Suppose that 2 roommates, Andy and Bob, are trying to pick an apartment in Chicago. Locations can be chosen from set of alternatives A={ x: x exists [0,1]}. Andy and Bob both want to minimize their daily commute but they work at different locations: Andy at xA=0.3, while Bob at xB=0.6. Specifically, their utility functions are: ui(x)= -(x-xi)2. Question: What is the set of all Pareto Efficient outcomes in A, assuming no money can be exchanged
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Suppose that 2 roommates, Andy and Bob, are trying to pick an apartment in Chicago. Locations can be chosen from set of alternatives A={ x: x exists [0,1]}. Andy and Bob both want to minimize their daily commute but they work at different locations: Andy at xA=0.3, while Bob at xB=0.6. Specifically, their utility functions are: ui(x)= -(x-xi)2.
Question: What is the set of all Pareto Efficient outcomes in A, assuming no money can be exchanged.
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- You are considering going to a football game. However, the roads are cover in ice due to bad weather. Your ticket was a gift. You derive a value of z from attending the game, and a cost of D for driving on the icy roads. Your utility function is given by: ug(Z) + ui(D) = In(Z - 3) - In(2 - D). In your ultimate wisdom, you calculate that the cost of driving on the icy roads is 1 unit (So, D=1). What is the minimum value you must obtain from attending the game, so that you decide to go? Solution sent me fast ..Tom and Jerry are room mates. They spend a total of 80 hours a week together in their room. Tom likes loud music, even when he sleeps. His utility function is UT(CT, M) = CT + M, where CT is the number of cookies he eats per week and M is the number of hours of loud music per week that is played while he is in their room. Jerry hates all kinds of music. His utility function is M² 12 UJ = CJ Every week, Tom and Jerry each get 12 chocolate chip cookies sent from home. They have no other source of cookies. We can describe this situation with a box that looks like an Edgeworth box. The box has cookies on the horizontal axis and hours of music on the vertical axis. Let the bottom-left corner be the origin for Tom, and the bottom-right corner be the origin for Jerry. Suppose the dorm's policy is "rock-n-roll is good for the soul." Thus, M=80 in the initial endowment. Consider a trade between Tom and Jerry: Jerry gives Tom one cookie for reducing one hour of music. Then the change in Jerry's…Amy and Barbara share an office. They put a scent diffuser in the middle of the room, and they need to buy essence oil (G) to make the office smell good. They each can also buy cookies (x) as their own snacks. Each of them has $15 to spend on essence oil and cookies. Amy and Barbara's utility functions are UA (TA, GA, GB) = x²(G₁+G³)² and uB (TB, GA, GB) = x³ (GA+GB)³, where A and B are Amy's and Barbara's individual cookie consumption, and GA and GB are respectively Amy's and Barbara's contributions in dollars for the purchase of the essence oil. Let the price of cookies be p = 1 and the price of essence oil be pg = 1. Thus, given G₁ and GB, G = GA + GB is the total amount the essence oil that will be purchased, what is the Pareto optimal amount of the total contribution of G ? C a. 15 C b. 10 c. They will be no difference between the individual decision and the Pareto optimal decision. d. 5
- Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function u, (D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Martin's utility function is um(D,A)=D+4A. 1. Draw an Edgeworth box to show the initial endowments and the indifference curves (going through the initial endowments) for Joe and Martin. What are their utility levels from the initial endowments? 2. Calculate the marginal rates of substitution for Joe and Martin. Provide an economic interpretation. 3. Do the initial endowments represent a Pareto efficient allocation? Discuss. 4. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e.,…Joe and Martin, two roommates, have access to music in digital and analog formats. Each are initially endowed with 8 GB of high-resolution digital music and 4 vinyl LP's (analog) per month (there are a total of 16 GB's of music in digital and 8LP's in this case). Joe's preferences for music in digital and analog formats are represented by the utility function u,(D, A) = 2D + 2A, where D is the amount of digital music in GB's and A is the numberofLP's. Mạartin's utility function is um(D,A)=D+4A. 1. If Joe convinces Martin to exchange music at terms which would leave Martin at his initial utility level (i.e., without making him worse-off), what is the set of (D, A) that would make Joe better off. Show this on the Edgeworth box that you drew in part (a). What is the final allocation of music under these terms? What is the exchange rate (LP's per GB of digital music)? 2. On the Edgeworth box, show the set of exchange possibilities for Joe and Martin which would make at least one of them…Two officers are working in a police department. During a working day Officer One can either catch 20 criminals or she can write 60 reports. During a working day Officer Two can either catch 2 criminals of she can write 21 reports. The boss of the officers has the following utility function U=min(criminals; reports}. Officers want to make their boss as happy as possible. Find how many criminals will be optimally caught during the day.
- Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 2 -2 -2 Guitars 24 Losses Losses -600 -2 What is the least amount of money Jimi is willing to accept to sell one of his guitars? (just enter a dollar amount, i.e., "1000", not "$1000"Suppose that you are the owner of a bakery. The customers who buy the cakes you bake have different tastes x for the chocolate content, with x ranging from 0 to 1. The total number of customers is N = 100 are equally distributed along the [0,1] line. If x is the customer's most preferred chocolate content (location of the customer), and the cakes have chocolate content z, then customer x bears a unit utility cost of $1. Suppose that all customers' reservation price for a slice of a cake is $3. The marginal cost of producing one slice of a cake of any chocolate content is equal to $1. Suppose that you would always like to serve all the customers. a. Your company offers just one type of cake, say regular, with z =1/2 What price will you set for a slice of a cake? b. Suppose that in addition to regular chocolate cake z=1/2 you are also considering offering the high-chocolate variety, that is zHC = 3/4. What price will you set for the slice of your new cake? If running the high-chocolate…On Sundays, people in Los Angeles consider a boat to Catalina Island to spend the day on the beach there. The utility that a person gets from visiting Catalina is 1-[n/10] – p , where n is the number of visitors on the island and p is the price of round-trip transportation (by boat). (Note that a visitor obtains more satisfaction if there are fewer other visitors on the island). The utility of staying home is zero. In equilibrium, how many people visit the island on a given Sunday? ( Your answer should depend on p.)
- Suppose that you are the owner of a bakery. The customers who buy the cakes you bake have different tastes x for the chocolate content, with x ranging from 0 to 1. The total number of customers is N = 100 are equally distributed along the [0,1] line. If x is the customer’s most preferred chocolate content (location of the customer), and the cakes have chocolate content z, then customer x bears a unit utility cost of $1. Suppose that all customers' reservation price for a slice of a cake is $3. The marginal cost of producing one slice of a cake of any chocolate content is equal to $1. Suppose that you would always like to serve all the customers. What is the "marginal cost of each unit is (c)" ? What is the "set up cost of each store is F" ? What is the number of the retail shop (n)? What is the transportation cost ( t ) ? What is the reservation price (V) ?When Katerina goes running, she can either take water (W) or coconut water (C) with her to drink. She believes coconut water is three time more hydrating than plain water. Katerina just cares about the hydrating power of the drink. (i) Can Katerina's utility function be represented by U(W,C) =3C + W? (ii) Given U(W,C) =3C + W, Katerina has £28 pounds to spend on these two drinks. If a bottle of water costs £1 and a bottle of coconut water costs £2 what is Katerina's optimal choice? Note that MUw = 1 and MUc=3. %3D (iii) Explain under which conditions the tangency condition does not work. Given that the tangency condition does not work, discuss how we can find out the optimal consumption bundle for a consumer.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?