In a particular country, there are two types of individuals: native (n) and foreigners (f). Each dedicate their 8 hours of labor to producing either luxury (x) and non-luxury goods (y). Native workers' utility function is given by Un = x04y0.6 whereas foreigners' is given by U, = x02y0.8. Both individuals do not care whether they produce x or y. The production function for each good is given by x = y = 5l, where l is the total labor devoted to the production of each good. 4l and Px a) What must be the price ratio, /py, be? Interpret your answer
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- The Condorcet paradox illustrates Arrow’simpossibility theorem by showing that pairwisemajority votinga. is inconsistent with the principle of unanimity.b. leads to social preferences that are not transitive.c. violates the independence of irrelevantalternatives.d. makes one person in effect a dictator.Suppose X = R k + for some k ≥ 2, and we define x = (x1 , …, xk ) ≥ = (y1 , …, yk ) if x ≥ y; that is, if for each i = 1, …, k, xi ≥ yi . (This is known as the Pareto ordering on R k + ; it plays an important role in the context of social choice theory in Chapter 8.) (a) Show that ≥ is transitive but not complete. (b) Characterize ≥ Is asymmetric? Is≥ Negatively transitive? Prove your assertions. (c) Characterize ~ defined from ≥ in the usual fashion; that is, x ~ y if x ≥ y and y x. Is ~ reflexive? Symmetric? Transitive? Prove your assertions.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:
- 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.A decrease in the supply of in building materials (shortage) means that construction companies cannot get enough materials to complete all their projects. The owners of construction companies in Fiction Town have a choice between these two options: To lay off (temporarily fire) 10% of their least experienced workers. To reduce the hours of all employees by 5 hours a week, meaning they will be paid for 5 fewer hours of work. What happens to the average income of people who are employed as construction workers? The owners of the companies make profit from the payments made on their construction projects. What happens to the income of the owners? Assume that construction workers are counted as part of the average income in all of Fiction Town. What happens to the average income of people there? Why?Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by: Y = 10F + 20F2 – 0.6F3 a) If food availability in a two-person household is 20, would it be “rational” to share the food? Explain. b) If food availability in a two-person household is 30, would it be “rational” to share the food? Explain.
- Clarice has a utility function: U(Y) = 1000 - (100/Y), where Y is her income. clarice has just graduated from college and has a career choice for her first job of either working as a teacher and earning $40,000 or trying to become a theatre lighting director and earning $70,000 (if there is growth in the demand for theatre) or $20,000 (if there isn't growth in the demand for theatre). there is a 50% probability of growth. a consulting firm guarantees Clarice that it already knows whether there will be growth in the demand for theatre next year. what is the maximum amount Clarice should be willing to pay for this information?Satiation preference is monotonic. True or False, why?Heterogeneity in an endowment economy Suppose we have two typesof households: A and B. The utility maximization problem for a consumerof type i is max InCi,t+β ln Ci,t+1 Ct,Ct+1subject to Ci,t +Ci,t+1/ 1 + rt = Yi,t + Yi,t+1 / 1 + rt Note that the A and B households have the same discount rate and the same utility function. The only thing that is possibly different is their endowments. 1, Write down the Euler equation for households A and B.
- With the use of graphs state how the Consumer’s optimum in the Fisher’s Intertemporal Choice Model.Bart and Lisa are both optimizing consumers in the market for shirts and hats, where they pay $100 for a shirt and $50 for a hat. Bart buys 8 shirts and 4 hats, while Lisa buys 6 shirts and 12 hats. From this information, ignoring the minus sign, we can infer that Bart's marginal rate of substiution is _________ hats per shirt, while Lisa's is __________ hat's per shirtSuppose that each week Fiona buys 16 peaches and 4 apples at her local farmer's market. Both kinds of fruit cost $1 each. From this we can infer that: If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be greater than her marginal utility from the 4th apple she buys. Fiona is not maximizing her utility. If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be equal to her marginal utility from the 4th apple she buys. The law of diminishing marginal utility does not hold for Fiona.