This is my assignment
The questions in this problem refer to the following game: Player 2 a. Determine if either player has any dominated strategies. If so. identify them. b. Does either player have a dominant strategy? 1Why or why not? c. Use iterated elimination of dominated strategies to solve this game. Be clear about order in which you are eliminating strategies. Also specify whether you are eliminating strictly or weakly dominated strategies. (2p) Problem 1. Behavioral economics a} Explain the law of small numbers. b) What is loss aversion? c) How does loss aversion differ from risk aversion? Describe using pictures ofu functions. d) What is time inconsistency? Give an example. Problem 2. Behavioral economics Lisa Late has to finish a project in three days. The total amount of time that she has t: spend nishing the project is 12 hours. Lisa's preferences over working time over the three days can be described by the following utility function: u_ xf El 5x?+1 0,25 A where x: is the number of hours she spends on the project day t. As you can see. work day t has a higher cost than working day H1 and t+2. (5 p) a} 0n the first day (Monday) Lisa makes a plan for finishing the project that main her Monday utility function: u = x: 0.5x? 0.2m: . subject to the constrai 12 working hours in total xmxxw. How many hours does Lisa plan to wot day? b) Lisa spent 12!? hours working on the project on Monday. (in Tuesday morning utility function is: u = xf max: 0,25 x; . Since she must finish the projeci before Thursday she will set xTh=Dand her utility function to be maximized is th of = x3 0.51:: , subject to the budget constraint xxw=i 2-(1 2f?) How man: do Lisa plan to work each day?I c) Given your answers in question a and b, does Lisa have time-consistent prefer: Explain. Problem 1. Exchange In a pure exchange economy with two goods, and two individuals that act competitively, v know that at some Pareto efficient allocation. the MRS between the two goods for one individual is -2. a) What is the MRS for the other individual? b) What is the relative price? c) Show this situation in an Edgewcrth box. d) Explain why the allocation is Pareto efficient. Problem 1. Welfare economics A parent has two children named A and B and she loves both of the equally. She has a tot of 1000 SEK to give them. a} The parent has the following utility function: U = 45+ '5, where a is the amount t money that the parent gives to A, and b is the amount of money that the parent git to b. How will the parent divide the money? b) How will the parent divide the money if the utility function is: U = mtnfo. 3i}. c) How will the parent divide the money if the utility function is: U = made. 5}. d) How will the parent divide the money if the utility function is: U = 9' +5". Problem 2. Welfare economics A social planner has 1000 units of utility to distribute in a society with only two individual: she can therefore enforce any allocation such that 1000=U1+U2. a) If the social welfare function {SWF} is utilitarian, how will the planner distribute thi money between the two individuals? b) If the social welfare function [SWF} is Rawlsian, how will the planner distribute the money between the two individuals? c) Explain the median voter theorem. Problem 1. Externalities The government issues permits to trap lobsters and is trying to determine how many permits to issue. It costs 2000 a month to operate a lobster boat. If there are x boats in operation, the total revenue from the lobster catch per month will bi f(x)=1000(1 0x- x2 ). a) If the permits are free of charge, how many boats will trap lobsters? b) What number of boats maximises total profits? c) If the government wants to restrict the number of boats to the number that maximi total profits, how much should it charge per month for a lobster permit? Problem 2. Externalities Major Steelbone consumes two goods: bones (b) and steel (s). Her utility function is: U=? b2+s. Her budget is EDD and the price of bones (ps) is 2, and the price of steel (p5) is 1. a} How much of each good will she consume? b) Suppose that her friends do not like her consumption of bones. Their disutility can described by the function: b2. What quantity of bones should she consume to maximize social utility? c) What price of bones would be needed for her to consume the social optimal amoL of bones? d) Explain two ways in which she could be induced to consume the social optimal amount of bones. What are the potential problems with these methods? e} What kind of externality is this? Problem 3. Externalities Two farmers has the opportunity to put zero. one or two cows each on a common field. E cows daily milk production depends on how many cows there is on the common field. Total number of cows: 1 2 3 4 Each cows production: 3 5 3 2 That is. the first cow produces 3 litres of milk per day. the second 5 litres and so on. Each farmer likes to maximize her total production, and they make their decisions simultaneou (a) Illustrate this game in a normal form game matrix. (b) Is there a dominant strategy equilibrium? If not. is there a pure strategy Nash equilibr Explain. (c) Which is the pareto optimal number of cows on the field? (d) What is the actual problem here? (e) What is this situation called? (f) Give an example of another situation with this problem. Problem 1. Public goods Ten people have dinner together at the restaurant "Glade Ankan". They agree that the bill ' be divided equally among them. a} What is the additional cost to any one of them of ordering an appetizer that costs ZUUSEK) b) Why may this be an inefficient system? Problem 1 Consider an economy in which there are two goods, 1 and 2, whose prices are p, > 0 and p2 > 0, respectively. The two goods can only be consumed in non-negative amounts x, and X2, respectively. A consumer has preferences over R? which are represented by the utility function 1:R - R. (x1 12) " 1(x1, X2) := (x1 + 2)X2. The consumer's income is / > 0. (a) Formulate the consumer's utility maximization problem, find the first-order conditions for utility maximization, and find the Marshallian demand functions' x1(p1, p2, /) and x2(p1, p2. I) for goods 1 and 2, respectively. (Note: Use the Lagrangian method. Assume that the budget constraint holds with equality and that the solution is interior (i.e. x1 > 0 and x2 > 0), thus disregarding the non-negativity constraints on x, and x2.) Check that the second order conditions are satisfied.Q.4 Let us now consider an application. Suppose that we think of Robinson and Friday as two countries. Let their utility functions be the same as before, but let their initial endowments be DR, WR) = (3,9) and (wf , w, ) = (1,3). Hence, we can think of Robinson as a relatively rich country and Friday as a relatively poor country, in the sense that Robinson has more of both goods. Find the competitive equilibrium. [Note: You don't have to start over from scratch to do this. You can simply repeat your derivations from parts Q.1 and Q.2, once again making the guess that p1 = p2 and inserting the new values for the endowments.] If the rich country has more of everything, why are there gains from trade? One sometimes hears calls for the U.S. to curtail its foreign trade. Thinking of the U.S. as Robinson, what effect would this have in this model? Given your answer, why would people suggest such curtailment or, equivalently, what would such advocates think of as missing from our model
