QUESTION 9 In the Bertrand model, suppose that each firm has a marginal cost of £10 and that firm 1 sets a price of £9.99 , which of the following a best-response for firm 2? Click all the correct answers. O £9.99 O £10.01 O £11.01 O £10.00 O £9.98
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- a) Derive a bid-rent function for a "typical" firm. Draw a graph of the bid-rent function that is clearly labeled, including any intercepts or slopes.b) For a typical city, discuss what types of firms you are likely to see closest to downtown, and what types of firms you are likely to see further away. Do these firm locationsfit the model? Why or why not?c) Are these firms likely to change locations after covid? Why or why not?.COURSE: MICROECONOMICS - Stackelberg ModelIn a given market good there are only 2 firms that satisfy the demand, and their respective total cost functions are: CTi = 400 and the demand that is estimated is P = 120 - 2QIf the exception variable of both firms is the quantity they will produce, such that the decisions to produce are made sequentially firm number 1 will be the leader who decides the quantity to produce and firm number 2 (follower) decides based on the production of firm number 1, we ask:(a) quantity produced by each firm and its equilibrium price in the market.(b) Profit of each company at equilibrium and (c) Graph your resultsThree firms compete in the style of Cournot. All firms have a constant returns to scale technology: There are no fixed cost and each firm's marginal cost is constant. The market demand is given by Q(P) = 9 - P. Firm 1's marginal cost is MC1 = 1, firm 2's marginal cost is MC2 = 2. Let MC3 be the marginal cost of Firm 3. Which of the below is a necessary condition so that q > 0 for all three firms in a Nash equilibrium? a. MC3 < 1 b. MC3 < 4 c. MC3 < 3 d. MC3 > 1 e. MC3 < 2
- Suppose two Bertrand competitors, F1 and F2, make identical products for a market with inverse demand P = 600 – 0.5Q. Both firms have the same costs Ci = 20qi, and each firm has sufficient capacity to supply the entire market. a. What prices will the firms choose? How much might each produce and what profit would they make? Is the result a Nash equilibrium? Explain. b. Suppose F1 improves its efficiency, reducing its cost to C1 = 16q1. What will happen in this market? Explain. c. Assume now that the firms have their original identical costs, but that F1 has only 100 units of capacity and F2 has only 200 units of capacity. What prices will the firms choose now? Explain why neither firm will want to decrease its price at the equilibrium you identify. Why would neither firm want to increase its price? Prove this for F1.4. You are the manager of a firm that produces products X and Y at zero cost. Youknow that different types of consumers value your two products differently, but you are unable toidentify these consumers individually at the time of the sale. In particular, you know there arethree types of consumers (100 of each type) with the following valuations for the two products: Consumer Type Product X Product Y1 $90 $ 602 $70 $1403 $40 $160 a. What are your profits if you charge $40 for product X and $60 for product Y?b. What are your profits if you charge $90 for product X and $160 for product Y?c. What are your profits if you charge $150 for a bundle containing one unit of product X andone unit of product Y?d. What are your profits if you charge $210 for a bundle containing one unit of X and one unit ofY, but also sell the…V5. You are the manager of Taurus Technologies, and your sole competitor is Spider Technologies. The two firms' products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P =290 - 3Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $500, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.) What are your profits if you do not make investment? What are your profits if you do make investment? Instructions: Do not include the investment of $500 as part of your profit calculation. Should you invest the $500? no or yes
- consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7We now consider a duopoly model where the firms offer products with different qualitiesand consumers differ from each other in how much they care for quality. Suppose the firms offer their products with quality si ∈ [0, 1] and consumers’ ‘location’ in terms ofhow much they care about quality is given by a parameter θ ∈ [0, 1] and consumers are uniformlydistributed over this interval. Suppose the firms first choose their quality s1 and s2 and then setprices p1 and p2. A consumer of type θ derives utilityvi = r − pi + θsifrom consuming a unit from firm i and where reservation price r is high enough that everyonepurchases from one of the two firms. Suppose the marginal cost of producing increases with quality.There are no fixed costs and the total variable cost isC(qi, si) = csiqiso that marginal cost is csi and increases with quality. Further, let c = 1 so marginal cost is siConsider the second stage where given a choice of qualities s1 and s2 with s1 < s2, the firmssimultaneously…Two firms with the same (constant) marginal costs are engaging in Bertrand competition. One of the companies exits the industry. As a aconsequence, the price for the other firm increases by 50%. What is the elasticity of demand in this market?O. 3O. 2O. 2.5O. 4
- The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P. (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)Please no written by hand 1. Suppose the automobile manufacturing industry has two firms, General Motors and Ford. Assume that the market demand function is Q = 1,000 − p, and each firm’s marginal cost and average cost are $40. a. What is the marginal revenue for General Motors? Assume, ??? represent residual demand for General Motors and ?? represents residual demand for Ford. b. What is the best response function for General Motors and Ford? c. What is the Nash-Cournot equilibrium in this market? d. Graph the best response curves for both General Motors and Ford, placing the quantity produced by General Motors (???) in the x-axis. Label intercepts and Nash-Cournot equilibrium.The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a purely competitive firm that produces novelty ear buds. Assume the market for novelty ear buds is a competitive market and that the price of ear buds is $6.00 per pair. Quantity of Ear Buds MC ($) ATC ($) 10 - 5.00 15 2.00 4.00 20 2.44 3.61 25 3.56 3.60 30 4.02 3.67 35 5.49 3.93 40 5.93 4.18 45 8.59 4.67 Instructions: In part a, enter your answer as the closest given whole number. In parts b–d, round your answers to two decimal places. a. If Buddies wants to maximize profits, how many pairs of ear buds should it produce each week? _ pairs b. At the profit-maximizing quantity, what is the total cost of producing ear buds? $ _ c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what will Buddies profit or loss be per week? $ _ d. Now assume the market price is $5.50 per…
