Frankfurter is served by a local monopoly producer. Compute the monopoly profit-maximizing price and the monopoly profit level. Show your computations. (c) Each phone costs c = $100 to produce. The producer owns exclusive patent rights which prevents competition in this market. On the demand side, there are: NH = 1000 consumers who are willing to pay a maximum mount of V H = $500 for a phone, NM = 3000 consumers who are willing to pay up to V M = $300 for a phone, and nil = 5000 consumers who are willing to pay a maximum amount of V L = $200 for a phone.

Each consumer chooses whether to buy one unit or not to buy at all. Compute the profit-maximizing price of this monopoly phone producer. Set # 5: Administrating Monopoly (a) The demand function for concert tickets to be played by the Ann Arbor symphony orchestra varies between instruments (N ) and students (S). Formally, the two inverse demand demand functions of the two consumer groups are given by PAN = 12 – CNN ND AS = 6 -sq . Thus, at any given consumption level instruments are willing to pay a higher price than students.

Assume that the orchestra’s total cost function is C(Q) = 10 + SQ where Q = CNN + sq is to total number of tickets sold. Solve the following problems. Draft?ii- excursiveness’s. TEX 2009/06/19 16:25 Page 6 of 33 Downloaded from: (I) Suppose the orchestra is able to price discriminate between the two consumer groups by asking students to present their student ID cards to be eligible for a student discount. Compute the profit-maximizing prices PAN and AS , the number of sickest sold to each group of consumers, and total monopoly profit. It) Suppose now the local mafia has distributed a large number of fake student ID cards, so basically every resident has a student ID card regardless of whether the resident is a student or not. Compute the profit-maximizing price, the number of tickets sold to each group of consumers, and total profit assuming that the monopoly orchestra is unable to price discriminate. (iii) By how much the orchestra enhances its profit from the introduction student discounted tickets compared with the profit generated from ailing a single uniform ticket price to both consumer groups. B) Consider the market for the G-Shares (the latest fashion among people in their late thirties). G-Shares are solo Dye a single Tall Tanat carries ten patent Tort ten eagles. On ten mean sloe, there are NH = 200 high-income consumers who are willing to pay a maximum amount of V H = $20 for a pair of G-Shares, and nil = 300 low-income consumers who are willing to pay a maximum amount of V L = $10 for a pair of G-Shares. Each consumer chooses whether to buy one pair of Shares or not to buy at all. (I) Draw the market aggregate-demand curve facing the monopoly. It) The monopoly can produce each unit at a cost of c = $5.

Suppose that the G-Shares monopoly cannot price discriminate and is therefore constrained to set a uniform market price. Find the profit-maximizing price set by G-Shares, and the profit earned by this monopoly. (iii) Compute the profit level made by this monopoly assuming now that this monopoly can price discriminate between the two consumer populations. Does the monopoly benefit from price discrimination. Prove your result! (c) The demand function for concert tickets to be played by the Ann Arbor symphony orchestra varies between instruments (N ) and students (S).

Formally, the two demand functions of the two consumer groups are given by CNN = 240(pan )-2 and sq = 540(as )-3 . Assume that the orchestra’s total cost function is C(Q) = SQ where Q = CNN + sq is to total number of tickets sold. Compute the concert ticket prices set by this monopoly orchestra, and the resulting ticket sales, assuming that the orchestra can price discriminate between the two consumer groups. Page 7 of 33 (d) A brewery is allowed to sell beer in two domestic markets called market 1 and market 2.

Since both markets are located nearby each other, the brewery cannot rice discriminate, and therefore must set a uniform price p in both markets. The inverse demand function in market 1 is Pl = 60 -SQL . The demand in market 2 is pa ? 50 – sq , where SQL and sq are quantity demanded in each market (measured in cans), and the price is measured in cents. The cost of producing each can of beer is c = 30. Solve the following problems: (I) Compute the monopoly profit-maximizing uniform price, the quantity of beer sold in markets 1 and 2, and total profit. Ii) Suppose now the brewery is allowed to sell beer to a nearby town (call it market 3) located Just across the border. The inverse demand function in this town is pa = 40- sq . Due to the proximity of the three markets, the brewery cannot price discriminate and must set again a uniform price of p in all three markets. Compute the printmaking’s price, ten quantity solo In can market, Ana total pronto. (e) Discuss winter It Is illegal to price discriminate according to the U. S. Law. Explain which section of the law deals with price discrimination, and how this section should be interpreted. F) The demand function for concert tickets to be played by the Ann Arbor symphony orchestra varies between instruments (N ) and students (S). Formally, the two demand functions of the two consumer groups are given by CNN = 7290(pan )-3 and sq = 40960(as . Assume that the orchestra’s total cost function is T C(Q) = SQ, where Q = CNN + sq is to discriminate between the two consumer groups, say by requiring students to submit their student ID cards. (g) Impel is the sole producer of memory chips for supercomputers. Each chip costs c = 30 to produce.

