14.6. PRODUCT POSITIONING AND PRICE COMPETITION. Consider a duopoly where horizon- tal product differentiation is important. Firms first simultaneously choose their prod- uct locations, then simultaneously set prices in an infinite series of periods. Suppose that firms collude in prices in the second stage and anticipate they will do so at the the degree of product product-positioning stage. In this context, what do you expect differentiation to be?22
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- Select the correct statements. Note: Multiple correct, multiple selections. Topics covered: Stackelberg, Cournot, and Bertrand models. O A. Suppose the inverse market demand function is P (y) = a - by, and the marginal cost of each firm is K (same and constant). In this market, the market price will be higher if the market is a Stackelberg duopoly than the market price if it is a Cournot duopoly market. В. A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist. O C. Suppose, in a Stackelberg duopoly, the follower's output is measured on the horizontal axis. Profits to the follower will increase as we move to isoprofit lines that are further to the left. D. The equilibrium in Bertrand duopoly where both firms sell identical products is Pareto efficient. Е. In Cournot duopoly, if each firm has the same marginal MC = K, each firm produces the same level of output and earns the same profit.14.6. Product positioning and price competition. Consider a duopoly where horizon- tal product differentiation is important. Firms first simultaneously choose their prod- uct locations, then simultaneously set prices in an infinite series of periods. Suppose that firms collude in prices in the second stage and anticipate they will do so at the product-positioning stage. In this context, what do you expect the degree of product differentiation to be?.Problem 1. HHI in the Bertrand Triopoly Equilibrium It's a Bertrand Triopoly - hence we know there are 3 firms in the industry-in-question, who competes in "price". The inverse demand functions for Firm 1, 2, and 3 are as follows: q1 = 40 - 1.5p1 +0.5p2 +p3 q2 = 40 + 1.5p1 - 3p2+p3 q3 = 40 + 2p1 + 1.5p2 - 4p3 For each firm, the marginal cost of production is $2.50/unit produced and sold. Apparently, the firms' products are differentiated. You cannot impose symmetry across firms. Therefore, please solve each firm's profit maximization problem, impose equilibrium, and solve for each firm's "action" in equilibrium. After that, please calculate the Herfindahl- Hirschman Index (HHI) in the industry in equilibrium.
- bok rint An oligopoly producing a homogeneous product is comprised of three firms that act like a cartel. Assume that these three firms have identical cost schedules. Assume also that if any one of these firms sets a price for the product, the other two firms charge the same price. As long as they all charge the same price they will share the market equally; and the quantity demanded of each will be the same. Below is the total-cost schedule of one of these firms and the demand schedule that confronts it when the other firms charge the same price as this firm. Complete the marginal-cost and marginal- revenue schedules facing the firm. erences Mc Graw Hill Output Total cost Marginal cost Price Quantity demanded Marginal revenue 0 1 23456 7 8 $0 180 300 480 720 1,020 1,380 1,800 2,280 Short Anewor LA JUL 26 $780 720 660 600 540 480 420 360 Toolbar navigation (a) What price would be charged, what output would be produced, and what profit would be made by this firm? (b) If the firms…Discuss Many electronics stores like EMAX, and Jumbo have low-price guaranteepolicies. At a minimum, these guarantees promise to match a rival’s price, and somepromise to beat the lowest advertised price by a given percentage. Do these types ofpricing strategies result in cutthroat competition and zero economic profits? If not, whynot? If so, suggest an alternative pricing strategy that will permit these firms to earnpositive economic profits.While there is a degree of differentiation between major grocery chains like Albertsons and Kroger, theregular offering of sale prices by both firms for many of their products provides evidence that these firmsengage in price competition. For markets where Albertsons and Kroger are the dominant grocers, thissuggests that these two stores simultaneously announce one of two prices for a given product: a regularprice or a sale price. Suppose that when one firm announces the sale price and the other announces theregular price for a particular product, the firm announcing the sale price attracts 1000 extra customers toearn a profit of $5000, compared to the $3000 earned by the firm announcing the regular price. Whenboth firms announced the sale price, the two firms split the market equally (each getting an extra 500customers) to earn profits of $2000 each. When both firms announced the regular price, each companyattracts only its 1500 loyal customers and the firms each earned $4500 in…
- 11. Suppose there is a duopoly of two identical firms, A and B, facing a market inverse demand of P = 140 – 0.5Q, and cost functions of CA = 20QA and Cg = 20QB respectively. a. Find the Cournot-Nash equilibrium and profit for each firm. b. Suppose that A acts as the leader in a Stackelberg model and B responds. What are the respective quantities and profits of each firm now? Is it advantageous to move first? c. If the firms were able to collude, how much additional profit could they earn if they switch from simple single pricing to perfect price discrimination? d. Graph and label equilibria on the inverse demand.Ma3. You operate in a duopoly in which you and a rival must simultaneously decide what price to charge for the same homogeneous product. Assume each you and your rival can choose a “low price” or a “high price”. If you each charge a low price, you each earn zero profits. If you each charge a high price, you each earn profits of $3 million. If you charge different prices, the one charging the high price loses $5 million and the one charging the low price makes $5 million. What is the Nash equilibrium for the non-repeated version of this game? Now suppose the game is infinitely repeated. If the interest rate is 10%, can you do better than you could in the non-repeated version of this game? If your answer is “yes”, provide the players’ strategies and any other conditions that must hold.Think about firms such as the Coca Cola Company and PepsiCo who competeagainst each other in the monopolistically competitive market for soft drinks. Eachfirm produces a unique product, but each of these unique products is to some extenta substitute for the soft drinks produced by rival companies.Now imagine a situation where the firms within such a market are facing suchextreme competition that they are unable to make an operating profit. Characterisethis situation diagrammatically and explain what will happen to the market, payingparticular attention to the exit or entry of firms out of (or into) the market.
- 2. Walmart (firm 1) and Amazon (firm 2) are a duopoly in the grocery market. They are faced with an inverse demand of P(Q1, Q2) = 4 – 2(Q1+ Q2) and total costs of TC(Q;) = 2Q?, i = 1, 2. Note that the marginal cost is not constant! 1. Obtain the Cournot equilibrium quantities and profits. 2. Obtain the Stackelberg equilibrium in which Walmart moves first. Compare with the Cournot equilibrium. 3. Obtain the cartel outcome (= shared monopoly). Compare with Stackelberg and Cournot.2. Walmart (firm 1) and Amazon (firm 2) are a duopoly in the grocery market. They are faced with an inverse demand of P(Q1,Q2) = 16– 2(Q1+Q2) and total costs of TC(Q.) = 20?, i = 1,2. Note that the marginal cost is not constant! 1. Obtain the Cournot equilibrium quantities and profits. 2. Obtain the Stackelberg equilibrium in which Walmart moves first. Compare with the Cournot equilibrium. 3. Obtain the cartel outcome (- shared monopoly). Compare with Stackelberg and Cournot.Scenario: Madison Company is a large manufacturer and distributor of cake supplies. It is based in Chicago(Headquarters) and Trinidad. It sends supplies to firms throughout the United States and the UnitedKingdom. It markets its supplies through periodic mass mailings of catalogs to those firms. Itsclients can make orders over the phone and Madison ships the supplies upon demand.The main competition for Madison’s in the United States comes from one U.S. firm and oneCanadian firm. A British firm has a small share of the U.S. market but is at a disadvantagebecause of its distance. The British firm’s marketing and transportation costs in the U.S. marketare relatively high. Given that one-third of the company sales are exported to the United Kingdom and invoices forexports are in US dollars, the demand for its exports is highly sensitive to the value of the Britishpound. In order to maintain its inventory at a proper level, it must forecast the total demand for itsproducts which is…