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ECON 100 Tutorial: Week 10 www.lancaster.ac.uk/postgrad/alia10/ a.ali11@lancaster.ac.uk office hours: 3:45PM to 4:45PM tuesday LUMS C85 Question 1 Classify each of the following markets as highly contestable, moderately contestable, slightly contestable or non-contestable. If it depends on the circumstances, explain in what way. Key characteristic of a contestable market: Firms are influenced by the threat of new entrants into a market. (a) satellite broadcasting highly / moderately / slightly / non (b) hospital cleaning services highly / moderately / slightly / non (c) banking on a uni campus highly / moderately / slightly / non (d) piped gas supply highly / moderately / slightly / non (e) parcels delivery highly / moderately / slightly / non (f) siting for the Olympic games highly / moderately / slightly / non (g) bus service to the area where you live highly / mod./ slightly / non Question 2 Why, under oligopoly, might a particular industry be collusive at one time and yet highly price competitive at another? Because the market environment, or the firm’s assessment of it, may well change. For example, if just one firm in an oligopoly introduces a price cut, the other firms may feel obliged to follow suit, with the result that collusion breaks down. Alternatively, a new firm may enter the market (e.g. a foreign multinational), or costs may change, or rivals develop new varieties of the product, etc. Question 3 Explain under what conditions collusion is likely to a) collapse Collusion is likely to collapse in a single game, or in a finite number of games. b) be maintained, in a prisoners’ dilemma model If the game is repeated and the players do not know how many games are left (i.e. an “infinite” number of games), collusion can continue How do we know that collusion could be maintained in an “infinite” repeated game? Let’s look at the following game: We are going to play a card game in which groups of students will form teams. Each team gets a pair of playing cards, one red card (Hearts or Diamonds) and one black card (Clubs or Spades). The numbers or faces on the cards do not matter, just the color. Each team will be asked to play one of these cards by holding it to your chest (so we can see that you have made your decision, but not what that decision is). Your earnings are determined by the card that you play and by the card played by your opposing team. If you play your red card, then your earnings in pounds will increase by £2, and the earnings of the person matched with you will not change. If you play your black card, your earnings do not change and the dollar earnings of your opposing team go up by £3. So, If you each play your red card, you will each earn £2. If you each play the black card, you will each earn £3. If you play your black card and the other person plays his or her red card, then you earn zero and the other person earns the £5. If you play red and the other person plays black, you earn the £5, and the other person earns zero. All earnings are hypothetical. Here are the payoffs, written as a normal-form game. black black (£3, £3) red (£0, £5) Red Player ONE First we’ll play one round. Talk about your strategies quietly with your teammates before you make your decision. Player TWO (£5, £0) (£2, £2) Player TWO black black (£3, £3) red (£0, £5) Red Player ONE Now we’ll move the teams around, so you have a new opposing team. Same rules. Keep adding up your winnings if we play more than one round. (£5, £0) (£2, £2) Player TWO black black (£3, £3) red (£0, £5) Red Player ONE For a final round, let’s have the two highestscoring teams play a single game against each other, and the two lowest-scoring teams play a single game against each other. (£5, £0) (£2, £2) Question 4(a) The following information describes the demand schedule for a unique type of apple. This type of apple can only be produced by two firms because they own the land on which these unique trees spontaneously grow. As a result, the marginal cost of production is zero for these duopolists, causing total revenue to equal profit. Price Quantity per of Boxes Box (£) 12 11 10 9 8 7 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Total Revenue (Profit) 0 55 100 135 160 175 180 175 160 135 100 55 0 Question 4(b) If the market were characterised by Bertrand competition, what price and quantity would be generated by this market? Explain. In a Bertrand competition model, Competition reduces the price until it equals marginal cost (which is zero in this case), therefore P = £0 and Q = 60. (See Tutorial 9, Slides 14 and 15 for a detailed explanation of why P = MC