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Chapter: 5 -Problem: 8 >> Consider a monopolist who sells a product that contains two attributes A and B. Each of these attributes can be of high or of low quality. Low quality gives utility ui = 0 and high quality utility ui = 1/2, i = A, B. The willingness to pay for the product is the sum of the ‘attributes’ utilities plus some small, positive fixed value, u0 > 0- i.e., u0 + uA + uB. Nature draws high and low quality wi
Answer Preview: 1. The firm advertises the existence of the product. By the unravelling argument, it also reveals any attribute with high quality and consumers correc…

, Two firms (firm 1 and firm 2) compete in a market for a homogenous good by setting quantities. The demand is given by Q (p) = 2 - p. The firms have constant marginal cost c = 1.1. Draw the two firms reaction function. Find the equilibrium quantities and calculate equilibrium profits.2. Suppose now that there are n firms where n ? 2. Calculate equilibrium quantities and profits.
Answer Preview: For the two firms, the profit function can be expressed as = p(Q) - cQ, where p(Q) = 2 - Q (from the …

, Consider a monopolist selling computer software. Software is of high or low quality and is chosen by Nature: quality is high with probability ? and low with probability 1 – ?. Consumers can buy the software in period 1 and consume it in periods 1 and 2, where the discount factor is ? < 1. Software is produced at fixed cost Fi and marginal costs ci, i = H, L. The software producer learns quality be
Answer Preview: In this market, the monopolist will choose to sell the software in period 1. This is because the mon…

, A firm sells a product in a market where there are two types of consumers, high and low-valuation consumers. There are equally many of the two types of consumers, and the total number of consumers is normalized to 1. The product has value 3 to the high-valuation consumers and value 1 to the low-valuation consumers. All consumers have unit demand, i.e., they buy either one unit or do not participat
Answer Preview: To find the profit maximizing price, we need to determine the price at which the quantity demanded i…

, Consider the following version of the lemons problem. There is a continuum of buyers and sellers in the market; the total mass of each group is 1. Each seller has one car to sell and each buyer wishes to buy at most one car, but only sellers know the quality of their cars before trading. It is common knowledge however that the quality of cars, denoted s, is drawn from a uniform distribution on the
Answer Preview: 1 . The supply of cars by type 1 sellers at a given price p is equal to * s , where is the fraction …

, Suppose there are two groups of consumers, group 1 of size ? and group 2 of size 2 - ?. Consumers have unit demand. Consumers in group 1 have willingness-to-pay for a high-quality good equal to 3 and for a low-quality good equal to 2. Consumers in group 2 have willingness-to-pay equal to 2 independent of the quality of the good. A monopolist sells the product to consumers. With probability 1/2 it
Answer Preview: 1 . The profit - max im izing prices for the high - quality and low - qu…

, Chapter: 3 -Problem: 10 >> Consider a Hotelling model in which two firms are located at the opposite ends of the unit interval and serve a unit mass of consumers, who are uniformly distributed on this interval. Each consumer has unit demand and her utility if she buys from ?rm 1, located at 0, is r –?x - p1, where x is the consumer’s location on the line, her utility if she buys from firm 2, located at 1, is r -? (1- x) -p2
Answer Preview: 1. To solve for the Nash equilibrium, let us first determine the consumer who is indifferent between the two firms. Given prices p 1 and p 2 , the loc…

, A study by Brynjolfsson and Smith on retail price for books and CDs finds that price dispersion (weighted by market shares) is lower for internet retailers than for conventional retailers. Discuss.
Answer Preview: The study by Bry n j olf sson and Smith on retail prices for books and CDs found that price d…

, Chapter: 4 -Problem: 4 >> Consider a country that can be divided into two distinct markets of different sizes: market 1 is small (in the sense that it can only accommodate one firm), while market 2 is larger (in the sense that it can accommodate two firms). Two firms are active in the country: firm A is a national company that is active on both markets; firm B is a local company and is only active on market 2. Demand condi
Answer Preview: 1. Local pricing. On market 1, firm As profit is given …

, Suppose that advertising expenditures are wasteful in the sense that they only redirect existing demand and do not increase consumer utility. Can such advertising be total surplus increasing? Explain.
Answer Preview: Even if advertising only redirects existing demand and does not increase consumer utility, it can st…

, Consider a market in which firms have private information about their quality s ? [0, 1]. Quality is drawn from the uniform distribution on the 0-1 interval; this is common knowledge among firm and consumers. After observing its type the firm decides whether to reveal its quality to consumers (it has the choice whether or not to reveal its quality but not to mislead; a justification is that the fi
Answer Preview: Answer: 1. If the government mandates information disclosure, then the firm has no choice but to rev…

