Managerial Economics: Topic 8b Short-run competition

1. Managerial Economics: Topic 8bShort-run competition Applying game theory to analyse mass markets with a few competing suppliers (=oligopoly)

2. Oligopoly Oligopoly = Competition between a few producers (not perfect competition) Assume high entry barriers no more entrants set of competitors is given. In class: We�ll deal with markets in which oligopolists produce exactly the same thing = extreme There are (optional) readings on markets in which oligopolists produce differentiated products.

3. Plan of Topic 8

4. Competition in mass markets with homogenous products What happens when firms compete in quantity? What happens when firms compete in price?

5. a) Competition in quantities= �Cournot� Oil refining industry Only 2 producers: Shell and Mobil Each chooses simultaneously whether to have high production or low production Afterwards, see what the world-market-clearing price is for the total oil produced (all your oil will sell, for that market-clearing price) ? You�re choosing quantity, but without knowing how much your competitor is choosing. If you are Shell, what do you do?

6. Quantity competition

8. Competitive Equilibrium Both choose �medium� production But the real question is more complicated: If Shell, can anywhere from 0 to 1000 units, how much does it produce? Answer = best response to the output level of Mobil.

9. Best responses in Cournot competition Remember, once the market sees how much each has produced, customers purchase at the market-clearing price. If Mobil decides to produce 100 units, and Shell is producing 250 units, total output for sale is 350 ? market clearing price is $650 If Mobil produces 200 units, market-clearing price is $550 If Mobil produces 300 units, market-clearing price is $450 It�s as though Mobil is facing a new demand curve, called the residual (�leftover�) demand curve: Total output = QM + 250 = 1000 � P ? QM = 750 � P if QS=250

10. Mobil�s residual demand curve, if Shell is producing 200 units 750 -2Q = 200 2Q =550 ? Q=275750 -2Q = 200 2Q =550 ? Q=275

11. More Best Responses: Next question: If Mobil knew that Shell would produce 251, how much would Mobil produce? If Mobil knew that Shell would produce 252, how much would Mobil produce? � We want a general answer to the question: If Mobil knew that Shell would produce an amount QS, how much would it produce? (Mobil knows the exact value of QS, and will fill it in later)

12. Mobil knows demand curve, Mobil�s Marginal Cost, Output of Shell

13. Best response: We want a general answer to the question: If Mobil knew that Shell would produce an amount QS, how much would it produce? (Mobil knows the exact value of QS, and will fill it in later) General Answer: Mobil wants to produce its monopoly quantity, minus half of what Shell is producing: QM = (Monopoly Q) � (half of QS)

14. Best Response: We want a general answer to the question: If Mobil knew that Shell would produce an amount QS, how much would it produce? (Mobil knows the exact value of QS, and will fill it in later) Example: if Mobil knows Shell would produce 250, it wants to produce QM = 400 � 0.5QS = 275

15. Only for nerds: Mathematics of Cournot BEST RESPONSE: If Mobil knew that Shell would produce an amount QS, how much would Mobil produce? Total output Q = QM + QS Rearranging the demand equation gives us the residual demand curve: P = 1000 � QS � QM Firm M maximizes its profits by setting MR equal to MC: TRM = P?QM = [1000 � QS � QM]?QM Take the derivative, as in a monopoly problem, but treat QS as a constant (because it�s fixed, and Mobil knows what it is): MRM = 1000 � QS � 2QM Set MR equal to MC, which in this case is 200. ? QM = 400 � 0.5QS

16. ASIDE: Quantity Competition = Strategic Substitutes ? QM = 400 � 0.5QS If Shell has a larger output, Mobil chooses a smaller output. Reason = to keep market price high. If Shell produces nothing, Mobil produces 400 million tonnes of oil (=monopoly). If Shell produces 200 million, Mobil produces 300. If Shell produces 400 million, Mobil produces 200.

17. Intuitively: in Equilibrium� If you produce 1 more unit � I produce 0.5 less units ? Each of us is producing less than the monopoly quantity BUT ? In total, we will produce more than the monopoly quantity (i.e. each of us will produce more than � of the monopoly quantity) ? Too much output, profits not maximised.

