The French autoroute network is composed of toll motorways with entrances marked as such. A motorist entering the network obtains a ticket from a toll booth and pays a toll when leaving the motorway. Given the number of vehicles traveling these routes, congestion at both entrances and exits is common. Suppose that four groups, each of 50 motorists, use an autoroute. The price each group is willing to pay, v, differs among groups and falls as the amount of congestion, c, increases in the following way: vij = vi max-cj; i, j = 0,..., 3, where vi max = 0.4-0.1 * i euros per kilometer is the maximum group i is willing to pay to use the motorway and cj = 0.06 * j euros per kilometer is the loss in value as more groups use it. The marginal cost of using the autoroute, not including the marginal cost of congestion, is zero. a. If the toll charged for using the autoroute equals a motorist's marginal private cost-the price in a competitive market-how many vehicles per minute will use it? Which groups will use it? b. In the social optimum, which groups of drivers will use the autoroute? That is, which collection of groups using it will maximize the sum of the motorists' utilities?

The French autoroute network is composed of toll motorways with entrances marked as such. A motorist entering the network obtains a ticket from a toll booth and pays a toll when leaving the motorway. Given the number of vehicles traveling these routes, congestion at both entrances and exits is common. Suppose that four groups, each of 50 motorists, use an autoroute. The price each group is willing to pay, v, differs among groups and falls as the amount of congestion, c, increases in the following way: vij = vi max-cj; i, j = 0,..., 3, where vi max = 0.4-0.1 * i euros per kilometer is the maximum group i is willing to pay to use the motorway and cj = 0.06 * j euros per kilometer is the loss in value as more groups use it. The marginal cost of using the autoroute, not including the marginal cost of congestion, is zero. a. If the toll charged for using the autoroute equals a motorist's marginal private cost-the price in a competitive market-how many vehicles per minute will use it? Which groups will use it? b. In the social optimum, which groups of drivers will use the autoroute? That is, which collection of groups using it will maximize the sum of the motorists' utilities?