, Chapter: 2 -Problem: 12 >> Consider a duopoly market for a homogeneous product in which firms set quantity. Inverse demand is P (q) = 1- q with q = q1 + q2. Firm 1 has marginal costs equal to 0.7. Firm 2 has marginal cost 0.65 with probability 1 / 2 and 1 with probability 1 / 2.1. Suppose that the cost type is publicly observed by both firms prior to the quantity setting. Characterize the equilibrium outcome of this game.2.
Answer Preview: 1. Firm share information : High costs: Firm 1: Firm 2: Low cost: Firm 2: Firm 1: …

, Suppose that two software companies launch a new software each. One of them is called COOL, the other GREAT. There is a unit mass of consumers. All of them consider the two software offers as identical. Both software’s are produced at zero marginal costs and consumers are willing to pay r for the software.1. Suppose that firms set prices and compete only in one period. Characterize equilibrium pri
Answer Preview: 1. In the one-period market, the equilibrium prices, allocation, and profit would be: (i) Both firms will set a price of r; (ii) Half of the consumers …

, Reconsider the simple Hotelling model in which consumers are uniformly distributed on the unit interval and firms are located at the extremes of this interval. Now take consumer’s participation constraint explicitly into account. Derive the equilibrium depending on the parameter ?. [Be careful to distinguish between different regimes with respect to competition between firms!]
Answer Preview: In the Hotelling model with a participation constraint, consumers will only participate in the marke…

, Chapter: 5 -Problem: 5 >> Consider a monopolist who has one unit of a product. The outside option of not selling the product is c. This product has high quality sH with probability ? and low quality sL with probability 1 - ?. There are two consumers, each of whom has valuation vH for high quality and vL for low quality. We assume that vH > c > vL. Furthermore, we assume that ?vH + (1 - ?) vL > c. Consumers bid for the obje
Answer Preview: 1. Solved by backward induction. Consumers will bid according to their valuation in the second stage …

, Chapter: 5 -Problem: 9 >> A business school offers an MBA program with two areas of specialization: finance and marketing. For simplicity, suppose that the school is facing only two potential students: one who is interested only in finance and his utility from studying in the school is 2sF - p and the other who is interested only in marketing and his utility is sM - p, where sF is the quality of the finance courses, sM is
Answer Preview: This problem is based on the paper The Economics of Quality Indexes by Glazer and McGuire. 1. If the students can tell the quality of the courses before they enroll, each will enroll if by doing so sh…

, Suppose that two firms with constant marginal costs compete in prices in a homogeneous product market. All consumers have unit demand and a willingness to-pay r. A share ? of consumers is informed about the prices in the market. The share (1 – ?) = 2 goes to firm i = 1, 2 and decides whether to buy (these consumers do not know that a product from firm j ? i exists). Firms set prices and then consu
Answer Preview: In a symmetric Nash equilibrium, both firms would set the same price, p, and share the market equall…

, Consider as above a market in which firms have private information about their quality s ? [0, 1]. Quality is drawn from the uniform distribution on the 0-1 interval; this is common knowledge among firm and consumers. After observing its type the firm decides whether to reveal its quality to consumers (it has the choice whether or not to reveal its quality but not to mislead; a justification is th
Answer Preview: The firm's problem can be written as a principal-agent problem, where the firm (the principal) wants to choose the price and information disclosure po…

, Consider a market in which firms 1,……., N set simultaneously capacities for a homogeneous product and afterwards a third party, which observes market demand and the capacity choice of each firm sets the market clearing price. Suppose that inverse demand is linear and of the form P (q) = a - q, where p is the price, a a positive constant, and q aggregate output,  qi is the quantity sold by firm i.
Answer Preview: The Nash equilibrium for this market is for each firm to …

, Consider the Hotelling model in which consumers are uniformly distributed on the [0, 1]-interval and firms A and B are located at the extreme points. Firms produce a product of quality si. Consumer x ? [0, 1] obtains utility uA = (r - tx) sA - pA if she buys one unit of product A and uB = (r – t (1 - x)) sB - pB if she buys one unit of product B. Each consumer buys either one unit of product A or
Answer Preview: The utility function represents the indirect utility of a consumer x, who can choose between product…

