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Explain why the equilibrium of the Bertrand model is a Nash equilibrium.

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- You are a medical group manager. Some market research has suggested that the price elasticity of demand for the services of your physicians is −4.1. The marginal cost for the average unit of physician service in your group is approximately $536. A. Using the economic pricing model formula, calculate your profit-maximizing price for each unit of physician services. B. Suppose that your medical group is considering new contracts with two particular businesses to provide physician services to their employees. If the marginal cost for each service unit is the same as with the rest of your customers, but the price elasticity of demand from the first new business customers is −0.9, and the second group of business customers is −4.4, how would that change your profit-maximizing price for each of the new groups? Would you recommend that your medical group obtain contracts with both new groups, just one of them or none? Explain your reasoning. C. In order to maximize your profits, what specific…Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by P(Q) = ( 300 − Q, if Q < 300) (0, otherwise), where Q = q1 + q2. Firm 1 has a cost function C1(q1) = 40q1, and firm 2 has a cost function C2(q2) = 50q2. Answer the following questions. 1. Assume the game lasts only one period. Compute the equilibrium price, quantities and profits for both firms. 2. If firm 1 becomes the monopolist on this market, what quantities will firm 1 choose to produce? Denote this quantity as QM. 3. One possible strategy is that each firm produces QM 2 . Would the resulting outcome be better for both firms (Pareto improvement)? Explain why this is not the equilibrium in the one period game. 4. Assume this game is infinitely repeated and the interest rate in this economy is r. For what values of r the strategy in (3) is sustainable by using a “Grim Trigger” strategy?Textbook publishers hope to maximize profits. Authors, however, face very different incentives. Authors are typically paid royalties, which are a specific percentage of total revenue from the sale of a book. And so, for example, if an author's contract says that she will receive 20 percent of the revenues from the sale of a text and the publisher's total revenues are $100,000, the author's royalties will be $20,000. Who will prefer a higher price for the text, the publisher or the author or both prefer the same price?
- Two firms compete on price every year. The inverse demand function each firm faces depends on which firm has chosen the lowest price that year. The one that did captures the entire market. If, on the other hand, both prices are the same then they split the market evenly. Consumers round up prices to the nearest integer. For the firm with the lowest price p, demand is given by: q = 24-2p: Marginal costs are constant and equal to $4 for both firms. a. Define the Normal form of the stage game and determine the Nash Equilibria, the Cooperative Equilibrium and the Optimal Deviation from cooperation. b. For the once repeated (2 stages) game, determine if a Nash Equilibrium exists that improves on simply playing the (better) Nash Equilibrium of the stage game twice c. For the infinitely repeated game, determine what the interest rate would have to be to prevent the firms from cooperating. d*. Determine the relation between the interest rate and the number of punishment periods in a…Carl and Simon are two pumpkin growers who are the only sellers of pumpkins at the market. The demand function for pumpkins is Q = 16,400 – 400P, where Q is the total number of pumpkins that reach the market and P is the price of pumpkins. Suppose further that each farmer has a constant marginal cost of $1 for each pumpkin produced. Assume that Carl can tell, by looking at Simon's fields, how many pumpkins Simon planted and how many Simon will harvest in the fall. (Suppose that Simon will sell every pumpkin that he produces.) Therefore, Carl sees how many pumpkins Simon is actually going to sell this year. Carl has this information before he makes his own decision about how many to plant. If Simon plants enough pumpkins to yield Qs this year, then Carl knows that the profit maximising amount to produce this year is Qcarl = O 8,000 – Qs/2. O 16,400 – 400Qs. O 16,400 – 800Qs. O 4,000 – Qs/2. O 12,000 – Qs.Suppose two firms, A and B, have a cost function of ?(??) = 30??, for ? = ?, ?. The inverse demand for the market is given by ? = 120 − ?, where Q represents the total quantity in the market, ? = ?? + ??. 1. Solve for the firms’ outputs in a Nash Equilibrium of the Cournot Model. 2. Let Firm A be the first mover, and Firm B be the second mover. Solve for the firms’ outputs in a SPNE of the Stackelberg Model.
- A store estimates is customer inverse demand is P= 6.1 - 2.6Q, and the marginal cost of each rental is $0.48. If they use block pricing, what should the price be for the entire package?#2In the graph below we model the long-term rental market (i.e. contract of 6 months or more), assuming it is perfectly competitive. Let's try to model the impact that short-term rental platforms might have on this market. To do so, let's compare a market without such platform (before) and a market after the platforms have been introduced. In the figures, the vertical axis r is the price, while Q is the quantity of rental accommodation. Which figure best represents the introduction of short-term rental platforms? a) top-left b) top-right c) bottom-left d) bottom-right Their effect is to cause a) an increase b) a decrease or c) neither an increase nor a decrease in rental prices?and a) an increase b) a decrease or c) neither an increase nor a decrease in rental accommodation?
- Two firms, A and B, sell the same good X in a market with total demand Q = 100 – P. The two firms compete on quantities and decides how much to produce simultaneously. Firm A cost function is C(qA) = 40qA. Firm B cost function is C(qB) = 60qB. 1. Find the best reply functions of both firms and represent them in a graph. 2. Find the quantity produced by each firm in a Nash equilibrium. 3. Find the firms and consumers surplus. 4. Compare the surplus of firms found above with the surplus arising when both firm cooperate to sustain a monopoly outcome. 5. Assume now that A and B compete as in a Stackelberg model. A chooses first and B chooses after observing the choice of A. Find equilibrium quantities produced by each firm and the market equilibrium price.Walmart can be viewed as a first mover. Now suppose both Walmart and HEB are considering whether and how to enter a potential market. Market demand is given by the inverse demand function p= 900−q1−q2, where p is the market price margin, q1 is the quantity sold by Walmart and q2is the quantity sold by HEB. To enter the market, a retailer must build a store. Two types of stores can be built: Small and Large. A Small pantry store requires an investment of $50,000, and it allows the retailer to sell as many as 100 units of the goods at zero marginal cost. Alternatively, the retailer can pay $175,000 to construct a Large full-service supermarket that will allow it to sell any number of units at zero marginal cost. Assume Walmart stays out of the potential market (i.e.Walmart chooses not to enterN1at the first stage,q1= 0). Calculate HEB’s profit for the following cases: a.) HEB chooses not to enter N at the second stage after viewing Walmart’schoice. b.) HEB chooses to build a small…Does a market equilibrium exist in an oglipolistic market? If so, how is it determined?











