Cournot model

curnot model for duopoly market

1. COURNOT MODEL FOR DUOPOLY MARKET

2. Presented by, Yagnesh Sondarva 04-2664-2015 MSc. Agri.Extension BACA, Anand

3. Market Structure Number of firms in market Product Differentiation Markets are often described by the degree of concentration Monopoly is one extreme with the highest concentration - one seller Perfect competition is the other extreme with innumerable sellers Oligopoly involves few sellers engaging in strategic competition

4. Number of Sellers

5. PERFECT

6. Perfect Competition Many Firms Homogeneous Products examples: farm commodities like wheat, Pulses

7. Monopolistic Competition Many Firms Differentiated Products Examples : retail trade

8. Monopoly One Firm One Product Example : railway , post , electricity, Insurance (government monopoly)

9. Oligopoly A ) Homogeneous Products Oligopoly Few Firms Homogeneous Products Examples: steel ,chemical. B ) Differentiated Products Oligopoly Few Firms Differentiated Products Examples: automobile , computer

10. Oligopoly Market has a small number of sellers Pricing and output decisions by each firm affects the price and output in the industry Oligopoly models ( Cournot , Bertrand) focus on how firms react to each other’s moves

11. Oligopoly – Characteristics Product differentiation may or may not exist Barriers to entry Small number of firms Scale economies Patents Technology Name recognition Strategic action

12. Oligopoly Examples Automobiles Steel Aluminum Petrochemicals Electrical equipment

13. Management Challenges Strategic actions to deter entry Threaten to decrease price against new competitors by keeping excess capacity Rival behavior Because only a few firms, each must consider how its actions will affect its rivals and in turn how their rivals will react

14. Interdependence Your actions affect the profits of your rivals. Your rivals’ actions affect your profits

15. An Example You and another firm sell differentiated products such as cars. How does the quantity demanded for your cars change when you change your price?

16. Oligopoly – Equilibrium If one firm decides to cut their price, they must consider what the other firms in the industry will do Could cut price some, the same amount, or more than firm Could lead to price war and drastic fall in profits for all Actions and reactions are dynamic, evolving over time

17. Oligopoly – Equilibrium Defining Equilibrium Firms are doing the best they can and have no incentive to change their output or price All firms assume competitors are taking rival decisions into account Nash Equilibrium Each firm is doing the best it can given what its competitors are doing We will focus on duopoly Markets in which two firms compete

18. Duopoly models Cournot model Edgeworth model Chamberlin model Price leadership model Bertrand model Kinked demand curve Centralized cartel model Market sharing cartel model

19. Cournot model Developed by French economist Augustin cournot in 1838.

20. Cournot model Oligopoly model in which firms produce a homogeneous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce

21. Assumptions of Cournot Model Four assumptions: there are two firms and no other firms can enter in the market, the firms have identical costs, they sell identical products the firms set their quantities simultaneously.

22. O A B D DB = demand curve Suppose OA=AB max daily output of each producer Total output=OA+AB=OB

23. D K O A B P DB= demand curve OA=daily max output OA= max profit Ma x revenue =OAPK Profit of A As profit A producer

24. P Q D O A H B B producer B assume A will produce ½ of OB=OA PB = demand curve for him B produce AH=1/2 AB Total output OA+AH=OH Price fall =HQ Total profit=OHQF Is less than OAPK of 1 st condition As profit = OAGF Bs profit =AHQG Profit of A reduced due to AH produced by B Bs profit G K F As profit As profit

25. P Q D O A H B G K F As profit As profit A PRODUCER A will consider & assume B will continue produce AH So A produce 1/2(OB-OH)=OT Reduce OA to OT A produce= OT B produce=AH Total output=OT+AH=ON Price =NR Total profit=ONRS As profit =OTLS More than OAGF Bs profit=TNRL More than AHQF T R N S L As profit Bs profit G

26. B surprised by reduction of output to OT by A and Also find his share of total profit is less than A So B assume A will continue produce OT And B find his maximum profit by producing output=1/2(OB-O T)=1/2 TB B increase output to ½ TB Producer A consider and find that he can maximize his profit by producing output=1/2 OB-output of B This process of adjustment and readjustment by each producer will continue , A being forced gradually to reduce his output B being able to increase his output gradually until total output OM is produced OM=2/3 OF OB And each producing same amount of output A= OC B=CM OC=CM

27. P Q D O A H B G K F As p T R N S L A will consider & assume B will continue produce AH So A produce 1/2(OB-OH)=OT Reduce his production A produce= OC B produce=CM Total output=OC+CM=OM Price =MJ Total profit=OMJE As profit =OCWE Bs profit=CMJW As profit E J C W Bs profit M

28. Throughout the process of adjustment & readjustment each producer assume that the Other will keep his output constant at the present level & then always find his maximum profit by producing output ½(OB-present output of other )

29. P Q D O A H B G K F As p T R N S L As profit E J C W Bs profit M

30. A producer start by producing OA=(1/2OB) And continue reduce until OC Final output OC of A =OB(1-1/2-1/39…….)=1/3 OB =1/2 OM B producer start by producing AH=1/4 of OB And continue increase until CM Final output CM of B =OB(1/4+1/16+1/64…..)=1/3 OB=1/2 OM TOTAL OUTPUT =0B(1-1/2+1/4-1/8+1/16-1/39+1/64……) =2/3 OB =OM

31. A = 1/3 OB = OC B = 1/3OB= CM ½ (OB-1/3 OB) which is equal to 1/3 OB=OC=CM When each producing 1/3 OB so that total output of both are 2/3 OB no one is able to increase profit by further adjustment in output EQUILIBRIUM Total output is 2/3 of OB Each one producing 1/3 of OB

32. Criticism Behavioural pattern of firm is naive . Means firm not know from past miscalculation of competitors reaction. Quantity produced by competitor is as assumed constant at a each stage Model can be extended to many number of firms however it is a closed model in that entry is not allowed number of firms remain same through out adjustment process. It doesn’t say how long adjustment period will be.

33. Thank you