, Chapter: 2 -Problem: 14 >> Suppose that two identical firms in a homogeneous-product market compete in prices. The capacity of each firm is 3. The firms have constant marginal cost equal to 0 up to the capacity constraint. The demand in the market is given by Q (p) = 9 - p. If the firms set the same price, they split the demand equally. If the firms set a different price, the demand of each one of the firms is calculated ac
Answer Preview: At the prices p 1 = p 2 = 3, both firms produce at full capa…

, Chapter: 4 -Problem: 11 >> Consider a monopolist providing a product over several periods. The monopolist  has constant marginal costs of production of c in each period. Consumers consider to consume one unit of a good in each period. The consumer population is of mass 1. Half of all consumers have a high valuation ?H for the product, which is the same in each period. The other consumers have a low valuation ?L with ?H > ?L
Answer Preview: 1. The profit-maximizing price is either p = H or p = L . If the monopolist commits to set price p = H in every period, he will make per-period profit of H - c) =2. If he sets price p = L in every per…

, In the recent financial crisis, rating agencies have become a focus of attention. The market has traditionally been dominated by a few big agencies, currently Standard & Poor, Moody?s and Fitch. In 2006, the Securities and Exchange Commission (SEC) introduced measures to speed up the approval process for rating agencies with the aim to increase competition. However, in response to the financial cr
Answer Preview: The decision by the Federal Reserve to only accept collateral that has been appraised by one of the …

, Chapter: 3 -Problem: 16 >> Consider a Hotelling duopoly in which firms are located at the extreme points of the unit interval and consumers of mass 1 are uniformly distributed on the unit interval. The price of the two products is given and equal to 1, p1 = p2 = 1 (e.g. because the price is fixed upstream); production costs are zero. The quality of product i is denoted by si ? [2, 3]. The quality of each product is drawn in
Answer Preview: 1. Independent of s j , firm i always discloses if s i (2, 3]. To see this, note that profit of firm i is i = q i 1. Demand q i is determined as follo…

, Which model, the Cournot or the Bertrand model, would you think provides a better first approximation to each of the following industries / markets: the oil refining industry, farmer markets, cleaning services. Discuss!
Answer Preview: The Cournot model and the Bertrand model are two different approaches to modeling competition in a market. The Cournot model is based on the assumptio…

, Chapter: 2 -Problem: 6 >> Consider a duopoly market with a continuum of homogeneous consumers of mass 1. Consumers derive utility vi ? {vH; vL} for product i depending on whether the product is of high or low quality. Firms play the following 2- stage game: At stage 1, firms simultaneously invest in quality: The more a firm invests the higher is its probability ?i of obtaining a high-quality product. The associated investm
Answer Preview: 1. Bertrand competition: v 1 = v 2 , * 1 = * 2 = 0 If v i > u j , i * = and j = 0, i j. the …

, Chapter: 1 -Problem: 1 >> Consider the market for shoes in country A. Demand is assumed to be 100 - p where p is the final consumer price. Suppose that country A does not produce shoes and that there are two importers B and C. The export prices for shoes in both countries are PB = 59.99 and PC, respectively. Furthermore suppose that country A is a small country so that its demand does not influence export prices. Suppose t
Answer Preview: In the absence of a free-trade agreement with country B, the consumers in country …

, Consider a market in which firms 1,……,N are equidistantly distributed on a circle with circumference 1. Firms have constant marginal costs of production c, which are the same for all firms. Consumers are uniformly distributed on the circle (and have mass 1). A consumer x incurs a transportation ? |x - li| when buying from firm i. Here the distance between consumer and firm is the arc distance on t
Answer Preview: The demand function of firm i is given by the consumer's choice of the firm that offers the highest …

, Manufacturers issue warranties for their products, often beyond the mandatory minimum length. However, the warranty is restricted to require consumers to take proper care of the product. Discuss this restriction. Should consumer protection apply to any malfunctioning of the product within a given time period?
Answer Preview: The restriction that manufacturers put on warranties that require consumers to take proper care …

, Suppose there are 2 firms in a vertically differentiated market. Consumers buy either one unit of any of the two goods or they do not purchase in the market. If they do not purchase in the market their indirect utility is 0. If they purchase good i their indirect utility is ? si - pi, where ? is the preference parameter of a consumer, si is the quality of good i and pi is the price of good i. Assu
Answer Preview: The demand function of each firm depends on the prices and qualities of both goods. The consumer wil…

, Suppose two firms, firm 1 and firm 2, operate in a homogeneous good market. The supply of firm i, denoted by qi, is constrained by installed capacity ki, i.e., 0 ? qi ? ki for i = 1, 2. Firms have zero marginal costs of production for quantities weakly below their capacity. They cannot increase production beyond capacity. There is a group of consumers of size ?? who all have unit demand with the s
Answer Preview: To determine the allocation at stage 2 for given capacity choice, we first need to consider the interaction between firms at stage 2, where they are competing in prices. We can use a standard Bertrand …

