Bob and Ray are thinking of buying a sofa. Bob's utility function is Ug(S, MB) (1 + S) Mg and Ray's utility function is UR(S, MR) = (4 + S)MR, where S= 0 if they don't get the sofa and S = 1 if they do and where MB and MR are the amounts of money they have respectively to spend on their private consumptions. Bob has a total of $800 to spend on the sofa and other stuff. Ray has a total of $4,000 to spend on the sofa and other stuff. The maximum amount that they could pay for the sofa and still arrange to both be better off than without it is $1,200. $2,200. $650. $1,800. $1,000.
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- Suppose that Romeo in Problem 8 has the utility function U= S° RS2, and Juliet has the utility function U= S2RS5, where SRis Romeo's spaghetti consumption and Sj is Juliet's. They have 42 units of spaghetti to divide between them. Juliet would want to give Romeo some spaghetti if she has more than 28 a) units. Romeo would want to give Juliet some spaghetti if he has more than 26 units of spaghetti. C) Romeo and Juliet would never disagree about how to divide the spaghetti. d) Romeo would want to give Juliet some spaghetti if he had more than 21 units of spaghetti. Juliet would want to give Romeo some spaghetti if she has more than 30 units e) of spaghetti.Consider a town with a single street of 1 km long with 3,000 people spread uniformly along it. Two stores, 1 and 2, are located at the opposite ends of the street and sell the same product (store 1 is locatedattheleftend).Thecostofwalkingist1 =$6perkmtostore1andt2 =$9perkmtostore2for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is U1(x) = 100 – p1 – t1x, where pi is a price of the product at store i = 1,2. The net utility from buying at store 2 is U2(x) = 100 – p2 – t2(1 – x). The average cost of the product for each store is c = 4. (a) Assume that all consumers buy product from the sellers. Find the demand functions Di(p1,p2) and the profit functions πi(p1,p2) for each store i = 1,2 as functions of prices p1,p2.(b) Find the equilibrium prices.2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.
- Suppose that Bartolo and Emilio spend their incomes on two goods, food (F) and clothing (C). Bartolo's preferences are represented by the utility function: 16 15- U(F,C) 10FC 14- 13 while Emilio's preferences are represented by the utility function: U(F,C) 0.20F2C2 12 11 . 10- With food on the horizontal axis and clothing on the vertical axis, identify on a graph the set of points that give Bartolo the same level of utility as bundle (10,5). Do the same for Emilio. Then, identify the set of bundles that give Bartolo and Emilio the same level of utility as bundle (15,8) 8- 1.) Using the three-point curved line drawing tool, graph an indifference curve for Bartolo that includes bundle (10,5) and that also contains bundles with 4 and 5 units of food. Label the curve U 6- 2.) Using the three-point curved line drawing tool, do the same for Emilio including bundle (10,5) and bundles with 4 and 5 units of food. Label the curve U1 3.) Using the three-point curved line drawing tool, graph an…3. Christina loves pizza and hates burger. Her utility function is U(p – b) = p – 6", where is the number of pizzas she consumes and b is the number of burgers she consumes. John likes both pizza and burger. His utility function is U(p, b) = p + 2\b Christina has an initial endowment of no pizzas and 8 burgers. John has an initial endowment of 16 pizzas and 8 burgers. a. Graph the initial endowment and label it E b. If Christina hates burgers and John likes them, how many burgers can Christina and John be consuming at a Pareto optimal allocation? What is John's marginal utility for pizzas and burgers? Mark the locus of Pareto optimal allocations of pizzas and burgers between Christina and John on the grapsh above.At a different table, Juan wins $600 in a blackjack game. Similarly, he has to choose between $600 or the chance to play a new game. In this game, Juan has a 60% chance of winning nothing and a 40% of winning $1,000. The following graph presents the utility function of Juan with respect to money: U(w) U(w) U(1,000) U(700) U(600) U(400) 400 600 700 1,000 w 10.2.2 1.0 point possible (graded, results hidden) By how much money would his winnings need to increase or decrease so that Juan is indifferent between the $600 and the new game? (in case of an increase, insert a positive number; in case of a decrease, insert a negative number).
- Eric, Kenji, and Paolo are roommates who are trying to decide how much money each should contribute to a party they are throwing. • Paolo does not care about the party and is on a tight budget. Therefore, he prefers to contribute no money to the party, and his utility declines at a constant rate as the roommates increase the amount of money they spend. • Kenji would ideally contribute $15 because he only wants to buy pizza. However, he would prefer contributing $55 to contributing $0 and not having a party at all. • Eric wants to buy a $120 keg of beer and $45 worth of pizza. Therefore, he would ideally like each to contribute $55 to the party, but if the others are unwilling to contribute that much, he would settle for buying just the pizza (and contributing $15 each) and asking guests to bring beer. Suppose the three roommates vote on spending either $0, $15, or $55 on the party using the Borda count system of voting. That is, each roommate awards three points to his first choice,…Two roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn’t, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn’t, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.What is the Nash equilibrium of this game? Group of answer choices Joe cleans, John doesn’t John cleans, Joe doesn’t Both of them clean the apartment Neither of them clean the apartment4. Show how to construct the reference dependent utility function for two friends Kate and Mary whose gains and losses are listed as follows : Kate's net worth is $ 4.5 million ( decreased from $ 5.5 to $ 4.5 million ) Mary's net worth $ 3.2 million ( increased from $ 3 to $ 3.2 million ) ( First determine the reference point ( use a parameter ) and then derive reference utility function for each ) .
- Nicolaus I Bernoulli offers his friend Pierre Rémond de Montmort a game where they need to repeatedly toss a fair ducat until they get a head for the first time. The game stops then, and they count the number n of coin tosses it took to get the desired outcome, and Montmort gets 2^n ducats. Assume that Montmort's utility function is u(w)=w^0.14. How much should Montmort pay to play this game?2. Alex and Bill share a flat. Alex enjoys reading in silence, while Bill enjoys listening to loud music. Bill controls his music system, which can produce noise levels up to 100 Decibels. Bill has no cash but Alex has £100. Their utility functions are given by: UA = 10(100 – D)i + (100 – M), %3D Ug = 10(D)i + M, where D denotes the Decibel level chosen by Bill, and M denotes any cash given to Bill by Alex. (a) Explain how Bill's music level affects Alex. Find the contract curve between Alex and Bill. Why is there a unique Pareto efficient noise level? (b) What is the maximum amount Alex would be willing to pay Bill to turn down the music to the Pareto efficient level? What is the minimum amount Bill would be willing to accept in order to turn down the music to the Pareto efficient level? Can the Pareto efficient noise level be achieved through private bargaining?Every week since lockdown, Jack spends his entire budget to purchase 2 boxes of fried chicken and 3 cream puffs. Each box of fried chicken costs $8 and each cream puff costs $5. Suppose Jack's marginal utility from fried chicken is 12, and his marginal utility from cream puffs is also 12. What should Jack do if he wants to increase his utility? a) Increase fried chicken consumption and reduce cream puff consumption. b) Increase both cream puff and fried chicken consumption. c) Maintain current consumption. d) Increase cream puff consumption and reduce fried chicken consumption.