A particular road is used by N drivers each day. Each driver obtains a benefit v from the journey and incurs a cost c(N) that increases with the number of drivers on the road due to congestion. Suppose that the cost incurred is given by c(N) a + bN, for some positive numbers a, b. If the agent decides not to use the road, they receive 0. You may assume throughout that the number of drivers N can be any real number (rather than an integer). Each driver uses the road at most once. (ii) Show that the number of drivers that join the road is V - a Ne =
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- Studying has both costs and benefits. If you continue tostudy (e.g., for a test) for as long as the marginal benefitsof studying are greater than the marginal costs, and youstop studying when the two are equal, will your actionbe consistent with having maximized the net benefits ofstudying? Explain your answer.Suppose total benefits and total costs are given by B(Y) = 150Y − 6Y2. Then marginal benefits are options: 150Y - 6. 150 − 12Y. 150 - 3Y. 6Y.Karen goes to the casino with 1000$ and plays the following strategy: In her first game, she putsin 1$. If she wins, she finishes playing and takes her profit home. If she looses a game, she willplay another game and put in twice as much money as she did in the previous game. If she wins,she will finish playing and take her profits home. She will keep going with that strategy, untilshe either wins a game or runs out of money.(a) Create a table for n = 1, 2, ..., 10 which lists: (a) The amount of money she puts in in game n;(b) the sum of the amount of money she has put in in all games up to this game n; and (c)her overall profit if the game n is the first game she wins.(b) What is the likelihood of her loosing 8 games in a row?(c) How many games can she loose in a row before she cannot afford to continue with herstrategy of doubling her bet?(d) Given the low likelihood of loosing, is this a smart strategy for Karen to pursue?
- Kayla and Kevin are friends who go together to a used textbook seller who has two copies ofthe biology book that they both need for their class this semester. The cost to the seller ofacquiring the books was $25 each and no other students will need this book. Kayla states thatshe is willing to pay $40 for the book, while Kevin says he is willing to pay $80. Which ofthe following describes the most likely conclusion to this scenario? Group of answer choices The seller will sell the books to both Kayla and Kevin for $40 each because if they tried tocharge Kevin a higher price, Kayla would engage in arbitrage. The seller will sell one book to Kayla for $40 and one book to Kevin for $80 because thismarket meets all three requirements for price discrimination. The seller will sell the books to both Kayla and Kevin for $80 each because Kevin's highervalue exceeds Kayla's willingness to pay. The seller will sell the books to both Kayla and Kevin for $25 each because that is howmuch the…Suppose that an incumbent can commit to producing a large quantity of outputbefore the potential entrant decides whether to enter. So, the incumbent Örst chooseswhether to produce a small quantity or a large quantity. The rival then decides whether toenter. If the incumbent commits to the small output level and if the rival does not enter,the rival makes $0 and the incumbent makes $900. If it does enter, the rival makes $125and the incumbent earns $450. If the incumbent commits to producing the large quantity,and the potential entrant stays out of the market, the potential entrant makes $0 and theincumbent makes $800. If the rival enters, the best the entrant can make is $0, the sameamount it would earn if it didnít enter, but the incumbent earns only $400. Show the gametree. What is the SPNE?Q2. Preferences and utilityLet's assume that country A prefers not to make additional concessions (outcome C1) to country B than granting those concessions (outcome C2), but a continued war (outcome C3) would be worse than making the additional concessions (C2). The following utility function over the outcomes specifies the intensity of preferences for country A over the outcomes: u(C1) = 1, u(C2) = 0.3, and u(C3) = 0. Country A can choose to refuse concessions (action A1) or allow concessions (action A2). The outcome that will occur is a function of the "type" of country B's leader.If country A refuses concession (A1), country B will not initiate a war (outcome C1) if country B's leader is amicable, while it will enter a war (outcome C3) if the leader is belligerent. There is a probability p(S1) = 0.6 that country B's leader is amicable and a probability p(S2) = 0.4 that country he's belligerent. If country A allows concession (A2), both in case of country A is amicable p(S1) and…
- . Profit The revenue from sales of x units of a productis given by R(x) = 200x - 0.01x2, and the cost ofproducing and selling the product can be describedby C(x) = 38x + 0.01x2 + 16,000.a. Producing and selling how many units will givemaximum profit?b. What is the maximum possible profit from producing and selling the product?Suppose two parents present their 16-year-oldwith a list of the cars that they will allow him tobuy. If the parents decide to add another vehicle tothe list, is that affecting the choice architecture fortheir son? Why or why not?Problem 4 A person has been mugged in the street by a thief, and there are n witnesses. All of the witnesses prefer someone else to chase the thief but none of them want to be the person trying to catch her. Each person gets 0 utility if the crime goes unreported, v if the crime is reported by someone else, and v −c if they report the crime. Moreover, we assume that the cost of chasing the thief is less than the utility of catching the thief: c < v. a. Define the strategic game described above. b. Find players’ best responses. c. Find the Nash equilibria of the game.
- Consider a small town with two competing restaurants: Doug’s Diner and Betty’s Bistro. There is 1000profit to be made in the market. Each period, the restaurants simultaneously decide whether to offer high orlow quality food. In order to offer high quality food, each restaurant must hire an expert chef, which incursan additional cost of 100. The restaurants split the profit equally if they offer the same quality of food. Ifone restaurant offers high quality food while the other offers low quality food, the high quality restauranttakes four fifths of the profit and the low quality restaurant takes one fifth of the profit.(a) Draw up the normal form game matrix, showing the players, strategies, and payoffs.(b) Determine the Nash equilibrium of this game.(c) Explain how the restaurant owners could both be better off than in the Nash equilibrium if they wereable to cooperate. Is the town as a whole better off or worse off when the firms cooperate? Why or whynotA law is passed providing for compulsory vaccination and subjects a person toimprisonment for refusing to submit vaccination, except when it is apparent or it canbe shown that the person is not fit for vaccination because of his physical condition. Isthe law valid?Ali Receives Utility From (D)omestic Vaccines from Kayseri, and the Sinovac Vaccine-(F)oreign. The utility structure is U(D,F)=D x F. The price of the foreign vaccine because of increasing returns to scale is $200, whereas at its earlier stages, the domestic vaccine is produced at a higher cost, and higher price of $250. The government has given each and every citizen a fixed payment of $8000 to spend just on vaccines, but it has not specified which vaccines. a- Does Ali Solve the Utility Maximization Question in an interior equilibrium or a corner solution? How do you know? What condition does the interior equilibrium necessitate regardless. b- Find Ali's Utility Maximizing Level of Domestic and Foreign Vaccines when he uses just the government allowance on vaccines? What is his utility level? C- Suppose the government wants to decrease Turkey's health exports. It pushes a vaccine subsidy, just for domestic vaccines that makes the price of domestic equal to $160. How does the utility…