(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price pi and firm 2 charges price p2, then their respective demands are q1 = 12 – 2p1 +p2 and 42 = 12 + P1 – 2p2. So this is like Bertrand competition, except that when p1 > P2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c= 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, pi = the optimal price for firm 1 if it is known that firm 2 charges a price P2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. BR1 (p2) is
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- country where wine is difficult to grow. The demand for wine is given by p = $480 - .2Q, where p is the price and Q is the total quantity sold. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Imports are prohibited. Grinch has constant marginal costs of $6 and Grubb has marginal costs of $45. How much Grinch's output in equilibrium? | a) 1,350 b) 2,025 c) 337.50 d) 675 e) 1,012.50(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price pi and firm 2 charges price p2, then their respective demands are q1 = 12 – 2pi + P2 and 92 = 12 + P1 - 2p2. So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c= 4. That is, pi (a) Construct the best reply function BR1(p2) for firm 1. the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If BR1 (P2) is yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm l's demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0? (c) What prices for firm 1 are not…Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…
- Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…Alpha Gear is a fitness apparel company. One of their best selling products are their joggers. The company sells joggers under a block pricing scheme that charges $13 per pair of joggers if the customer buys up to 10 joggers and $8 if they buy 11 to 20 joggers. The demand curve is Q-1400 - 25P, and the marginal cost of making a pair of joggers is $5. What are the profits for Alpha Gear under this pricing scheme? 8975 8600 3600 12200 000Suppose two firms engage in simultaneous quantity competition. Both firms have 0marginal cost. Firm A : P(Q)= 24-Q Firm B: P(Q)= 24-2Q a) Find the Nash Equilibrium quantities q^NE and profits.(b) Find the Monopoly Quantity QM and Profit.(c) Now suppose the game is repeated infinitely and each firm has a common discountfactor δ. Find the required discount factor to sustain the following grim triggerstrategy as a SPNE: Play Q^M /2 if this has been played in every previous period,otherwise play q^NE.
- 1. Consider an industry with inverse demand given by p = 8 – q, where p is the price, and q is the quantity. There is one incumbent firm and one potential entrant. In the first stage of the game, the incumbent chooses its quantity qi. In the second stage, the potential entrant observes qi and chooses its quantity Ce. The potential entrant can also decide not to enter the market. The production technology of both firms are represented by the cost function C = 2q. To enter industry implies a fixed entry cost of F. (a) Find the equilibrium of the game, assuming that the potential entrant enters the industry. What are the profits of firms? (b) Assume that entry is not blockaded. For which values of F does the incumbent firm prefer to deter entry? (c) For which values of F, entry blockaded?Consider a simple monopolistic competition industry (many firms) in whicheach firm in the industry has one store. The store costs $200 per week andthe marginal cost is $10 per unit of output in addition to the fixed cost of the store. Hint: Mathematically this problem can be solved just like a monopoly problem. (a) If the typical the demand facing each individual firm is QD = 40−P eachweek, what price will a typical firm in this industry charge? (Hint: IfQD = 40 − P then P = 40 − QD and MR = 40 − 2QD). (b) Is the firm making a positive profit? What is the producer surplus? Whatis the profit after fixed costs? (c) Will new firms enter the market if demand stays the same and new firmsface the same demand and have the same costs? (d) In general, what is the long run profit of an average firm in a monopolistically competitive market.Table 2 below represents the payoff matrix for two firms, X and Y, who compete with each other. Payoffs are in millions of pounds (£) profit. Each firm may choose one of two strategies i.e. set a high price for its output or set a low price for its output. Neither firm knows what strategy the other will adopt. Table 2 11. Firm Y High Price Low Price Firm X High Price X-£7mn, Y-£7mn X=£1mn, Y=£15mn Low Price X-£15mn, Y-£1mn X=£4mn, Y=£4mn In the absence of collusion, which combination of strategies is most likely to occur? a) X sets a low price and Y sets a low price. b) X sets a high price and Y sets a low price. c) X sets a low price and Y sets a high price. d) X sets a high price and Y sets a high price.
- Billy Bob's is catering to Baruch College and there are two types of customers: faculty and students. There are 60 faculty members willing to pay $30 per meal while there are 500 students willing to pay $6 per meal. There are 560 meals available at the catering event. Suppose the total cost of catering the event, including the meals, is $1,000. How much profit will Billy Bob's earn if they can perfectly price discriminate? $800 O $2,000 $3,800 $4,8003) Assuming both firms behave as Bertrand duopolists, solve for p1 and p2. Show all work. Graph the reaction functions. Demand for firm 1’s product: Q1 = 160 – p1 +(1/2)p2 Demand for firm 2’s product: Q2 = 160 – p2 + (1/2)p1 And TC1 = 20Q1; TC2 = 20Q2B 20. Two-part tariff. A two-part tariff is another price-discrimination method where the producer of argood is able to capture the entire consumer surplus. An example of this might be an amusement park that charges a fee for entry (the tariff), and then charges the customer for each ride (by buying tickets). Let's investigate how a firm sets the optimal two-part tariff by assuming that we have 100 consumers each, with demand for rides of p=9-q, and the costs of running the amusement park are C(q)=100+q. (a) Uniform pricing. If the firm acts as a monopoly, setting a single price, what is its profit- maximizing price, quantity of rides (per person and aggregate), and profit? (b) Marginal cost pricing. If the firm sets its price per ride equal to marginal cost, what is the number of rides it will sell (per person and aggregate) and consumer surplus? (c) Two-part tariff. If the amusement park uses a two-part tariff, setting its entrance fee equal to consumer surplus while charging a price…