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Consider a two-city (A and B) regional economy where each city operates on the negatively sloped portion of its utility curve. In the initial equilibrium, the two cities are identical. Then air pollution (lead emissions) in city B decreases the brain power and productivity of workers in the city by 20 percent. Illustrate the effects of lead emissions on the regional equilibrium, indicating the direction of changes in city size (the number of workers) and regional utility.
The curve of urban utility shows worker utility as being a function of the number of workers.
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- On Sundays, people in Los Angeles consider a boat to Catalina Island to spend the day on the beach there. The utility that a person gets from visiting Catalina is 1-[n/10] – p , where n is the number of visitors on the island and p is the price of round-trip transportation (by boat). (Note that a visitor obtains more satisfaction if there are fewer other visitors on the island). The utility of staying home is zero. In equilibrium, how many people visit the island on a given Sunday? ( Your answer should depend on p.)Consider a Robinson Crusoe economy where Crusoe starts with 20 units of time (good 1) and no units of the consumption good (good 2). Crusoe owns the firm with technology given by y={y ER²|y₁ ≤0, y₂ <1- y₁}. Crusoe has utility function u = x₁ + x² Which 2 of the following 8 options are true: Every Walrasian Equilibrium must be Pareto efficient. O There are infinitely many Pareto efficient allocations. The production set satisfies constant returns to scale. O The production set satisfies possibility of inaction but violates no free lunch. O The production set violates free-disposal. The production set is closed. O Crusoe's preferences satisfy convexity. O The production set violates convexity.Question 22: Kathy gets utility from three things: the number of flowers in her local park (F), reading books in this park (R), and eating sushi (S). Four utility functions that might describe Kathy's preferences are shown below. In each case, discuss whether reading in the park (R) is non-essential and whether reading (R) and the number of flowers in the park (F) are weak complements. [medium] (a) U(F, R, S) = 2FR+ S (b) U(F, R, S) = /2FR+ S (c) U(F, R, S) = (V2FR)S (d) U(F, R, S) = /2F+ RS
- Rajiv is training for a biathlon, a winter racing sport that combines cross-country skiing and rifle shooting. Consider the following scenario: Rajiv has only 15 hours available to devote to his training this week. Each hour he spends skiing is one hour that cannot be spent working onhis shooting. Which basic principle of individual choice do these statements best illustrate? People face trade-offs. Rajiv has an incentive to spend more time on skiing than on shooting. People usually exploit opportunities to make themselves better off. Rajiv can use time most efficiently by spending the same amounts of time on skiing and shooting.10) If prices and income in a two-good model double, what will happen to the budget line? A) The intercepts of the budget line will increase. B) The intercepts of the budget line will decrease. C) The slope of the budget line may either increase or decrease. D) There will be no effect on the budget line. E) Insufficient information is given to determine what effect the change will have on the budget line.Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
- For Miranda, catching fish is not just a profitable activity, it is also her only viable source of food. She derives utility from consuming fish q as well as leisure time r, by the function U (q, r) = √gr Again, let p denote the price of fish and let w = 1 be the hourly wage that Miranda earns from working. She has a total of l = 24 hours per day to divide between labor and leisure, so that l + r = 24. a) Suppose that Miranda's expenditure on fish comes entirely from her wages pq = wł. Rewrite this condition as a budget constraint. What is the "price" of leisure and what is Miranda's "income" I? b) Write Miranda's utility maximization problem and state the first order conditions. (c) Find Miranda's demand for fish qd(p) and leisure r(p), and her indirect utility v(p).An individual's utility function is given by: U (q1 , q2) = q11/2 . q2 Suppose we know that the individual is maximizing their utility by consuming 9 units of good #1 (q1=9) and six units of good #2 (q2=6). If the current price for good #1 is $1 (p1=1), what must be the price of good #2 (p2) and what must be the individual's current income (y) available to spend on the two goods? a.) p2 = b.) y=Extend the model of the jungle to the case in which the number of houses is smaller than the number of agents. In this case, an allocation is a function from the set of agents to the set H U {homeless} with the property that no two agents are assigned to the same house. Each agent has a preference ordering over H U {homeless}. Assume that this ordering is strict; assume also that every agent prefers to be allocated any house than to be homeless. Define an equilibrium for this extended model and show that it always exists.
- Consider an economy where all production and all consumption is carried out by a single agent, Robinson Crusoe. Robinson, as a consumer, is endowed with H hours of time. His utility depends in hours of leisure, h, and coconuts, y: u(h, y) = (h)1−βyβ with 0 ≤ h ≤ H,β ∈ (0,1). Robinson, as a firm, can transform hours of labor, z, into coconuts y. His technology of production is given by y = f(z) = zα with α ∈ (0, 1). Let p denote the price of coconuts, w denote the price of leisure/labor, and π denote the firm’s profits. Note that the budget constraint of Robinson is py ≤ w(H − h) + π. Note that the budget constraint of Robinson is px ≤ w(H − h) + π, and that in equilibrium in the market of coconuts x = y and in the labor market h + z = H. Find the equilibrium allocation and price vector in equilibrium.Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…Suppose you get two job offers when you graduate. First offer is in LA and pays $6000 permonth. The price of food in LA is $3 and price of housing is $5. The second offer is in SanFrancisco and pays $10000. Both food and housing is more expensive in SF at PF = 4 and PH = 6respectively. If your utility function is U (F, H) = F1/4 H 3/4 which job offer should you accept?