Consider the Bertrand model we covered in the lecture and answer the quesiton below. Assume that each firm in the Bertrand Duopoly model can only choose non-negative integer quantities: 0, 1, 2, ... . Assume the demand is Q(P)=10-P and the marginal cost is 0 for each firm. Given this information, which of the following is FALSE? [Hint: Check values of profit functions.] A. If firm 2 sets price equal to 1, then the best response of firm 1 to this price is 1 B. If firm 2 sets price equal to 4, then the best response of firm 1 to this price is 4 C. If firm 2 sets price equal to 2, then the best response of firm 1 to this price is 1

Consider the Bertrand Duopoly model we covered in the lecture where firm 1's marginal cost is 1 and firm 2's marginal cost is 2 (different marginal costs, the rest is the same as the model introduced in the lecture). Then, which of the following claims is TRUE? [Hint: Check profitable deviations.] A. Prices (p1 ,p2) = (1, 2) is a Pure Strategy Nash equilibrium B. Prices (p1 ,p2) = (2, 2) is a Pure Startegy Nash equilibrium C. Prices (p1 ,p2) = (0,0) is not a Pure Strategy Nash equilibrium.

The Bertrand model of price setting assumes that a firm chooses its priceGroup of answer choicesindependently of what price other firms charge.subject to what price rival firms are charging.so that joint profits are maximized.without considering the shape of the demand curve. PreviousNext

n lectures, we considered two models of duopoly competition: Cournot(quantity) competition and Bertrand (price) competition. It seems morerealistic to think of firms’ competing in prices than in quantities, but theCournot outcome seems more ‘realistic’ than the Bertrand outcome. Thisproblem considers a third model of duopoly competition. Like Bertrand, thetwo firms will compete in prices rather than quantities. Unlike the Bertrandmodel, however, the products of the two firms are not identical. In economicsjargon, the products are di§erentiated. Instead of my solving the model onthe board in class, you will solve it in this problem set. But don’t panic: Iwill walk you through the model step by step.The Game.• We can think a ‘city’ as a line of length one.• There are two firms, 1 and 2, at either end of this line.— The firms simultaneously set prices p 1 and p 2 respectively.— Both firms have constant marginal costs, c.— Each firm’s aim is to maximize its profit.• Potential customers are evenly distributed along the line, one at eachpoint.— Let the total population be one (or, if you prefer, think of demandin terms of market shares).• Each potential customer buys exactly one unit, buying it either fromfirm 1 or from firm 2. So total demand is always exactly one.• Consider a customer at a position y on the line. She is distance y fromfirm 1 and distance (1  y) from firm 2.3— The customer at position y on the line is assumed to buy fromfirm 1 ifp 1 + ty 2 < p2 + t(1  y)2 ; (a)to buy from firm 2 ifp 1 + ty 2 > p2 + t(1  y)2 ; (b)and to toss a fair coin if this is an exact equality.Interpretation. Customers care about both price and about the ‘distance’they are from the firm. If we think of the line as representing geographicaldistance, then we can think of the t(distance)2 term as the ‘transport cost’of getting to the firm. Alternatively, if we think of the line as representingsome aspect of product quality – say, fat content in ice-cream – thenthis term is a measure of the inconvenience of having to move away fromthe customer’s most desired point. As the transport-cost parameter t getslarger, we can think of products becoming more di§erentiated from the pointof view of the customers. If t = 0 then the products are perfect substitutes.What happens?(a) (2 points) Will either firm i ever set its price p i < c? Why?(b) (3 points) Suppose that firm 2 sets price p 2 . At what price can firm1 capture the entire market (that is, given p 2 , at what p 1 will all thecustomers buy from firm 1)?

Here we look at mark-ups. Choose all the correct answers.Question 3Answera.The price chosen by a monopolist is $4, and its average total cost equals $3. Hence, the mark-up equals to $1.b.Firms in a perfectly competitive industry may enjoy positive mark-ups in the long run.c.In general, Bertrand model with constant marginal costs that are symmetric across firms predicts positive mark-ups in equilibrium.d.In general, Bertrand model with firms facing different constant marginal costs predicts positive mark-ups in equilibrium. Hint: you can assume such equilibrium exists, because, for example, the lowest possible price change is $0.01.

What does Bertrand Paradox refer to?Group of answer choicesThe market price approaches a low level slowy as the number of firms gets very large.The market becomes competitive due to firms’ competition over the price.Firms end up charging a high price to earn higher profits.None of the other answers are correct.The market price becomes high because firms try to collude with each other to earn higher profits.