, Chapter: 4 -Problem: 9 >> Suppose that a supermarket offers a product selection consisting of products A and B. Consumers are willing to pay 10 Euro for one unit of product A and 10 Euro for product B. Consumers have heterogeneous shopping cost z. This shopping cost is uniformly distributed over the interval [0, 10]. Consumers are of mass 10. The firm has marginal cost of 6 for product A and 0 for product B.1. Calculate th
Answer Preview: 1. Profit-maximizing prices satisfy p A 10 and p B 10. Then consumers buy either both products or do not buy at all. Denote the consumer who is indiff…

, Chapter: 4 -Problem: 5 >> Consider a horizontally differentiated product market in which two firms are located at points l1 = 0 and l2 = 1 on the line. Firms produce at marginal costs c. There is a continuum of consumers of mass 1 who are uniformly distributed on the unit interval. They have unit demand and have an outside utility of -?. A consumer located at x ? [0, 1] obtains indirect utility v1 = r – ? (x)2- p1 if she b
Answer Preview: 1. The indifferent consumer is located at x = p 2 - p 1 /2 + . Hence, demand is Firms maximize profits (p i - c) q i (p i , p j ) with respect to pi. …

, Chapter: 2 -Problem: 15 >> Suppose two firms in an industry face linear inverse demand curves Pi (qi, qj) = 7- qi -qj , i = 1; 2, i ? j. Firms compete in a two-stage game; first they set capacity and then they set price or output. At the first stage firms set capacities, at this stage the marginal costs of capacity is 6. Suppose that firms have zero marginal costs of production up until installed capacity and that productio
Answer Preview: 1. Suppose that capacity is 7 NE in prices products are homogenous ! prices equal to MC 2. Suppose that capacity is 7 NE in quantities: 3. Consumers do not observe prices before consumption The approp…

, Consider the Cournot duopoly with linear demand P (q) = 1 - q with q = q1 +q2 and constant marginal cost. Firm one has marginal cost of zero. This is commonly known. The marginal cost of firm 2 is privately known to firm 2; firm 1 only knows that they are prohibitively high or zero and that both events are equally likely (this is commonly known). High marginal costs are assumed to be prohibitively
Answer Preview: In this game, the equilibrium can be characterized as follows: Firm 2 will not have an incentive to …

, Somewhere far away there exist two villages Apple-castle (A) and Orange-village (B). Each village has its grocery store which sells a particular brand. Suppose that initially connections are bad so that all inhabitants of A do their shopping in A and all inhabitants of B do their shopping in B. Some villagers propose a better connection between A and B.1. Do the grocery owners support this connect
Answer Preview: 1 . It is possible that both , one or none of the grocery owners support the project . …

, Consider a market with two horizontally differentiated products and inverse demands given by Pi (qi, qj) = a - bqi - dqj . Set b = 2=3 and d = 1/3. The system of demands is then given by Qi (pi, pj) = a - 2pi + pj . Suppose firm 1 has cost c1 = 0 and firm 2 has cost c2 = c (with 7c < 5a). The two firms compete in prices. Compute the firm profits:1. at the Nash equilibrium of the simultaneous Bertr
Answer Preview: 1. Nash equilibrium of the simultaneous Bertrand game. Firm 1 chooses p 1 to maximize 1 = (a - 2p 1 …

, Do you think that price discrimination between rich and poor countries is a feasible solution for giving poor developing countries better access to patented pharmaceuticals? In the answer you should draw upon the theory covered in the book.
Answer Preview: Price discrimination between rich and poor countries is not a feasible solution …

, Consider a monopolist who sells a single unit of a product that may be of high or low quality. Both events occur with probability 1/2. There are at least two identical consumers. Consumers are willing to pay 1 for a functioning product and 0 for a product that breaks down. A high quality product breaks down with probability 1/4 whereas a low-quality product breaks down with probability 3/4. Consid
Answer Preview: Answer: 1. If the monopolist has a cost of 0 to produce and sell the product independent of its qual…

, Chapter: 5 -Problem: 4 >> A firm produces a single product whose quality is either high or low (the firm knows the quality but cannot choose it) and sells it to consumers in each of two periods. The marginal cost of production is 4 if quality is high and 3 if quality is low. In each period there are N consumers, each of whom is interested in buying at most one unit in each period and is willing to pay 10 if quality is high
Answer Preview: 1. Suppose that consumers believe that if the firm sponsors x TV ads, then its quality is high. If the low quality firm does not advertise, consumers …