18. Graphically: quantity competition The line QM = 400 � 0.5QS is called a �best response� or �reaction� curve: it expresses what quantity Mobil will want to produce, for any given quantity Shell produces.

19. Nash equilibrium in Cournot competition Is there a Nash equilibrium to this game? A Nash equilibrium occurs when both players are playing their best response to the other player we need to find the best response curve for Mobil Then: the intersection of the best response curves is a Nash equilibrium Qs=200, Qm=300Qs=200, Qm=300

20. Nash equilibrium in Cournot competition Suppose Shell has MCS=300 Then we can calculate Shell�s best response too: If Shell were a monopoly, it would produce: 350 ? QS = 350 � 0.5QM solve the 2 equations at once for QM* and QS*: by substitution Qs=200, Qm=300Qs=200, Qm=300

21. ASIDE: quantity competition Nash equilibrium is when Shell and Mobil are playing a best response, i.e. the intersection of the two �reaction� curves

22. Finding the Nash equilibrium At the intersection, both best response curves hold true at the same time: QM = 400 � 0.5Qs QS = 350 � 0.5QM This is called a system of two equations. You solve by substitution: try and put one equation only in terms of QS: QS = 350 � 0.5QM = 350 � 0.5(400 � 0.5QS) = 350 � 200 + 0.25QS 0.75QS = 150 QS = 200 Then you use that to get QM: QM = 400 � 0.5Qs = 400 � 0.5(200) = 300

23. Outcome From the reaction curves we see that each firm produces less than it would if it were a monopoly. But each firm produces more than half the monopoly quantity Adding their output together, the firms produce more than a monopolist would. Each earns less than half of monopoly profits Competing in quantities yields low profits as we�ll see, price competition yields even lower profits!

24. Tough price competition

25. Tough Price Competition CD ROM phonebooks 1986: Nynex charged $10,000 per disk for NY directory ProCD and Digital Directory Assistance Workers in China at $3.50 daily wage Outcome similar to �Perfect� competition (competition between a huge number of sellers) Charge $200 each Price forced down to marginal cost

26. Same demand curve, but 2 firms

27. b) Competition in Prices = �Bertrand� Firms post prices simultaneously, afterwards see what they sell The goods are perfect substitutes (ex: flour, sugar). Consumers will buy from the firm with the lowest price. If two firms set different prices, then the low-price firm gets the entire demand. The firms are not capacity constrained: they can meet the whole market�s needs ? e.g. Either firm can supply 800 or more units to the market.

28. Nash equilibrium Each firm has a marginal cost of c. This is a simultaneous game (but there are too many price choices to draw table). ? Is there a Nash equilibrium, or more than one? The only Nash Equilibrium in this market in that market is that both firms will sell for a price of c, and make zero profit.

29. Bertrand competition:Nash equilibrium price = MC What is my best response to my competitor charging a price P2 that is greater than c? I want to charge a price P1 just below P2. But then is my competitor at a best response? No, he wants to price just below P1. What if your competitor charges c (marginal cost)? Then your best response is to charge c as well. ? The only Nash equilibrium is P1=P2=c.

30. Usual objection But won�t each firm realise that if it cuts its price the other firm will follow? (hold that thought�we�ll address it in Topic 10)

31. Aside: �Zero Profit� Outcome is P = c, where c is the marginal cost. If firms have no fixed costs, they earn zero profits. No fixed costs are covered In the long run, firms will exit the market = why firms rarely produce exactly the same product

32. Bertrand competition versus perfect competition Oddly enough we get the same result as in a market with a huge number of sellers (�perfect competition�): P = MC Yet there may be very few sellers in the market; maybe only 2 if they found another way to increase price, they�d earn profits likely to try and change the game: Differentiate their products = most common tactic Differentiating the products softens price competition: price no longer falls to MC. Merge (then they�d earn monopoly profits) Collude (illegal) or tacitly collude Limit their capacity = looking at this next.

33. Conclusion: Short-term competition This analysis is focused on the short-run: Firms are not taking into account that they compete against each other period after period That makes sense for a very infrequent choice, like building capacity: you treat it as a one-shot game. But it makes much less sense for day-to-day competition ? Topic 10: Repeated games Topic 9: Commitments that change the game