in Bertrand competition.) Price Quantity per of Boxes Box (£) 12 11 10 9 8 7 6 5 4 3 2 1 0 0 5 10 15 20 25 30 35 40 45 50 55 60 Total Revenue (Profit) 0 55 100 135 160 175 180 175 160 135 100 55 0 Question 4(c) If these two firms colluded and formed a cartel, what price and quantity would be generated by this market? These duopolists would behave as a monopolist, produce at the level that maximises profit, and agree to divide the production levels and profit. According to the table, Profit is maximised at where P = £6, Q = 30 for the market. What is the level of profit generated by the market? Profit = £6 x 30 = £180. And what is the level of profit generated by each firm? Each firm produces 15 units at £6 and receives profit of £90 (half of the £180). Price Price per per Box Box (£) (£) Quantity Quantity of of Boxes Boxes Total Total Revenue Revenue (Profit) (Profit) 12 11 10 9 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 5 10 15 20 25 25 30 30 35 35 40 40 45 45 50 50 55 55 0 55 100 135 160 175 175 180 180 175 175 160 160 135 135 100 100 55 55 Question 4(d) If one firm cheats and produces one additional increment (five units) of production, what is the level of profit generated by each firm? When the two firms are colluding, they produce 15 units each, for a total output of 30 and a price of £6. If the Cheating firm produces 5 more units, the total output will be 35, which will cause the price to drop to £5. Price Quantity Total Cheating firm: 20 x £5 = £100 Other firm: 15 x £5 = £75 per Box (£) of Boxes Revenue (Profit) 6 5 30 35 180 175 Question 4(e) If both firms cheat and each produces one additional increment (five units) of production (compared to the cooperative solution), what is the level of profit generated by each firm? Both firms have moved from 15 units to 20 units each. Total output will be 40, which causes price to drop to £4. Each firm: 20 x £4 = £80. Question 4(f) If both firms are cheating and producing one additional increment of output (five additional units compared to the cooperative solution), will either firm choose to produce an additional increment (five more units)? Why? What is the value of the Nash equilibrium in this duopoly market? FIRM TWO Produce 25 Produce 20 Produce 20 FIRM ONE Price Quantity Total No, because the profit per Box of Boxes Revenue would fall for the (£) (Profit) cheater to 25 12 0 x £3 = £75 0 which the £80 11 is below 5 55 profit part (e). 100 10 from10 9 15 Therefore, the Nash135 8 20is each firm 160 equilibrium 7 25 175 producing 20 units (40 30 for6the market) at a 180 price 5 35 175 of £4, creating £160 of 4 40 160 profit and 3 for the 45 market135 each 2 duopolist 50 receives 100 £801 profit. 55 55 £80, £80 £75, £60 Produce 25 £60, £75 £50, £50 Question 4(g) Compare the competitive equilibrium to the Nash equilibrium. In which situation is society better off? Explain. The Nash equilibrium has a higher price (£4 compared to £0) and a smaller quantity (40 units compared to 60 units). Society is better off with competitive equilibrium (Bertrand equilibrium). Question 4(h) Describe what would happen to the price and quantity in this market if an additional firm were able to grow these unique apples. (Do not attempt to calculate quantitative changes – the direction of change is all that is required.) The new Nash equilibrium would have a lower price and a larger quantity. It would move toward the competitive solution. Question 4(i) Use the data from the duopoly example above to fill in the boxes of a prisoners' dilemma normal form game. Place the value of the profits earned by each duopolist in the appropriate boxes. FIRM ONE Payoffs are Revenue (PxQ) for each firm. Price is determined by the total market quantity in the Table (part a). Market Quantity is the sum of the quantities of the two firms. Example: Firms 1 chooses Q = 15 and Firm 2 chooses Q = 20. Market Q = 15+20 = 35 units, therefore Market P = £5 Payoff for each firms is PxQ Firm 1: 15 x £5 = £75 Firm 2: 20 x £5 = £100 Price per Box (£) Quantity of Boxes Total Revenue (Profit) 6 5 30 35 180 175 FIRM TWO Question 4(i) Use the data from the duopoly example above to fill in the boxes of a prisoners' dilemma normal form game. Place the value of the profits earned by each duopolist in the appropriate boxes. FIRM TWO collude (15) collude (15) cheat (20) FIRM ONE Payoffs are Revenue (PxQ) for each firm. Price is determined by the total market quantity in the Table (part a). Market Quantity is the sum of the quantities of the two firms. Example: Firms 1 chooses Q = 15 and Firm 2 chooses Q = 20. Market Q = 15+20 = 35 units, therefore Market P = £5 Payoff for each firms is PxQ Firm 1: 15 x £5 = £75 Firm 2: 20 x £5 = £100 £90, £90 £100, £75 cheat (20) £75, £100 £80, £80 Question 4(j) What is the solution to this prisoners' dilemma? Explain. FIRM TWO collude (15) cheat (20) FIRM ONE collude (15) £90, £90 £100, £75 cheat (20) £75, £100 £80, £80 The dominant strategy for each is to cheat and sell 20 units because each firm’s profit is greater when it sells 20 units regardless of whether the other firm sells 15 or 20 units. Question 4(k) What might the solution be if the participants were able to repeat the "game?" Why? What simple strategy might they use to maintain their cartel? They might be able to maintain the cooperative (monopoly) production level of 30 units and each produce 15 units because if the game is repeated, the participants can devise a penalty for cheating. This is because if the game is repeated, the participants can devise a penalty for cheating. The simplest penalty is "tit-for-tat." Question 5 An alternative to the Cournot model, where firms choose q’s, is the Betrand model (see above), where firms choose p’s. Of course firms can only have different p’s if they are selling differentiated products. Gasmi et al (J Econ & Man 1992) estimated the demand for coke as QC=58-4PC + 2PP where C=coke and P=pepsi. If MC = AC = 5 then profits are given by C=(PC-5)(58-4PC+2PP) where the first bracket is per unit profit and the second bracket is the number of units sold. The slope of this profit function shows how C’s profits vary with PC. Multiply out the brackets in the profit function and then apply the rule to get the slope. Hence show what C’s best response function is (ie how Pc depends on Pp). Question 5 We have: QC=58-4PC + 2PP where C=coke and P=pepsi. If MC = AC = 5 then profits are given by C=(PC-AC)(QC) C=(PC-5)(58-4PC+2PP) We want to find the slope of the profit function, or take the derivative of it. Before we do that, we need to multiply out the brackets in the profit function and then apply “the rule” to get the slope. This will give us C’s best response function is (ie how Pc depends on Pp). C=(PC-5)(58-4PC+2PP) C=58PC-4PC2+2PCPP-290+20PC-10PP C=-4PC2+2PCPP+78PC-290-10PP continued on next slide Question 5 We left off with: C=-4PC2+2PCPP+78PC-290-10PP To find the slope of C, we are going to take the derivative with respect to PC: dC/dPC=-8PC+2PP+78 Profits are maximised when the slope is 0, so the next step is to set dC/dPC equal to zero and solve for PC: 0=-8PC+2PP+78 8PC=2PP+78 PC=(2PP+78)/8 PC=PP/4+9.75 So, PC=PP/4+9.75 is C’s best response function to Pepsi’s price choice. Question 5 ctd. They also estimate that the demand curve for pepsi was QP = 63.2 - 4PP + 1.6PC. Using the same approach derive the best response for Pepsi. We have: QP = 63.2 - 4PP + 1.6PC where C=coke and P=pepsi. If MC = AC = 5 then profits are given by P=(PP-AC)(QP) P=(PP-5)(63.2 - 4PP + 1.6PC) Next, we’ll multiply out the brackets in the profit function and then apply “the rule” to get the slope of the profit function. This will show us what P’s best response function is (ie how PP depends on PC). P=(PP-5)(63.2 - 4PP + 1.6PC) P=63.2PP-4PP2+1.6PCPP-316+20PP-8PC P=-4PP2+1.6PCPP+83.2PP-316-8PC continued on next slide Question 5 ctd. In the previous slide, we left off with: P=-4PP2+1.6PCPP+83.2PP-316-8PC To find the slope of P, we are going to take the derivative with respect to PP: dP/dPP=8PP+1.6PC+83.2 Profits are maximised when the slope is 0, so the next step is to set dP/dPP equal to zero and solve for PP: 0=8PP+1.6PC+83.2 8PP=1.6PC+83.2 PP=(1.6PC+83.2)/8 PP=PC/5+10.4 So, PP=PC/5+10.4 is Pepsi’s best response function to any price that Coke may choose. Question 5 ctd. Show what the equilibrium prices are. In the previous slides, we found best response functions for each firm: PP=PC/4+9.75 and PC=PP/5+10.4 A Nash Equilibrium can be found by finding the intersection of these two lines (i.e. where both players play their best response strategy). To find this, we can plug the second function into the first: PP=(PP/5+10.4)/4+9.75 PP=(PP/5)/4+10.4/4+9.75 PP=PP/20+2.6+9.75 PP=PP/20+12.35 PP-PP/20=12.35 19PP/20=12.35 PP=12.35*20/19 PP=13 continued on next slide Question 5 ctd. Show what the equilibrium prices are (ctd). In the previous slides, we found best response functions for each firm and we found PP by plugging one function into the other: PP=PC/4+9.75 and PC=PP/5+10.4 and PP=13 Now, to find PC, we can plug PP=13 into PC=PP/5+10.4: PC=PP/5+10.4 PC=13/5+10.4 PC=2.6+10.4 PC=13 So, the best response functions intersect at PC = 13 and PP = 13 Have a nice Holiday! (Also, don’t forget to start studying for Exam 2 (it’s on 24/01/2014) and check Moodle for the Week 11 worksheet.)