Shane Murphy www.lancaster.ac.uk/postgrad/murphys4 ECON 102 Tutorial: Week 9 Shane Murphy www.lancaster.ac.uk/postgrad/murphys4

Question 1(a) Two aeroplane manufacturers are considering the production of a new product: A 550 passenger jet. Both are deciding whether to enter the market and produce the new plane. The payoff matrix is as shown below (payoffs are Boeing, Airbus). Identify two possible equilibrium outcomes in this game. The two possible equilibria are: (1) Boeing produces and Airbus does not, and (2) Airbus produces and Boeing does not. If the manufacturers found themselves in one of these two cells, neither would want to change its strategy, because given that one company is producing, the other will do better by not producing. Note: There was an error in the payoffs in the worksheet on Moodle. These are the corrected payoffs.

Question 1(b) Two aeroplane manufacturers are considering the production of a new product: A 550 passenger jet. Both are deciding whether to enter the market and produce the new plane. The payoff matrix is as shown below (payoffs are Boeing, Airbus). Suppose the European Union decides to subsidise Airbus with a subsidy of £25 if it enters the market. Revise the payoff matrix to account for this subsidy. What is the new equilibrium outcome? Because of the subsidy, producing is a dominant strategy for Airbus. Because Boeing knows Airbus will produce, it will choose not to.

Question 1(c) Compare the two outcomes (pre- and post-subsidy). What qualitative effect does the subsidy have? Without any subsidy: Without the subsidy, either Boeing or Airbus may produce, but we cannot determine which one (since Boeing and Airbus are quite similar). The subsidy is a tool used by the EU to ensure that Airbus is the one that will end up producing. With the £25 subsidy for Airbus if it enters the market: Because of the subsidy, producing is a dominant strategy for Airbus. Because Boeing knows Airbus will produce, it will choose not to.

Question 2 An incumbent firm can choose between fighting an entrant and accommodating an entrant by yielding some market share to the entrant. Can you create a 2x2 table of payoffs such that the dominant strategy for the incumbent is to accommodate? So, here are the two choices: The entrant has to choose between entering or not; the incumbent has to choose between fighting and accommodating. To understand how the payoffs work, think of the incumbent deciding between holding price and surrendering market share, or lowering price to hold onto market share. Holding price means sharing (monopoly) profits; lowering price means holding share but obtaining lower profits. So, if we suppose monopoly profits are 200, and competitive profits are 100 divided between the firms. The incumbent has to commit itself to one of the two strategies. The payoff matrix is (Incumbent, Entrant): On these payoffs, accommodation is a dominant strategy for the incumbent in that regardless of what the entrant does, he cannot do better than accommodate (hold price). The entrant has a dominant strategy: he does better by entering regardless of what the incumbent does. Note: Answers will vary. This is just one example of a correct answer

Question 3 Suppose the entrant decides that he wishes to signal to the incumbent that he doesn’t want a price war. Suppose he believes that a price war would not be in their interests, and also that a small share of a profitable market would be preferable to a large share of a market where prices dropped substantially. To illustrate this, he decides to commit himself to a small sale of entry. Assuming that the entrant moves first, can you create a decision tree that reflects these beliefs? An example of a decision tree that reflects these beliefs. E = Entrant decision; LO = Small scale entry; HI = large scale entry. I = incumbent decision; Hold = keep price as before entry; Drop = lower price to hold share. Note: Answers will vary. This is just one example of a correct answer

Question 4 Why might subsidies to R&D by governments reduce economic welfare?   A subsidy lowers the cost and risk associated with spending on R&D. Given the “prize” in an innovation race, anything that lowers the cost and risk will increase expenditure on R&D. Since, even without a subsidy, it is possible that total resources expended on R&D in an innovation race can exceed the net value of the end result, a subsidy increases the probability of this happening. An additional note: One way to think about this is that an R&D race is quite often a prisoner’s dilemma. So the NE is for both (all?) firms is to engage in R&D. But if it is a race (e.g. development of new drugs), there can only be one winner, who patents the drug, so in that sense the R&D race is wasteful. So an R&D subsidy, by encouraging more firms to engage in R&D (you could imagine a model with more than 2 firms, with a fixed cost (which may differ by firm) of engaging in R&D. Then a government R&D subsidy would encourage more firms to join the race, which increases the waste from the R&D race. On the other hand, the opposite could also be true (hence the question: why MIGHT). An R&D subsidy, by encouraging more firms to engage in R&D, may lead to new outcomes and hence raise welfare.

Question 5 How would it be profit enhancing for firms in an industry with a few large producers to maintain significant volumes of unused capacity?   Unused capacity can be used as a credible threat to increase production if necessary. This can, for example, deter potential new entrants or enforce collusion among existing producers (by raising the possibility of a tit-for-tat strategy). Maintaining the capacity implies a sunk cost for the producer. It allows the producer to easily expand production at little additional cost (low MC). This is what makes the threat credible. If the unused capacity deters new entrants and helps enforce collusion, then it can be profitable despite the cost of maintaining the unused capacity. Examples of this would be with oil prices and OPEC.

