Suppose there are four people in the market, two people with u=X1X2 and two people with u=min{x1,x2}. Suppose everyone has the same income (m;=m), and p2-1. What is the demand curve of x1 for the market? Qd=m/p1 + 2m/(p1+1) Qd =4m/(p1+1) Qd=4m/2p1+2m/(p1+4) Qd=4m/(p1+1)
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- Help meThe movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p₂ cents, the number of movie tickets that international students are willing to buy per year is given by: 92-87-0.3p₂. The total costs for the movie theater depend on the total number of tickets sold, q₁+92, and are given by the following total cost function C(q₁+92)=(91+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. How many movie tickets will domestic students buy (9₁)? How many movie tickets will international students buy (9₂)?The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p₂ cents, the number of movie tickets that international students are willing to buy per year is given by: 92-87-0.3p2. The total costs for the movie theater depend on the total number of tickets sold, q₁+92, and are given by the following total cost function C(q₁+9₂2)=(91+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. If this is the case, then how much will the movie theater charge to domestic students (p.)? How much will the movie theater charge to international students (P₂)? Note: You should round all…
- The movie theater in Glendon has two types of customers: domestic students (group 1) and international students (group 2). At a price of p, cents, the number of movie tickets that domestic students are willing to buy per year is given by: q₁-170-0.7p₁. At a price of p2 cents, the number of movie tickets that international students are willing to buy per year is given by: 9₂-87-0.3p₂. The total costs for the movie theater depend on the total number of tickets sold, 9₁+92, and are given by the following total cost function C(q₁+92)=(9₁+9₂)². Suppose that the movie theater can identify which students are domestic and which students are international, and students are unable to resell movie tickets to each other. This enables the theater to charge different prices to domestic vs international students. The movie theater's management receives too many complaints from students about the fact that they charge different prices to domestic vs international students, so they are forced to charge…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 =$9perkmtostore2for each consumer. The net utility of a consumer located at point x from buying a product at store 1 is U1(x) = 100 – p1 – t1x, where pi is a price of the product at store i = 1,2. The net utility from buying at store 2 is U2(x) = 100 – p2 – t2(1 – x). The average cost of the product for each store is c = 4. (a) Assume that all consumers buy product from the sellers. Find the demand functions Di(p1,p2) and the profit functions πi(p1,p2) for each store i = 1,2 as functions of prices p1,p2.(b) Find the equilibrium prices.Suppose Jimi has reference dependent preferences over guitars and money as in Tversky and Kahneman (1991). His utility functions are given below. Gains Gains 400 -2 -2 2 Guitars 2$ Losses Losses i-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., "10o0", not "$1000"
- 3. Maximize x1, x2 such that 232 u(x₁, x₂) = x³ x3 P1x1 + P2x2 = mFinn is in charge of decorations for an upcoming festival, and he is planning to decorate withclovers (C) and flags (F). Suppose his preferences over decorations can be represented by theutility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry aboutrestricting to whole-number answers.(a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I.(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the threefirst order conditions.(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: Youdo not need to solve the constrained optimization any more than this.)Violet buys pies (x) and champagne (y) with her income of $400 and her utility function over pies (x) and champagne (y) (assumed to be divisible goods, where any real number unit pie or champagne is feasible) is Cobb-Douglas and given by u(x, y) = xy. The price of champagne is pY = $10 per bottle. (a) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each additional pie is half-price, i.e., pX = $5. Draw her budget set, carefully labelling all relevant points. calculate the quantities of pies and champagne she will consume when she maximizes her preferences. (b) (HARDER! We haven’t covered this scenario in class) Pies cost pX = $10 per pie if she buys between zero and 20 pies; if she buys more than 20 pies, each pie purchased is half-price, i.e., pX = $5. The discount applies to all units purchased, not the additional ones! Draw her budget set, carefully labelling all relevant points. Calculate the quantities of pies and champagne she will…
- 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?There are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 5 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4,0) and (x₁, x₂) = (0,4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. b) Statement 2: Jeff's preferences are strictly convex. c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x₂)=( d) Evaluate…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?