 2

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How would we discover Firm 1 & 2\'s benefit augmenting yields? In the Cournot Model, neither one of the firms got the see the other\'s yield before settling on its decision. In the Stackelberg Model, Firm 2 gets the chance to see Firm 1\'s yield before settling on its decision. Address: How can Firm 1 utilize this further bolstering its good fortune? Firm 1 ought to consider how Firm 2 will react to its decision of yield.

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Given Firm 1\'s decision of yield, what is Firm 2\'s benefit augmenting yield? It is again ideal for Firm 2 to set minor cost equivalent to negligible income: MC 2 = MR 2 . Firm 2\'s Total Revenue: TR 2 = P(Q)Q 2 = (a – b(Q 1 + Q 2 ))Q 2 = aQ 2 – bQ 1 Q 2 – bQ 2 . Firm 2\'s Marginal Revenue: MR 2 = TR 2 " = a – bQ 1 – 2bQ 2 MC 2 = MR 2  0 = a – bQ 1 – 2bQ 2 *  2bQ 2 * = a – bQ 1  Q 2 * = ( a – bQ 1 )/(2b) = R 2 (Q 1 ).

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Given Firm 2\'s best reaction, what is Firm 1\'s benefit amplifying yield? It is ideal for Firm 1 to set minor costs equivalent to negligible income: MC 1 = MR 1 . Firm 1\'s Total Revenue: TR 1 = P(Q)Q 1 = (a – b(Q 1 + Q 2 ))Q 1 = aQ 1 – bQ 1 2 – bQ 1 Q 2 . In any case, Q 2 = R 2 (Q 1 ), so TR 1 = aQ 1 – bQ 1 2 – bQ 1 R 2 (Q 1 ). Firm 1\'s Marginal Revenue: MR 1 = TR 1 " = a – 2bQ 1 – bR 2 (Q 1 ) – bQ 1 R 2 " (Q 1 ) But R 2 (Q 1 ) = ( a – bQ 1 )/(2b) & R 2 \'(Q 1 ) = - b/(2b) = - 1/2, so MR 1 = a – 2bQ 1 – b ( a – bQ 1 )/(2b) – bQ 1 (- 1/2) = a – 2bQ 1 – a/2 + bQ 1/2 + bQ 1/2 = a/2 – bQ 1 MC 1 = MR 1  0 = a/2 – bQ 1 *  bQ 1 * = a/2  Q 1 * = a/(2b)

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What is Firm 2\'s benefit expanding yield, the cost, & benefits? Q 2 * = R 2 (Q 1 *) = ( a – abdominal muscle/(2b))/(2b) = ( a – a/2)/(2b) = a/(4b) P* = a – b(Q 1 * + Q 2 *) = a – b(a/(2b) + a/(4b)) = a – (a/2 + a/4) = a/4  1 * = P*Q 1 * = ( a/4) (a/(2b)) = a 2/(8b)  2 * = P*Q 2 * = ( a/4) (a/(4b)) = a 2/(16b) * =  1 * +  2 * = a 2/(8b) + a 2/(16b) = 3a 2/(16b)

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For a = 100 & b = 5 Q 1 * = a/(2b) = 100/(2 5) = 10 Q 2 * = a/(4b) = 100/(4 5) = 5 P* = a/4 = 100/4 = 25  1 * = a 2/(8b) = 100 2/(8 5) = 250  2 * = a 2/(16b) = 100 2/(16 5) = 125 * =  1 * +  2 * = 250 + 125 = 375

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How do the models look at?

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Monopolistic Competition Model Recall that for monopolistic contenders Products are particular, yet close substitutes. There is free section & exit. Suggestions Demand for one association\'s item will fall when a contender diminishes cost. There can be no monetary benefits over the long haul. Suppositions Two Firms Firm 1\'s Demand: Q 1 = D 1 (P 1 ,P 2 ) Firm 2\'s Demand: Q 2 = D 2 (P 2 ,P 1 )

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Firm 1 MC 1 = MR 1 (P 1 , P 2 ) MC 1 " > MR 1 \'(P 1 , P 2 ) P 1 > AVC 1 Firm 2 MC 2 = MR 2 (P 2 , P 1 ) MC 2 " > MR 2 " (P 2

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