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.
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- We learned that we can use choice between a gamble over someone's best and worst outcomes and getting an outcome of interest (like getting pizza) for certain as a way to assign numeric values to utility (on a scale of 0 to 1). Using this method, if you are indifferent between the following: A gamble that has a 0.3 chance of your best possible outcome (and no lower chance), and a 0.7 chance of your worst possible outcome. Getting pizza for certain. it means that your utility for getting pizza is:Problem 4 A person has been mugged in the street by a thief, and there are n witnesses. All of the witnesses prefer someone else to chase the thief but none of them want to be the person trying to catch her. Each person gets 0 utility if the crime goes unreported, v if the crime is reported by someone else, and v −c if they report the crime. Moreover, we assume that the cost of chasing the thief is less than the utility of catching the thief: c < v. a. Define the strategic game described above. b. Find players’ best responses. c. Find the Nash equilibria of the game.Suppose you would have to pay Alicia at least $150 to get her to part with a ticket she just bought to see her favorite band play next Friday. Loss aversion implies that if Alicia had not yet bought the ticket, she would: Multiple Choice no longer be interested in purchasing it. be willing to pay more than $150 for it. be willing to pay exactly $150 for it. be willing to pay less than $150 for it.
- Ding Ding is a cat philosopher. He spends his time on two activities. Sleep and thinking. Both activities produce pleasure to Ding Ding. How effective Ding Ding is in each activity varies day by day. But on a given day, if he spend “s” effective hours in sleeping and “t” effective hours in thinking, his utility is u(s,t)=s^2+t. you can assume that time is continuous in answering the following question. (A) Let us first ignore that there are only 24 hours each day. Label “s” on the x-axis and “t” on the y-axis in a diagram. Draw two indifference curves u(s,t)=s^2+t=24^2=576, and u(s,t)= s^2+t=12^2=144. On each indifference curve, you have to mark at least the coordinates of four points to illustrate the shape of it. (B) Describe in words how these two indifference curves in (a) relate to each other.Oliver takes $2500 with him to a camp and there is 50% chance he will lose $900 on his way. Suppose Oliver can buy an insurance policy that will totally cover his loss, what maximal amount will he be willing to pay for such insurance? Oliver’s utility function is given by the function U(E) = E0.5 where E is the amount that he spends on the camp without any saving. a. $325 b. $475 c. $650 d. $535Suppose 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.
- EXERCISE 1Below is a production possibilities table for consumer goods (Food) and capital goods(Robots):A B C D EFood 0 1 2 3 4Robots 10 9 7 4 01. Show these data graphically. Upon what specific assumptions is this productionpossibilities curve based?2. If the economy is at point C, what is the cost of one more food? Of one morerobot? Explain how the production possibilities curve reflects the law ofincreasing opportunity costs.3. If the economy characterized by this production possibilities table and curvewere producing 3 food and 2 robots, what could you conclude about its use ofavailable resources?4. What would production at a point outside the production possibilities curveindicate? What must occur before the economy can attain such a level ofproduction?EXERCISE 2Explain how (if at all) each of the following affects the location of a country’s productionpossibilities curve:1. The quality of education increases.2. The number of unemployed workers increases.3. A new technique…Ken walks into an ice-cream parlor.Waiter: “We have vanilla and chocolate today.”Ken: “I’ll take vanilla.”Waiter: “I almost forgot. We also have strawberry.”Ken: “In that case, I’ll take chocolate.”What standard property of decision making is Kenviolating? (Hint: Reread the section on Arrow’simpossibility theorem.)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 ..
- Jacob is considering buying hurricane insurance. Currently, without insurance, he has a wealth of $80,000. A hurricane ripping through his home will reduce his wealth by $60,000. The chance of this happening is 1%. An insurance company will offer to compensate Jacob for 80% of the damage that any tornado imposes, provided he pays a premium. Jacob’s utility function for wealth is given by U(w) = In (w). (A) What is the maximum amount Jacob is willing to pay for this insurance? Show work and explain.Suppose that at current consumption levels an individual's marginal utility of consuming an extra sandwich is 10 whereas the marginal utility of consuming an extra coffee is 2. Then the MRS (of coffee for sandwiches) that is, the number of sandwiches the individual is willing to give up to get one more coffee is a 5 b. 2 C.1/2 d. 1/5Assume that someone has inherited 2,000 bottles of wine from a rich uncle. He or she intends to drink these bottles over the next 40 years. Suppose that this person’s utility function for wine is given by u(c(t)) = (c(t))0.5, where c(t) is each instant t consumption of bottles. Assume also this person discounts future consumption at the rate δ = 0.05. Hence this person’s goal is to maximize 0ʃ40 e–0.05tu(c(t))dt = 0ʃ40 e–0.05t(c(t))0.5dt. Let x(t) represent the number of bottle of wine remaining at time t, constrained by x(0) = 2,000, x(40) = 0 and dx(t)/dt = – c(t): the stock of remaining bottles at each instant t is decreased by the consumption of bottles at instant t. The current value Hamiltonian expression yields: H = e–0.05t(c(t))0.5 + λ(– c(t)) + x(t)(dλ/dt). This person’s wine consumption decreases at a continuous rate of ??? percent per year. The number of bottles being consumed in the 30th year is approximately ???