, "Purple Dream" has the monopoly on the production of purple light-emitting diodes (LEDs). It faces geographically separated markets, market 1 and 2. The demands are qA = 1 - pA and qB = 1/2 - pB, respectively. The transport and production costs are set to zero.1. Assume that the firm chooses to set a uniform price across the two markets. What is the profit maximizing uniform price? What are the qu
Answer Preview: To find the profit maximizing uniform price, the firm needs to set the price at which the quantity d…

, Give five examples of product markets in which product differentiation is likely to be a determining factor for competition in the market place. Give five examples in which the imperfections in competition are likely to be the result of factors different from product differentiation.
Answer Preview: Product differentiation is a marketing strategy in which a company creates a product that is perceived as unique or superior to its competitors. Here …

, Chapter: 1 -Problem: 2 >> Consider a monopolist with a linear demand curve: q = a - bp, where a, b > 0. It produces at constant marginal cost c and has no fixed cost. Assume that 0 < c < a / b. 1. Find the monopoly price, quantity, and profits.2. Derive the inverse demand curve P (q). Draw P (q), the MR-curve, and the MC-curve in a diagram. Explain why we need the assumption c < a / b.3. Does it matter that the monopolist
Answer Preview: 1. The monopoly chooses p to maximize = (p - c) (a - bp). The first-order condition yields a bp- bp …

, It is not difficult to navigate in Lonely-Line City: a single street runs from kilometer 0 to kilometer 1 along which 100 inhabitants are equidistantly distributed.  [Approximate the consumer distribution by a continuum on [0, 1] with a mass of 100.] To keep the place residential the local government has decided that no shops are allowed within the city limits. As it happens, there exists one shop
Answer Preview: 1. In this situation, the two shops will set their prices such that they are equal to the wholesale price plus the cost of transportation, t. Thus, the prices set by the two shops will be c + t. The s…

, Chapter: 3 -Problem: 18 >> Two firms (1 and 2) produce a homogeneous good at zero marginal cost. They face two types of consumers: a mass N of consumers are informed about the prices, p1 and p2 of the two firms and therefore buy from the cheapest firm; a mass M of consumers are uninformed in the sense that they only know the price of one firm and therefore have a demand only for this firm. We assume that M = M1 +M2, where M
Answer Preview: 1. We start by solving the second-stage for any price p i [0, R] set by firm 1. Firm 2 has two optio…

, Chapter: 3 -Problem: 19 >> Consider a market for a homogenous product with n identical price-setting stores, where n is determined by free entry. Each store has a cost function C (q) = ?q, where q is the number of customers the store serves. There are M + 15 consumers in the market, each of whom wishes to buy up to one unit and is willing to pay for it up to r = 1. The number of 15 consumers know the prices charged by all t
Answer Preview: 1. First, if n = 1 then the store will maximize profits by setting p * = 1 and will earn profit (M + 15) - (M + 15) 1/2 > 0. This will induce entry. Hence, there cannot exist a pure-strategy equilibri…

, Chapter: 2 -Problem: 10 >> Consider two sellers 1 and 2 and a continuum of buyers. Seller i offers product i at price pi and incurs zero marginal cost of production. Buyers are identical and derive utility ui from one unit of each product. Thus their utility is ui if they buy one unit of product i and zero units of product j, j ? i; it is u1 + u2 if they buy one unit of each product. Additional units do not give any extra u
Answer Preview: 1. For p 1 u 1 …

, Chapter: 3 -Problem: 21 >> Consider a market for a homogenous product with n identical stores, where n is determined by free entry. Each store has a cost function C (q) = 4 + q, for q ? 4 and c (q) = ? for q > 4 (in other words, each store can sell up to 4 units and its cost of selling the first q units is 4 + q). There are L consumers in the market, each of whom wishes to buy up to 1 unit and is willing to pay for it up to
Answer Preview: 1. 2. z = 0) all consumers can become informed at zero cost firms can only set one price price must be such that no more entry occurs, i e. all firms must earn zero profits monopolistic competition = …

, Chapter: 4 -Problem: 3 >> A monopoly faces a continuum of consumers who are distributed uniformly on the unit interval (i.e., the "numberöf consumers in each given interval is the same). The total mass of consumers is 1. Each consumer is interested in buying at most one unit. Consumers differ in the way they perceive the monopoly’s output. Assuming for simplicity that the monopoly is located at point 0, the utility of a co
Answer Preview: 1. Given p, the address x of the consumer who is just indifferent between buying and not buying is given by r - p tx 2 = 0. Hence, X =r- p / t. 2. For …

