3. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house andmust decide how to allocate rooms X, Y and Z.An 'allocation' is where each housemate is assigned to exactly one room. For example,Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y).Utilities for each room are given below:Room XUtility for A7Utility for B9Utility for C 2Room Y437Room Z214 (d) Which of the Pareto optimal allocations maximise total surplus (utility) andwould all housemates weakly prefer this allocation over any other?(e) Suppose the housemates decide to allocate the rooms by randomly assigning RoomX to someone, Room Y to someone and Room Z to someone. Explain whether thisalways leads to an allocation which is Pareto optimal or maximises total surplus.(f) Suppose the housemates decide to allocate the rooms according to the 'randomserial dictatorship' rule studied in lectures.Explain what this rule is and whether in this case it always leads to an allocationwhich is Pareto optimal or maximises total surplus.

(d) To determine the Pareto optimal allocations that maximize total surplus, we need to find the…

imal allocations maximise total surplus (utility) and eakly prefer this allocation over any other? s decide to allocate the rooms by randomly assigning F o someone and Room Z to someone. Explain whether tion which is Pareto optimal or maximises total surplu s decide to allocate the rooms according to the 'rando

imal allocations maximise total surplus (utility) and eakly prefer this allocation over any other? s decide to allocate the rooms by randomly assigning F o someone and Room Z to someone. Explain whether tion which is Pareto optimal or maximises total surplu s decide to allocate the rooms according to the 'rando

