3. Suppose there are two firms competing in a market. Both firms have the cost function c(x) =10x/2 while the demand function is given by x(p) = 100 – 0.1p. a. Find the profit maximizing quantity and price if the firms are playing a pricing game.

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Question 3:Suppose the inverse demand for a good is given by P = 50 – 4Q, where Q is the totalquantity supplied by all firms in the market. Suppose each firm in the market has a constantmarginal cost of 18.Q3 a) Assume the market consists of two firms that set their quantities simultaneously.Calculate the duopoly levels of production and the equilibrium price. Q3 b) Now assume firm 1 chooses its production level before firm 2 does. What will be theequilibrium quantities, price and profits in this case?Q3 c) Now instead suppose that the two firms compete over prices rather than quantities.What will be the equilibrium price and profits of firms 1 and 2 in this case? Finally, if firm 1manages to lower its marginal cost to 14, what will be the new equilibrium price, quantitiesand profits?

Consider the Bertrand pricing game from class. If both firms have identical marginal cost of $10 and consumers will purchase from whichever firm is cheapest as long as the price is under $50, what will be the Nash equilibrium? A B C D 50, 50 50, 10 10, 10 10,50

Consider the following static game with two firms as the players. Each firm must decide either to upgrade (U) an existing good to a new version; or not upgrade it (N). The decisions are simultaneous. If a firm chooses to upgrade, they have to pay a fixed cost of 7. If they don’t upgrade, there is no fixed cost. The marginal cost is always equal to 3. The demand side of the market is as follows: If neither firm upgrades, each firm sells 2 units at price 4. If both firms upgrade, each firm sells 3 units at price 5. If only one firm upgrades, the one who upgrades sells 5 units at price 5, and the other firm does not sell anything.

Consider an industry with two identical firms (denoted firm 1 and 2) producing a homogenous good. Firms compete in quantities. Firm 1 has a constant marginal cost of 20. Firm 2 has a constant marginal cost of 80. Demand in the industry is given by D(p) = 380 - p. Let q1 and 92 denote the quantities of firm 1 and 2, respectively. Derive the Nash equilibrium in quantities. What is the total production in this industry?

2.   Four firms (A, B, C, and D) play a pricing game (i.e. Bertrand).  Each firm (i) may choose any price Pi from 0 to ¥, with the goal of maximizing its own profit. Firms A and B have MC = 10, while firms C and D have MC = 20.  The firms serve a market with the demand curve Q = 100 – P.  All firms produce exactly the same product, so consumers purchase only from the firm with the lowest price.  If multiple firms have the same low price, consumers divide their quantities evenly among the low-priced firms. Assume the firms choose price simultaneously.   a. There are many equilibria in this simultaneous-move pricing game. Provide one equilibrium combination of prices, and argue that no firm has a unilateral incentive to deviate from these prices.   Now assume firm A chooses price first. Firm B observes this choice and then chooses its own price second. Firm C chooses price third, and firm D chooses price last. b. Again, there are many equilibria in this sequential-move pricing game.…

Consider a town in which only two residents, Eric and Ginny, own wells that produce water safe for drinking. Eric and Ginny can pump and sell as much water as they want at no cost. For them, total revenue equals profit. The following table shows the town's demand schedule for water. Note: the second picture of the last blank has 4 option A. nash equilibrium B tying c resale price maintenance D predatory pricing

Imagine a small town with three car repair shops competing for a limited number of customers. Explain why the three shops working together to keep their prices high is unlikely to be a Nash equilibrium.

I need help with c and d