, A consumer with income m who consumes a product of quality si and pays pi obtains the utility sim = 6 - pi. If instead the consumer decides not buy the good, the resulting utility is zero. Consumer income m is uniformly distributed on the interval [2, 8] with the density 1/6. The total mass of consumers is equal to 1. There are two firms in the market. Firms 1 and 2 offer the qualities s1 and s2,
Answer Preview: The demand for firm i is given by the inverse demand function p(q) = 6 - sim = 6 - si m. Since m is …

, Some firms incur costs to offer a lower quality: i) Intel dismantled the mathematical coprocessor in some versions of the 486 CPU, ii) IBM has developed software to make some of their printers slower, and iii) Sony deliberately limited the capacity of some MiniDiscs to 74 instead of 80 minutes. Why do you think that the firms do this? What do you think that the welfare consequences are?
Answer Preview: It is possible that the firms you mentioned made these choices in order to segment the marke…

, Chapter: 3 -Problem: 8 >> Consider the vertical differentiation model presented in Section 5.3. Suppose that the quality of the product can be described by some number si∈ [s, sÌ…] ⊂ R+. Consumers are identified by θ ∈ [θ, θ] ⊂ R+, which measures their preference for quality. Consumers are distributed uniformly on [θ, θ] and are of masswhen consuming a unit of good i (where γ is supposed to be sufficiently la
Answer Preview: 1. The indifferent consumer satisfies r - p 1 +s 1 = r - p 2 +s 2 . Solving for gives Th…

, Chapter: 2 -Problem: 2 >> Consider a duopoly in which homogeneous consumers of mass 1 have unit demand. Their valuation for good i = 1; 2 is v {i} = vi with v1 > v2. Marginal cost of production is assumed to be zero. Suppose that firms compete in prices.1. Suppose that consumers make a discrete choice between the two products. Characterize the Nash equilibrium.2. Suppose that consumers can now also decide to buy both produ
Answer Preview: 1. Nash equilibrium given by p 1 = v 1 - v 2 , p 2 = 0, 1 = v 1 - v 2 and 2 = 0. 2. Nash equilibriu…

, Chapter: 4 -Problem: 12 >> Consider a market with network effects (i.e., a consumer’s utility depends on the number of users of a product) in which each consumer has a willingness to pay equal to xi where xi is the number of consumers buying product i = 1, 2. The products are functionally identical and thus consumers are indifferent between any products in the market, given equal numbers of units sold. Suppose that the incu
Answer Preview: 1. It is easily found that p 1 = 1, p 2 = 0, x 1 = 1, x 2 = 2. Firm 1 makes profit 1 = 1, whereas fi…

, Chapter: 4 -Problem: 13 >> A software company sells two applications, noted A and B, that are totally unrelated to one another. The marginal cost of production for each application is constant and is equal to 10. The company faces four categories of potential buyers, which are characterized by a pair of reservation prices as depicted in the following table; it is assumed that each category counts the same mass of consumers,
Answer Preview: 1. The two applications have similar demand schedules. It is easily found that for each application the profit-maximizing prices are p A = p B = 60; a…

, Chapter: 5 -Problem: 12 >> Consumers wish to buy a product and get a utility 10 if the product is of high quality and is working, and a utility of 4 if the product is of low quality and is working. If a product does not work, then the utility from having it is 0 irrespective of its quality. Ex ante, only the firm knows the quality of its product (but cannot choose it). Consumers expect that the product is of high/low qualit
Answer Preview: 1. Absent a warranty, consumers agree to pay (10/4/5 + 4/1/5) = 2 = 44 / 10 = 4 4. 2. Suppose the firm offers a warranty and consumers believe that it…

, Chapter: 4 -Problem: 15 >> Suppose that, as in Section 11.3.2, each of two firms 1 and 2 provides two components A and B. The offerings of both firms are horizontally differentiated. A consumer of type (?A, ?B) ? [0, 1]2 derives a net surplus r – ?A - (1 – ?B) - p1A - p2B if she buys component A from firm 1 at price p1A and component B from firm 2 at price p2B. Correspondingly, for other systems of A and B. The gross surplu
Answer Preview: 1. Under independent selling, firm i faces Hotelling demand 1/2 - (p i z -p j z ) / 2 for component z. Thefirms profits are Solving the system of four first-order conditions gives equilibrium prices p …