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 6PA

See similar textbooks

Similar questions

Suppose that there were two competing types of high-definition DVD players, Greenbeam and Mosdef. Greenbeam enjoyed an initial advantage in the market for high-definition DVD players because there were more motion-picture production companies offering movies compatible with its system. Which of the following is an illustration of a network externality? Mosdef benefited from more consumers buying Greenbeam DVD players. O Consumers bought Mosdef players in increasing numbers, while Greenbeam lost market share and eventually went out of business. Consumers bought Greenbeam players in increasing numbers, while Mosdef lost market share and eventually went out of business. More production companies adopted the Mosdef format for their movies because the Mosdef player had the superior format, despite the fact that more consumers purchased Greenbeam players.
The magazine Science 84 planned to announce a contest in which anyonecould submit a request for either $20 or $100. If fewer than 20% of the submissions requested $100, then everybody would receive what they requested. If 20% or more asked for $100, then everybody would get nothing. Although the magazine wound up not running the contest, because Lloyds of London was unwilling to insure against losses, we can still analyze what equilibrium would predict. Suppose 100,000 people might participate in the contest, and assume that payoffs are measured in money.a. Assume that every possible participant submits a request for either $20or $100. Find a Nash equilibrium.b. Now suppose that a request form comes only with the purchase of Science 84 and that the magazine costs $21.95. Then each person’s strategy set has three elements: do not buy the magazine, buy the magazine and submit a request for $20, and buy the magazine andsubmit a request for $100. Suppose zero value is attached to…
In game theory, a dominant strategy is the best strategy to pick, no matter which moves are chosen by the other player. O to make the exact same move that was made by the other player. the choice that causes the payoff for the other player to be minimized, regardless of the payoff it earns the best strategy to pick, assuming the other player makes his or her best possible choice. to allocate all personnel resources towards defensive talent in order to dominate opposing offenses. 46°F
Monopoly: End of Chapter Problem 5. Firms use price discrimination to increase their profits by converting part or all of consumer surplus to producer surplus. Which of the following market conditions is not necessary for a firm to engage in price discrimination? O A firm must have the ability to prevent arbitrage. A firm must have the ability to separate consumers intoigroups based on their elasticities of demand. O A firm must have the ability to hide their prices from consumers. A firm must have some market power. Publisher: Worth Publishers 7:41 PM Question Source: Chiang 4e - Economics Principles For A Changing World 39°F A O 1 a I E 4) 23 12/12/2021 a
Exercise 6.1Suppose that two airlines decide to collude. Analyse the game between these two companies. Suppose that each of them can charge for tickets a high price or a low price. If one of them charges 100 euros, it gets few profits if the other also charges 100 euros and high profits if the other charges 200 euros. On the other hand, if the company charges 200 euros, it obtains very little profit if the other charges 100 euros and an average profit if the other also charges 200 euros. a) Represent the matrix of results of this game. b) What is the Nash equilibrium in this game? Explain your answer. c) Is there an outcome that would be better than the Nash equilibrium for the two airlines? How could it be achieved? Who would lose out if it were reached?
in the sample imit pricing model, the entrant moves first to choose to Enter the market or Stay Out. Once the entrant moves, the incumbent fem choose to Fight or Share, If the entrant choose to stay out, the entrant receives zero profit while the incumbent ears the monopoly prett. Suppose when the incumbent and the entrant Fight, they compete in Bertrand style and when the incumbent Share the market, the firms compete in Cournot style. Complete the following game by fill in the associated payoffs at the end nodes and solve the game using the backward induction (e. find the equilibrium path. Assume both the entrant and incumbent have the same marginal cost of 2 and the inverse demand is P-14-Q Incumbent: Share Enter Fight Entrant Stay Out If Entrant enters and Incumbent shares, the payoff for the Entrant is If Entrant enters and Incumbent fights, the payoff for the Entrant is If the Entrant stays out, the payoff for the Entrant is At equilibrium, Entrant will choose and the payoft for…
Suppose you run a marketing survey and find you have two types of customers high-value customers willing to pay 16 and low-va consumers willing to pay just 10. Your survey tells you that there are equal numbers of high- and low- value customers. Obviously , have two possible options price high (16) and sell only to the high value group, or price low (10) and sell to everyoneThe costs incurred is 5 per unit and sales only happen to high -value consumers 50 % of the timeWhich price should you choose ? Select the correct response price high price low it depends price both high and low
N=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…
Suppose that there are two competing types of high-definition DVD players, Greenbeam and Mosdef, and each uses a different format. The DVD players are subject to network externalities: the more people who use one type of player, the more production companies adopt that particular format for their movies, and the greater the value of that player to each user. Greenbeam and Mosdef entered the market at around the same time. Which of the following is likely to happen if Greenbeam sells its DVD players at its profit-maximizing price, but Mosdef sells its DVD players at a much lower price than Greenbeam's at the early stages? 1 O Mosdef will dominate the market for high-definition DVD players. O Greenbeam will dominate the market for high-definition DVD players. O Greenbeam and Mosdef will have equal market shares. O Neither Greenbeam nor Mosdef will succeed, and a new company could easily enter and dominate the market. Tr
AT&T and Verizon have two pricing strategies: Set a high (monopoly) price or set a low (competitive) price. Suppose that if they both set a competitive price, economic profit for both is zero. If both set a monopoly price, AT&T makes an economic profit of $100 million and Verizon makes an economic profit of $200 million. If AT&T sets a low price and Verizon sets a high price, AT&T makes an economic profit of $200 mil- lion and Verizon incurs an economic loss of $100 million; if AT&T sets a high price and Verizon sets a low price, AT&T incurs an economic loss of $50 million and Verizon makes an economic profit of $250 million. Create the payoff matrix for this game. What is the equilibrium of this game? Is the equilibrium efficient?
Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?
Suppose we have 5 people who might attend up to 2 theatre shows at the local theatre. There’s a drama and a comedy. The marginal cost of a seat on any given night is both constant and negligible (you can safely ignore it), so profit maximization and revenue maximization amount to the same thing. Below are the maximum willingness to pay values (a person will pay a price up to that value, but no greater) for a seat for each of the 5 people for the two shows. The theatre is a profit-maximizing firm. What individual ticket price (i.e., the price for anybody attending the show would be the same, but it could be different across shows) would separately maximize profit for each show?