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 6PA

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23. Anita (A), Ben (B) and Carlos (C) are housemates who have moved to a new house and must decide how to allocate rooms X, Y and Z. An 'allocation' is where each housemate is assigned to exactly one room. For example, Anita → Room Z, Ben → Room X and Carlos → Room Y is allocation (Z, X, Y). Utilities for each room are given below: Room X 7 9 2 Room Y 4 3 7 Room Z 2 1 4 Utility for A Utility for B Utility for C (a) How many possible allocations are there in total? (b) Identify the two allocations which are not Pareto optimal and explain why they are not Pareto optimal. (Hint: is the allocation (Y,Z) Pareto timal?) (c) Suppose we square Carlos' utility from each room (i.e. uc (Z) becomes 16). Would the set of Pareto optimal outcomes change? Why/why not? (d) Returning to the utilities from part (a), which of the Pareto optimal allocations maximise total surplus (utility) and would all housemates weakly prefer this allocation over any other? (e) Suppose the housemates decide to allocate…
Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. Find Alexi's income-consumption curve for slices of bread for incomes between $0 and $21, assuming a price of $1 per slice.
Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. In a graph, draw total utility as a function of number of toasted slices, assuming that Alexi buys 1 toaster.
5. Sheila and Bruce are taking a canoe trip. Sheila brought 10 boxes of peanuts (x) and 15 bags of chips (y). Sheila's utility function is U*(x,y) = lnvx*+ Invy°. Bruce also brought 20 boxes of peanuts and 5 bags of chips. Bruce's utility function is UB(x.y) = min[x', y'I. a) Illustrate the endowment point and draw a sample set of indifference curves through the endowment point. b) If Sheila and Bruce trade what will be the pattern of mutually beneficial trade? c) If the terms of trade are the number of bags of chips (y) per box of peanuts (x) then what is the largest value that these terms can be for a mutually beneficial trade in this economy? d) Find one mutually beneficial trade where the terms of trade are 1 bag of chips (y) per 2 boxes of peanuts (x). Suppose that Sheila and Bruce set up two competitive markets for peanuts and chips. Below you will show that if the price of peanuts (x) is $1 and the price of chips (y) is $2 then the markets for both peanuts and chips will clear.…
Kip is trying to decide whether to take a one-day martial arts class at Rex Kwan Do. The fee for the class is $400. Kip will also have to pay his brother Napoleon $150 for that day in return for giving him a ride into town. Instead of taking the class Kip could spend all day on the computer chatting with his girl, LaFawnduh. This gives him a value of $300. On the other hand, he could spend all day working with his Uncle Rico and making sweet moolah. Uncle Rico has promised to pay him $350 on that day if he works with him. What is Kip’s marginal cost of joining Rex Kwan Do? Group of answer choices $650 $550 $400 $300 $350 $150 $900
Suppose that there are three beachfront parcels of land available for sale in Astoria, and six people who would each like to purchase one parcel. Assume that the parcels are essentially identical and that the selling price of each is $745,000. The following table states each person's willingness and ability to purchase a parcel. Willingness and Ability to Purchase (Dollars) Alyssa 720,000 Brian 690,000 Crystal 680,000 Nick 900,000 Rosa 810,000 Tim 770,000 Which of these people will buy one of the three beachfront parcels? Check all that apply. Alyssa Brian Crystal Nick Rosa Tim Assume that the three beachfront parcels are sold to the people you indicated in the previous section. Suppose that a few days after the last of those beachfront parcels is sold, another essentially identical beachfront parcel becomes available for sale at a price of $732,500. This fourth parcel _____________be sold…
Anthony, Edward, and Gavin are roommates and are deciding which item to add to their apartment. They each suggest a first choice and then vote on the options. Their first choice, second choice, and third choice preferences are as shown in the following table: 1st Choice 2nd Choice 3rd Choice Antony 50" TV PS4 New Couch Edward PS4 New Couch 50" TV Gavin New Couch Vד י50 PS4 Based on the table, complete the sentence below: The roommates will vote PS4 over a New Couch by| [ Select ] and a New Couch over a 50" TV by [ Select ] . If PS4 is preferred to a [ Select ] V and a [ Select ] is preferred to [ Select ] it might seem that it must be true that the [ Select ] V is the favorite. But in a vote of a a [ Select ] versus a PS4, the [ Select] v wins by 2-1 vote. Hence, when a [ Select ] occurs, choosing a single favorite that is always preferred by a majority becomes [ Select ]
Kip is trying to decide whether to take a one-day martial arts class at Rex Kwan Do. The fee for the class is $400. Kip will also have to pay his brother Napoleon $150 for that day in return for giving him a ride into town. Instead of taking the class, Kip could spend all day on the computer chatting with his girl, LaFawnduh. This gives him a value of $300. On the other hand, he could spend all day working with his Uncle Rico and making sweet moolah. Uncle Rico has promised to pay him $350 on that day if he works with him. What is Kip’s marginal cost of joining Rex Kwan Do? Correct answer: $900 why don't you include 300 also? explanation
John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?
Question 2 Kofi's utility function is given by U« (X,Y) = XY . The utility functions of his four friends - Esi (UE) John (U), George (Uc) and Osei (Uo) are: a. UE(X,Y) = 100XY b. U;(X,Y) = –XY c. Uc(X,Y) = XY – 10,000 d. U.(X,Y) = X – Y Which of these friends have the same preference as Kofi.
2. Two players have to divide a perfectly divisible cake of size 2. Half of the cake is made of chocolate, while the other half is made of marzipan. If a piece of cake contains a units of chocolate cake and y units of marzipan, player 1 gets utility U(x, y) = x + y, from this piece, while player 2 gets utility V(x, y) = 2x+y, from this piece. That is, player 1 cares only about the total size of the piece, while player 2 is values chocolate twice as much as marzipan. The players use the divide-and-choose protocol one player divides the cake into two, and the other chooses one of the two pieces. More precisely, the divider splits the cake into two pieces (x, y) and (1-x,1- y) (where 0≤x≤ 1 and 0 ≤ y ≤ 1. The chooser may choose either the piece (x, y) or the piece (1-2, 1-y). a) Use backwards induction to prove (or argue for) the the following claim: "In any subgame perfect equilibrium, the chooser is indifferent between the two pieces." Solve by backwards induction, for the subgame…
Julia and Ralph need to decide which one of them will take time off from work to complete the rather urgent task of pruning their trees. Julia is pretty good with a pole saw; she can prune the trees in 1 hour. Ralph is somewhat slow; it takes him 6 hours to prune the trees. Julia earns $120 per hour as a business consultant, while Ralph earns $15 per hour as a lifeguard.Keeping in mind that either Julia or Ralph must take time off from work to prune the trees, who has the lowest opportunity cost of completing the task?