Two firms produce and sell differentiated products that are substitutes for each other. Their demand curves are Firm 1: Q₁ = 40-3P₁+ P2 Firm 2: Q₂ = 40-3P 2+ P₁ Both firms have constant marginal costs of $2.30 per unit. Both firms set their own price and take their competitor's price as fixed. Use the Nash equilibrium concept to determine the equilibrium set of prices. In um noch firm will produce unito of output (50 d to tuo donimo
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- Two competing firms must choose their quantity of production simultaneously. Each firm can choose either a High quantity of 3 or a Low quantity of 2. The price for both firms is 9-Q, where Q is the sum of both their quantities. Costs are zero; the profit is simply price times quantity. For example, if firm 1 chooses High and firm 2 chooses Low, then price is 9-(3+2)=4; payoff for firm 1 is 12 while payoff for firm 2 is 8. What is the unique Nash equilibrium? (Firm 1's strategy will be written before firm 2's.)Suppose that Flashfry and Warmbreeze are the only two firms in a hypothetical market that produce and sell air fryers. The following payoff matrix gives profit scenarios for each company (in millions of dollars), depending on whether it chooses to set a high or low price for fryers. Warmbreeze Pricing High Low Flashfry Pricing High 11, 11 2, 15 Low 15, 2 8, 8 For example, the lower-left cell shows that if Flashfry prices low and Warmbreeze prices high, Flashfry will earn a profit of $15 million, and Warmbreeze will earn a profit of $2 million. Assume this is a simultaneous game and that Flashfry and Warmbreeze are both profit-maximizing firms. If Flashfry prices high, Warmbreeze will make more profit if it chooses a price, and if Flashfry prices low, Warmbreeze will make more profit if it chooses a price. If Warmbreeze prices high, Flashfry will make more profit if it chooses a price, and if Warmbreeze prices low, Flashfry will make more profit if…Using a payoff matrix/table to determine the equilibrium outcome Suppose there are only two firms that sell smartphones, Flashfone and Pictech. The following payoff matrix/table shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its phones. Pictech Pricing High Low Flashfone Pricing High 10, 10 4, 12 Low 12, 4 9, 9 For example, the lower left cell shows that if Flashfone prices low and Pictech prices high, Flashfone will earn a profit of $12 million and Pictech will earn a profit of $4 million. Assume this is a simultaneous game and that Flashfone and Pictech are both profit-maximizing firms. If Flashfone prices high, Pictech will make more profit if it chooses a price, and if Flashfone prices low, Pictech will make more profit if it chooses a price. If Pictech prices high, Flashfone will make more profit if it chooses a price, and if Pictech prices low, Flashfone will make…
- Consider a market organized along a 1 mile stretch of road (from D=0 to D=1). Consumers along the stretch of road are uniformly distributed. There are two firms, with Firm 1 located at mile marker .5 and Firm 2 located at mile marker 1.0 and they compete on prices. Customers choose which store to shop at according to P + cD, where c=2 and D is the distance to the store. What is the Nash Equilibrium?Two duopolists are sharing a market in which they are contemplating whether to compete or to cooperate. If they cooperate and behave like a monopolist they will share the monopolist profit of $1800. If they compete each will get a profit of $800 but if one them cooperates while the other chooses to compete the one who cooperates gets $700 while the one who competes will end up with $1000. Set-up the game, explain the process and show the Nash-equilibrium reached when the game is played.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.
- Suppose that two clothing manufacturers, Lands’ End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands’ Ends Profit, LL Bean’s Profit) is attached in the payoff matrix below: a.) What is the Nash equilibrium and expected profits to LL Bean and Lands’ End of this game? b.) Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a priceof $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a1/3 chance of choosing each strategy. What’s the expected payoff to LL Bean? c.) Suppose that in hopes of raising…Jane and Sara are competing orange juice salespersons in Amherst. Their stands are next to each other on a street and consumers regard them as identical. The marginal cost of an orange juice is $1. The demand for orange juice every hour is Q = 20 − P where P is the lowest price between the two salespersons. If their prices are equal they split demand equally. a. If they set prices simultaneously (prices can be any real number), what is the Nash equilibrium price? b. If, against what we have assumed in class, orange juice salespersons have to charge prices in whole dollars ($1, $2, $3, etc), what are the Nash equilibrium prices? c. Assuming whole dollar pricing, if Jane sets her price before Sara, what price would she charge? Answer all 3 partsConsider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.
- Consider two firms that produce the same good and compete setting quantities. The firms face a linear demand curve given by P (Q) = 1 − Q, where the Q is the total quantity offered by the firms. The cost function for each of the firms is c(qi) = cqi, where 0 < c < 1 and qi is the quantity offered by the firm i = 1,2. Find the Nash equilibrium output choices of the firms, as well as the total output and the price, and calculate the output and the welfare loss compared to the competitive outcome. How would the answer change if the firms compete setting prices? What can we conclude about the relationship between competition and the number of firms?Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each…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.