This monopoly can sell in two markets with the following inverse demand functions: sq Pl = 120 – SQL and pa = 120 – . 3 (I) Compute the monopoly profit-maximizing prices in each market, Pl and pa , ales TM levels SQL and sq , and the monopoly total profit assuming that Impel can price discriminate between the two markets. (it) Now, due to a fire that nearly destroyed its factory, this monopoly cannot produce and sell more than 160 units. In other words, assume that the production capacity itty of Impel is limited to no more than 160 chips.

Compute the monopoly profit-maximizing prices in each market, Pl and pa , sales levels SQL and sq , and the monopoly total profit. Draft?ii- excursiveness’s. TEX 2009/06/19 16:25 Page 8 of 33 Downloaded from: (h) A monopoly sells in three markets with the following inverse demand functions: Pl -36 -IQ , pa=12 -sq . 2 For simplicity, assume that production is costless (c = O). Also, assume that the monopoly is unable to price discriminate, hence it must charge the same price in all three markets, p = Pl = pa = pa .

Compute the monopoly profit-maximizing price, p, aggregate sales, and total profit. Set # 6: Court Quantity Competition (Static) (a) In Ann darner tenet are two suppliers AT Olsten water, ladle Tall A Ana Tall Distilled water is considered to be a homogeneous good (well, all water taste the same, anyway). Let p denote the price per gallon, sq quantity sold by firm A, and CB the annuity sold by firm B. Firm A is located nearby a spring and therefore bears a production cost of CA = $1 per one gallon of water. Firm B is not located near a spring, and thus bears a cost of CB = $2 per gallon.

Ann Barber’s inverse demand function for distilled water is given by sq + CB 1 , p = 120 -Q = 120 – 22 where Q = sq +CB denotes the aggregate industry supply of distilled water in Ann Barber. Solve the following problems: (I) Formulate the profit-minimization problem of firm A. (it) Solve for firm Ass best-response function, sq = RA (CB ). (iii) Formulate the profit- minimization problem of firm B. ‘v) Solve for firm Bi’s best-response function, CB = ROB (sq ). (v) Draw the two best-response functions. Denote the vertical axis by sq , and the horizontal axis by CB . C (v’) Solve for the Court equilibrium output levels sq and CB . State which firm sells more water and why. (vii) Solve for the aggregate industry supply and the equilibrium price of distilled water in Ann Barber. (viii) Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why? Draft?ii- characteristics. TEX 2009/06/19 16:25 page 9 of 33 Downloaded from: b) In Watermill there are two suppliers of distilled water, labeled as firm A and firm B. Distilled water is considered to be a homogeneous good.

Let p denote the price per gallon, sq quantity sold by firm A, and CB the quantity sold by firm B. Both firms are located close to a spring so the only production cost is the cost of bottling. Formally, each firm bears a production cost of CA = CB = $3 per one gallon of water. Waterline’s aggregate inverse demand function for distilled water is given by p = 12-Q = 12 – sq – CB , where Q = sq + CB denotes the aggregate industry supply of distilled water in Watermill. Solve the following problems: (I) Solve for firm Ass best-response function, sq = RA (CB ).

Also solve for firm Bi’s best-response function, CB = ROB (sq ). Show your derivations. C c (it) Solve for the Court equilibrium output levels sq and CB . State which firm sells more water (if any) and why. (iii) Solve for the aggregate industry supply and the equilibrium price of distilled water in Watermill. (iv) Solve for the profit level made by each firm, and for the aggregate industry profit. Which firm earns a higher profit and why? (c) Solve for the Court equilibrium for the following market: p = 120 – Q, CA = $10, CB = $20. D) Solve for the Court equilibrium for the following market: p = 240 – Q/2, CA = $10, CB = $20. Sequential Moves (Quantity Game) (a) In Ann Barber there are two suppliers of distilled water, labeled firm A and firm B. Distilled water is given by p = 120- 1 sq + q B Q = 120 – , 22 where Q = sq +CB denotes the aggregate industry supply of distilled water in Ann Barber. Draft-to-characteristics. TEX 2009/06/19 16:25 page 10 of 33 Downloaded from: www. Shy. Com Suppose firm A sets its quantity produced sq , before firm B does.

That is, firm B sets its production level CB , only after observing the quantity produced by firm A. Solve the following problems. (I) Derive firm Bi’s (the follower) output best-response as a function of firm Ass output level, CB = ROB (sq ). (ii) Formulate and solve firm Ass (the leader) output profit-minimization problem. (iii) Compute the profit-maximizing output level produced by firm B (the follower). (v) Compute the aggregate industry supply of distilled water in Ann Barber and the equilibrium price. (v) Compute the equilibrium profit level of each firm. (v’) Compare the output and profit levels of firm

A as a leader in a sequential-move equilibrium to the output and profit levels in the Court equilibrium which you computed in Set # 6:(a). (vii) Compare the output and profit levels of firm B as a follower in a sequential-move equilibrium to the output and profit levels in the Court equilibrium which you computed in Set # 6:(a). (viii) Compare aggregate industry output, aggregate profit levels and the price level under a sequential-move equilibrium to those under the Court equilibrium. (b) Consider the following market: p = 12 – Q/2, and unit costs CA = $1 and CB = $2.