3. Demeter has 100 acres of land on which she can plant wheat or rice. The following table shows the income per acre that each crop will produce, both for a wet growing season and a dry growing season. Dry 700 Wet Wheat 200 Rice 700 200 2 The probability of a wet growing season is - and the probability of a dry growing season is Demeter's utility function over income is U(W) = ln W. What is Demeter's contingent income bundle if she plants only wheat? If she plants only rice? If she plants 50 acres of wheat and 50 acres of rice? (Note: A contingent income bundle is (Ww, Wa), where the “w" subscript indicates "wet" and the "d" subscript indicates "dry".) b. Use your answers in (a) to find an algebraic expression for Demeter's budget constraint over contingent income bundles. What is Demeter's expected utility function? What is her MRS function? а. с.
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- Betty is looking for a job. She considers job opportunities intwo cities. Bettyís utility is given by y- x, where y is the lifetime income andx is the amount spent on buying a house. The income from City 1 fluctuatesalthough the house price is stable. On the contrary, the income from City2 is stable while the house price fluctuates. If she moves to City 1, Bettycan earn a lifetime income y1 with probability alpha and 1 + y1 with probability1-alpha . The house price in City 1 is x1. Moving to City 2 means that Bettycan earn an income of y2. However, the house price is x2 with probabilitygamma and 1 + x2 with probability 1-gamma . Do the following: (a) Write down theexpected utilities associated with living in the two respective cities, i.e., V1and V2. (b) Derive the condition under which Betty chooses City 1.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…You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…
- 4. Marvin is given a number of choices between various lotteries where the possible outcomes include a vacation, a motorbike, a pair of shoes and a round of applause, or X = {v,m, s, a}. It is known that, according to Marvin's preferences, v > m > s > a. In addition, he claims he would be indifferent between the motorbike and a lottery that results in a vacation with probability 0.4 and a pair of shoes with probability 0.6, and he would furthermore be indifferent between a pair of shoes and a lottery that results in a motorbike with probability 0.5 and a round of applause with probability 0.5. Marvin has a utility function u: X → R (in other words u maps each element in X to a real number) and he in an expected utility maximiser (in other words his preferences conform to the axioms G1 to G6). 4.1. Assuming Marvin's claims about indifference are correct, derive u(m) and u(s) in terms of u(v) and u(a). 4.2. Von Neumann-Morgenstern utility functions are only unique up to positive affine…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.ayesha derives utility from travelling and outdoor dinning o weekends as given utility function U(t,d)=TD.the price of a day spent travelling is $160{Pt=160} and price of dining outdoor $200{Pd=200}.ayesha annual budget for this is $8000. find ayesha's utility maximizing choice of days travelling and dining outside. and alsoo find uutility level from consuming that bundles .show findings graphically
- The consumer choice is not restricted to the choice of consumptiongoods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has awage per hour of 10 euros. With her earned income she consumes. That isC=wH per day.She also decides how many hours to work of take leisure time each day.H=24-N, whereHis work and N is leisure. Her utility is given by (picture) Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif-ferent curve. What is the labor supply function?Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?The vending machine in Katherine's office building offers cans of pop and candies. Katherine's utility function is U = 3PC, where P is the amount of pop consumed per %3D week and C is the amount of candy consumed per week. Pop costs $1 and candy costs $0.5 per bag. If Katherine has $10 to spend, she will consume A bags of candy.
- Q1. A farmer believes there is a 50-50 chance that the next growing season will be abnormally rainy. His expected utility function has the form Expected utility = 0.5lnYNR + 0.5lnYR Where and represent the farmers income in the state of ‘normal rain’ and ‘rainy’ respectively. Suppose the farmer must choose between two crops that promise the following income prospects Crop YNR YR Wheat $83,000 $10,000 Maize $83,000 $15000 What mix of wheat and maize would provide maximum expected utility to this farmer?1. Now, imagine that Port Chester decides to crack down on motorists who park illegally by increasing the number of officers issuing parking tickets (thus, raising the probability of a ticket). If the cost of a ticket is $100, and the opportunity cost for the average driver of searching for parking is $12, which of the following probabilities would make the average person stop parking illegally? Assume that people will not park illegally if the expected value of doing so is negative. Check all that apply. A. 9% B. 18% C. 17% D. 10% 2. Alternatively, the city could hold the number of officers constant and discourage parking violations by raising the fine for illegal parking. Suppose the average probability of getting caught for parking illegally is currently 10% citywide, and the average opportunity cost of parking is, again, $12. The fine that would make the average person indifferent between searching for parking and parking illegally is ____ , assuming that people will not…2. Alice believes that her car would cost £12500 to replace if it was stolen or damaged. Based on crime statistics for the area she lives in, she believes that the probability of her car being stolen or damaged is 0.15. (i) Alice's utility function is given by U(w) = ln(w) for w > 0 and she as £35000 in the bank. Calculate how much Alice would be prepared to pay (in a single payment) to insure her car against theft or damage (ii) Repeat the calculation in the previous part but now assume Alice has £500000 in the bank.