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Suppose the Social Welfare Function is given by U = X0.25Y0.75 and the
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- Suppose that 10 people live on a street and that each of them receives $2 in marginal benefit for each streetlight on their street, regardless of the number of streetlights provided. If the marginal cost of a street light is 2x, where x is the quantity of streetlights, what is the Pareto efficient number of streetlights to provide?Analyze how pareto efficiency is achieved from consumption activities in an economyState the equilibrium conditions for Pareto efficiency equation
- Anna and Bess are assigned to write a joint paper within a 24-hour period about the Pareto optimal provision of public goods. Let A denote the number of hours that Anna contributes to the project and B the number of hours that Bess contributes. The numeric grade that Anna and Bess earn is a function, 23 In(A + B), of the total number of hours that they contribute to the project. If Anna contributes tA, then she has (24 - A) hours in the day for leisure. Anna's utility function is UA = 23 In(A + B) + In(24 - A); and Bess' utility function is UB = 23 In(A + B) + In(24 - B). If they choose the hours to contribute simultaneously and independently, what is the Nash equilibrium number of hours that each will provide? What is the number of hours each should contribute to the project that maximizes the sum of their utilities?John and Sotiris live on trees in two different forests. They each have eight hours to work in a day. John can grow a Yam in 1 hour or raise a Zebra in 2 hours. Sotiris can grow a Yam in 2 hours or raise a Zebra in 4 hours. Both John and Sotiris consume equal numbers of Yams and Zebras. When calculating the welfare benefits of markets, the standard analysis only includes the parties involved in exchange. Using the American Opioid Crisis as an example, explain how poorly regulated markets can cause harm to third parties not involved in exchange.Person 1 and person 2 are the only two residents of an economy. Person i (where i is either 1 or 2) has the utility function Here, Yi is person i’s income and β is parameter between 0 and 1. Assume that the social welfare function is where α is a parameter between 0 and 1. Initially, person 1’s income is 1 and person 2’s income is 2. a) Express W in terms of Y1 and Y2. If a social indifference curve shows all the pairs (Y1, Y2) that yield the same value of W, what would a social indifference curve look like if it were drawn in the (Y1, Y2) quadrant? Find an algebraic expression for the slope of a social indifference curve. b) Imagine that income redistribution is costless, in the sense that the economy can reach any pair (Y1, Y2) that satisfies the condition Draw a graph of the attainable pairs in the (Y1, Y2) quadrant. This set is called the “utility possibility frontier.” Using this frontier and the social indifference curves,…
- Compare Pareto Efficiency with Pareto Optimality with daily life examplesBonnie and Clyde are working together. Suppose that their total profits are 170H, where H is the number of hours they work per year. Their utility functions are, respectively, Ug(CB, H) = CB-0.01H² and UdCG H) = Cc- 0.04H², where Cg and Care their private goods consumptions and His the number of hours they work per year. If they find a Pareto optimal choice of hours of work and income distribution, the number of hours they work per year is 1,700 2,400 850 1,600 750Define the Various Mathematical Implications of Homoskedasticity?
- Malaria Eradication Back on the Table In response to the Gates Malaria Forum in October 2007, countries are debating the pros and cons of eradication. Dr. Arata Kochi of the World Health Organization believes that with enough money malaria cases could be cut by 90 percent, but it would be very expensive to eliminate the remaining 10 percent of cases, so countries should not strive to eradicate malaria. Make a graph with the percentage of malaria cases eliminated on the x -axis and the marginal cost and marginal benefit of driving down malaria cases on the y -axis. On your graph: (i) Draw a marginal cost curve and marginal benefit curve that are consistent with Dr. Kochi’s opinion. (ii) Identify the quantity of malaria eradicated that achieves allocative efficiency.Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.What are the Pareto optimal allocations from this set of feasible allocations: (8,3) (0,1) (3,2) (4,5) (1,0) (-2,10) (3,8) (9,1) (0,0)