Question 6 The demand for widgets is given by P = 150 – 2Q, where P is the price of a widget, and Q is the quantity of widgets offered to the market. Two firms supply widgets to the market, and face a constant production cost of £30 per widget. The two firms compete in quantities. What will be total output supplied to the market, the market price, the sales of each of the two firms and the profits of each of the two firms? What would total output and price be if the widgets were supplied as under perfect competition? What would total output, price and profit be if the widgets were supplied under a monopoly? Note: This question is based on the Cournot Duopoly example that you covered in Lecture last week. How do we know this is a Cournot Model? We know that it is based on the Cournot model because we are dealing with two firms producing identical products, facing the same constant unit costs and their key decision is on their capacity or quantity to produce. How do we solve a Cournot Model question? To answer it, we follow the exact same structure as the Cournot model, covered in slides 30-34 of the Week 8 Lecture slides. The demand for widgets is given by P = 150 – 2Q, where P is the price of a widget, and Q is the quantity of widgets offered to the market. Two firms supply widgets to the market, and face a constant production cost of £30 per widget. The two firms compete in quantities. What will be total output supplied to the market, the market price, the sales of each of the two firms and the profits of each of the two firms? What would total output and price be if the widgets were supplied as under perfect competition? What would total output, price and profit be if the widgets were supplied under a monopoly?

Question 6 (Cournot Model) What will be total output supplied to the market, the market price, the sales of each of the two firms and the profits of each of the two firms? We know: The market demand is P = 150 – 2Q And the Constant unit cost is £30. From Lecture slides 30-32, we know that 𝑞 1 = 𝑞 2 = 𝑎−𝑐 3𝑏 . We can plug in a and b from our demand curve, which is in the format of P = a – bQ, and can plug in the constant unit cost in for c. So, we have 𝑞 1 = 𝑞 2 = 150−30 3×2 𝑞 1 = 𝑞 2 =20 So then, the total amount of output supplied by the two firms in this market will be: 𝑄= 𝑞 1 + 𝑞 2 =40 To find the market price, we can take Q and plug it into the demand equation: 𝑃=150−2𝑄=70 To find the profit of each firm, we can plug into either firm’s profit function (both are identical in the Cournot model): 𝜋= 𝑃−𝑐 𝑞 𝜋 = 70−30 20 =800 Total profit is the profit of both firms added together: 𝜋 1 + 𝜋 2 =1,600   Note it may be helpful for the students to see the derivation of the results again (this was performed in the lectures). Start by noting that the firm’s profit is equal to total revenue minus total cost: 𝜋 1 =𝑇𝑅−𝑇𝐶=𝑃 𝑞 1 −𝑐 𝑞 1 = 150−2 𝑞 1 −2 𝑞 2 𝑞 1 −30 𝑞 1 =120 𝑞 1 −2 𝑞 1 2 −2 𝑞 1 𝑞 2 Choose output to maximise profit by differentiating with respect to 𝑞 1 : 𝛿 𝜋 1 𝛿 𝑞 1 =120−4 𝑞 1 −2 𝑞 2 =0 Hence we get firm 1’s reaction function 𝑞 1 =30− 𝑞 2 2 , and by analogy, firm 2’s reaction function 𝑞 2 =30− 𝑞 1 2 . Substituting firm 2’s reaction function into firm 1’s reaction function gives: 𝑞 1 =30− 1 2 30− 𝑞 1 2 =20 Which is the same as above.

Question 6 (Perfect Competition) What would total output and price be if the widgets were supplied as under perfect competition? We know: The market demand is P = 150 – 2Q And the Constant unit cost is £30. In perfect competition our equilibrium is where P = MC. 𝑃=𝑀𝐶 𝑃=30 We can substitute this into the demand equation and solve for Q: 30=150−2𝑄 𝑄=60 So, if the two firms have identical outputs, we have 𝑞 1 = 𝑞 2 =30. Profits are equal to zero in this case, because it is a perfect competition outcome.  

Question 6 (Monopoly) What would total output, price and profit be if the widgets were supplied under a monopoly? We know: The market demand is P = 150 – 2Q And the Constant unit cost is £30. Again, from the lecture slides, we know that for a monopoly, equilibrium Q is: Q=𝑞= 𝑎−𝑐 2𝑏 . Plugging in we can re-write this as: 𝑄=𝑞= 150−30 2×2 =30 To find Market Price, we substitute this into the demand equation: 𝑃=150− 2×30 =90 To find the firm’s profit, we can plug into the the firm’s profit function: 𝜋= 𝑃−𝑐 𝑞 𝜋= 90−30 30 𝜋=1,800   So, comparing the three scenarios we find: The monopoly charges the highest price and earns the highest profit, followed by the Cournot duopoly, and the perfect competition case charges the lowest price and earns the lowest profit (zero economic profit). The monopoly has the smallest total output, followed by the Cournot case, and perfect competition has the largest total output.

Next Week Note: The Bertrand Model (which is included in your Week 8 lecture slides) will not be covered in any portion of this class. The Cournot Model on the other hand, will likely show up on your exams. Work through the week 10 worksheet and bring your completed work and any questions that you have. We’ll try to do some more maths problems, like today. If you’ve read through Chapter 10 in the book and are still having trouble with this material, the following two videos may be of help.