, Consider the linear Hotelling duopoly in which each firm produces a product with a firm-specific undesirable ingredient at zero marginal costs. Suppose that, absent advertising, consumers are not aware of this ingredient. In this case a consumer of type x derives utility r - tx - p1 if she purchases product 1 and utility r - t(1 - x) - p2 if she purchases product 2. If a consumer learns that produ
Answer Preview: In the case where firms cannot inform consumers about the undesirable ingredient in their products, the equilibrium can be derived as follows: The profit of firm 1 is given by: 1 = (r - p1 - tx) * q1 …

, Chapter: 5 -Problem: 6 >> A monopoly operates for two periods and produces a homogenous good whose quality is either high or low (the monopoly cannot choose the quality of the good). In the first period, the quality of the good is unobserved by consumers and their demand is q1 = s1 - p1, where s1 is the perceived quality of the good and p1 is the price in period 1. In the second period, the quality of the good becomes comm
Answer Preview: 1. In period 2, the quality of the good is common knowledge. Hence, the maxi- mization problem of the monopoly when the quality of the good is s {2, 4…

, Chapter: 4 -Problem: 14 >> Suppose that a monopolist produces two products, product 1 and product There is a mass 1 of consumers. A share ? of consumers are heterogeneous among each other and are described by their type ?. This type is distributed uniformly on the unit interval. The willingness-to-pay for product 1 is assumed to be r1 = ? and r2 = 1 – ?. A share (1 – ?) = 2 of consumers has willingness to pay r1 = 2/3 and r
Answer Preview: 1. Under independent selling, demand for product i (i = 1, 2) is determined by Q i = 1 - p i ; the optimal price are easily found as p * 1 = p * 2 = 1…

, Chapter: 2 -Problem: 9 >> Consider two quantity-setting firms that produce a homogenous good and choose their quantities simultaneously. The inverse demand function for the good is given by P = a - q1 - q2, where q1 and q2 are the outputs of firms 1 and 2 respectively. The cost functions of the two firms are C1 (q1) = c1q1 and C2 (q2) = c2q2, where c1 < a and c2 < (a + c1) / 2.1. Compute the Nash equilibrium of the game. W
Answer Preview: 1. The Nash equilibrium of the game is obtained by solving the …

, Consider the elasticities reported in the table below. The easiest way to think about the advertising elasticities is the following: Total demand consists of demand today and tomorrow. The short-run elasticity is the effect that advertising today has on demand today whereas the long-run elasticity is the effect that advertising today has on demand tomorrow. In which industries do you expect advert
Answer Preview: Based on the table, we can expect advertising intensity to be high in the following industries: Shor…

, Chapter: 3 -Problem: 1 >> Hong Kong Island features steep, hilly terrain, as well as hot and humid weather. Travelling up and down the slopes therefore causes problems; this has led the city authorities to imagine rather unusual methods of transport. One famous example can be found in the Western District, where one of the busiest commercial area of Hong Kong can be found. This area stretches from Des Voeux Road in Central
Answer Preview: 1. Before 1993. (a) The indifferent consumer is identified by xo such that r - tx o - p 1 = r - (t + ) (1 - x o ) - p 2 ; that is, x o = (t + - p 1 + …

, Chapter: 4 -Problem: 10 >> Suppose that a monopoly retailer has exactly 2 units of a perishable product available. It cannot increase its stock in the relevant period. Customers have unit demand and either a high or a low willingness to pay: 1 consumer is willing to pay r = 10 and 2 consumers are willing to pay r = 6. Customers arrive in random order at the shop. The retailer has to set a price for each of the 2 units. The
Answer Preview: 1. The retailers profit-maximizing price is either p = 10 or p = 6. If it sets p = 10 it sells to 1 consumer and makes profit 10. If it set p = 6 it s…

, Consider a monopolist that produces for two periods. The demand curves in both periods are qt = 1-pt for t = 1; 2. The marginal costs are c in the first and c – ?q1 in the second period. Here, ? is a small and positive number. There is a discount factor of between the periods.1. Explain briefly how the monopolist’s problem changes compared to a situation where the marginal cost is c in both period
Answer Preview: The monopolist's problem changes compared to a situation where the marginal cost is c in both perio…

