Consider an economy with 1,000 people and two goods, one private and one public. The people all have the same utility function Ui(Xi, G) = Xi – 100/G , where Xi is the quantity of the private good consumed by person i and G is the quantity of the public good. The price of the private good
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- brownie has $100 that he can spend on milk and gas. A gallon of milk costs $5.However, government gives its citizens a coupon that entitles people to 20%discount on their first 10 gallon milk purchases. Gas costs $4 per gallon andgovernment charges $1 for each gallon of purchased gas. John’s utility functionis U (x, y) = 9x+10y, where x and y represent gallons of milk and gas consumed,respectively. What is John’s optimal consumption of milk and gas?Question 3 Part bIf government removes the quantity restriction to which the coupon applies (i.e.20% discount is applied to any quantity of milk purchased), what will be John’soptimal consumption?Refer to the accompanying table. If the price of a t-shirt is $10 and the price of a sweater is $40, then the rational spending is satisfied when the consumer purchases t-shirts and. sweaters. Units 0 1 2 3 4 Utils per year from Utils per Year from T-shirts Sweaters Multiple Choice 1; 4 3; 2 4; 4 2; 3 0 75 135 180 210 0 400 720 960 1,120 xAllison has a golden goose that will lay an egg every year until forever. The first egg will be out next year, and each egg is worth $500. Allison's friend, Eric, offers a price to buy the golden goose from Allison today. The interest rate is 10%. From the cost-benefit analysis, under which of the following offers would Allison be willing to sell the goose to Eric? O A $4,500 B. $5.500 C. Allison would want to sell it to Eric with both $4,500 and $5.500. D. Allison wouldn't want to sell it anyway since the eggs would be laid out forever.
- Jane has 9 liters of soft drinks and 11 sandwiches. Bob, on the other hand, has 11 liters of soft drinks and 9 sandwiches. At these endowments, Jane's MRSds of soft drinks for sandwiches is 0.8 and Bob's MRSds is 2.3. a) Illustrate the situation in the E-box. Which of the following graphs represents the situation correctly? [Select] 11 sandwiches 0₂ sandwiches 0₁ Graph a Graph b 11 0₁ soft drinks 0₁ soft drinks b) Is this allocation efficient? [Select] c) If allocation is not efficient, what changes will make both consumers better off? [Select] For question (a), choose one answer from "graph a" and "graph b" For question (b), choose one answer from "yes" and "no" For question (c), choose one answer from "Jane should trade some of her soft drinks for Bob's sandwiches","Jane should trade some of her sandwiches for Bob's soft drink" and "It is already efficient" 112. Residents in a town are voting to decide where a new library will be built. The residents" homes are on the same street and the "map" of the town is represented below. The letters represent the location of each house. The numbers represent distance in 100 meters (in other words, house 'a' is 100 meters from house 'b' and 1200 meters from house i). Each house- hold would receive a utility of 12 if the library was built in front of that house; utility decreases by I unit as the distance to the library increases by 100 meters. Use the distance markers (the numbers) to indicate where the library should go according to the following aggregation methods:Question 6: Transitivity There is only one consumption good in the world (cities). Karen is moving – suppose that her preferencesover cities are described as follows: she strictly prefers city A to city B if either (1) the average rent in cityA is cheaper than in city B, or (2) the average rent is the same in both cities, and there are more goodrestaurants in city A than in city B. Are these preferences transitive? Justify your answer.
- 1. Write down an exchange economy model with two individuals and two goods, in whichthere is no consumption externality. State and explain the key assumptions of the model.Using the model, answer the following questions:(a) Explain carefully how the concept of Pareto efficiency differs from that of socialwelfare.(b) State the Second Theorem of Welfare Economics and explain carefully why it holds.What is the importance of the assumption of convex preferences to this theorem?3. Consider an exchange environment with two consumers, Consumer 1 and Consumer 2, and two goods, a and b. Consumer 1 is initially endowed with e₁,a = 0 of good a and e₁,b = 10 of good b, while €1,6 Consumer 2 is initially endowed with e2,a = 10 of good a and €2,6 = 0 of good b. The utility of Consumer 1 from consuming x1, a ER+ of good a and 1,6 ER is u1(x1,a,x1,b) = x1,a + x1,b, while the utility of Consumer 2 from consuming x2,a Є R+ of good a and x2,6 ЄR is U2(x2,a, X2,b) = √√x2,a + x2,b. (a) Consider general equilibrium in the context of this environment in which the price of good b is normalized to 1. Compute the equilibrium price pt of good a and find the corresponding equilibrium quantities consumed by the various consumers. (b) Consider the game in which, simultaneously, Consumer 1 submits a “demand curve" and Consumer 2 submits a “supply curve” to a market mediator. In particular, the strategy space of Consumer 1 is [0,10], and the strategy d of Consumer 1 corresponds to the…Units of the Good 0 1 5678AWN2 3 4 Total Utility Total Utility of X of Y 0 0 620 1740 1120 3030 1500 3960 1820 4710 2080 5280 2300 5730 2460 6060 2580 6300 For the next 3 questions, assume that an individual consumes two goods X and Y. The total utility (assumed measurable) of each good is independent of the rate of consumption of other goods. The prices of X and Y are, respectively, $20 and $30. If the consumer buys the fourth unit of X the Marginal Utility per Dollar Spent on X is 16 I If the consumer has $210 to spend on X and Y, the utility-maximizing bundle is The minimum budget necessary to move to a higher equilibrium consumption of X and Y is $ unit(s) of X and unit(s) of Y.
- The government of Freeland is considering introducing a carbon tax to tackle global warming. They have asked for your help in analyzing the impact. They give you the following information. The average person in Freeland eans €30 a week. She spends it on a carbon good and on all other goods. Her preferences satisfy the usual assumptions of consumer choice theory. The carbon good currently costs €2 a unit and the average person buys 5 units of a carbon good per week. The government is considering putting a tax of €1 on carbon and giving a transfer of €5 to the average person to compensate her for the price increase. Will this proposal make the average consumer better off, worse off or the same as they were before the proposal? Explain clearly. Will this proposal lead to any change in the amount of the carbon good bought by the average consumer? Explain clearly.The following graph depicts three families, X, Y, and Z, and their utility based on spending on education and other goods. Suppose free public education is provided and the new budget constraint is shown in red. What can be said about family Y because of free public education? Other goods spending EF G GA E1 EF E2 E3 B Education spending They have an increase in educational spending, but a decrease in spending on other goods They have an increase in both spending on other goods and in education They have an increase in spending on other goods, but a decrease in educational spending They have a decrease in both spending on other goods and in education O They do not have a change in their spending on other goods or in educationDraw some hypothetical indifference curves for John Q.Public on a diagram identical to the one you constructedfor Test Yourself Question 1.a. Approximately how much gasoline and how manyhot dogs will Mr. Public buy?b. How will these choices change if his income increasesto $140? Is either good an inferior good?c. How will these choices change if gasoline price risesto $3.00 per gallon? Test Yourself Question 1: John Q. Public spends all of his income on gasoline andhot dogs. Draw his budget line under several conditions:a. His income is $100, and one gallon of gasoline andone hot dog each cost $2.b. His income is $150, and the two prices remain thesame.c. His income is $100, hot dogs cost $2 each, andgasoline costs $2.50 per gallon. (See photo of answers for question #1)