, Chapter: 5 -Problem: 3 >> A firm has either a high quality or a low quality product (the firm cannot choose the quality of its product). The firm faces a continuum of consumers with a total mass one. Each consumer wishes to buy at most one unit. There are 2 types of consumers: 2/5 of the consumers are of type 1 and their utility is 10 - p if they buy a high quality product and 5 - p if they buy a low quality product; 3/5 o
Answer Preview: 1. If consumers can tell the products quality, then the firm will charge either 10 or 6 if quality is high and 5 or 3 if quality is low. To see which …

, Consider a duopoly for a homogeneous product. Firms i = 1, 2 set price-quantity pairs (pi, qi) simultaneously. If at these pairs some consumers are rationed, rationing is assumed to be efficient. Suppose firms are constrained by capacities ki > 0 and inverse market demand is P (q) = q-1. Does a Nash equilibrium in pure strategies exist? Is it unique? Characterize all Nash equilibria of this game.
Answer Preview: In this duopoly game with homogeneous products, a Nash equilibrium in pure strategies is a set of strategies such that each firm's strategy is a best …

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, Chapter: 5 -Problem: 13 >> A monopolist sells a product whose quality is unknown to consumers before they buy. It is common knowledge however that the product’s quality, s, is drawn from a uniform distribution on the unit interval. There is continuum of consumers with a total mass of 1. Each consumer is interested in buying at most 1 unit and gets a utility of s - p if he buys and 0 otherwise. The monopoly can send its prod
Answer Preview: 1. The monopolist will set a price equal to the maximal willingness of consumers to pay. Hence, if it sends its product for inspection, its profit is …

, Switching costs relax competition and their presence are therefore profit-enhancing. Is this statement necessarily correct? Explain.
Answer Preview: Switching costs can indeed relax competition and be profit-enhancing for the firms that im…

, Chapter: 5 -Problem: 2 >> A firm sells a product which may be of high or low quality, sH or sL, respectively.  High quality is to occur with probability ? and low quality with probability 1- ?. There is a unit mass of consumers with unit demand and the same willingness-to-pay for the product of a particular quality. Consumers like high quality more than low quality- i.e., consumer valuations (= willingness- to-pay) satisfy
Answer Preview: 1. 2. p = r H + (1)r L 3. 4. 'L = r L c < 0 by assumption. The low quality firm has n…

, Chapter: 2 -Problem: 1 >> Consider a monopolist who sells batteries. Each battery works for h hours and then needs to be replaced. Therefore, if a consumer buys q batteries, he gets H = qh hours of operation. Assume that the demand for batteries can be derived from the preferences of a representative consumer whose indirect utility function is v = u (H) - pq, where p is the price of a battery. Suppose that u is strictly in
Answer Preview: 1. The inverse demand for batteries is obtained by solving the following problem: The first-order conditions for this problem can be written as which is the inverse demand function for batteries. 2. T…

, Chapter: 3 -Problem: 13 >> Consider a horizontally differentiated product market in which firms are located at the extreme points of the unit interval. Firms produce at marginal costs equal to zero. A continuum of consumers of mass 1 are uniformly distributed on the unit interval. They have unit demand and have an outside utility of -?. A consumer located at x ? [0, 1] obtains indirect utility v1 = r1 - tx - p1 if she buys
Answer Preview: 1. For prices such that demand is strictly positive for each firm, demand of firm 1 is 2. Maximize s…

, Chapter: 2 -Problem: 22 >> Consider the same setting except that firms face a different demand function and that firms set prices at stage 3. Let demand be Qi = 1 - pi- dpj with d > 0 so that products are substitutes and d < 1. Characterize the equilibrium of this game. Does firm 2 have an incentive to share its private information?
Answer Preview: Suppose that firm 2 decides to share its information at stage 2. If its costs are high, firm 1 knows …

, Reconsider the duopoly model with linear individual demand and differentiated products. Show that prfits under quantity competition are higher than under price competition if products are substitutes and that the reverse holds if products are complements.
Answer Preview: Sure! I'll start by defining some terms: In a duopoly, there are two firms that dominate a market and have some control over the prices they charge. …

, Chapter: 4 -Problem: 8 >> A monopolist produces a good with constant marginal cost equal to c, c < 1. Assume for now that all consumers have the demand Q (p) = 1 - p. The population is of size 1.1. Suppose that the monopolist cannot discriminate in any way among the consumers and has to charge a uniform price, pU. Calculate both the price that maximizes profits and the profits that correspond to this price.2. Suppose now t
Answer Preview: 1. The monopoly chooses p to maximize = (p - c) (1 - p). The profit-maximizing price is easily found as p U = (1/2) (1 + c). The corresponding profit …

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12 Reviews for Industrial Organization Markets and Strategies Textbook Questions And Answers