Q1. Let X be a public good and Y be a private good. Two individuals, A and B, derive utility from the consumption of X and Y according to the following quasi-linear preferences: U (X,Y)=DaX+Y and U" (X,Y)= BX2 +Y, where a + Band both a and B are greater than one. If the marginal rate of transformation between X and Y is C, find X.
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- Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They consume both good X, a private good, and the protection from the fort, P. One unit of good X costs 1 unit while one unit of P costs 2 units, so the budget constraint for each is given by: Xi + 2Pi = 100. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2log(Pj + Pd) (a) How much protection, P, will be privately provided? What is optimal consumption of X, the private good? (b) What are the socially optimal amounts of protection, P, and consumption, X, of the private good? How do the socially optimal amounts compare to that privately provided? Explain why.Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2 × log(PJ + PD)The budget constraint for each is given by:Xi + 2 × Pi = 100 (a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is.Consider an economy with a private good and public good. The economyconsists of two consumers whose utility functions are:u1(x1, y) = 1/2 ln x1 +1/2 ln y and u2(x2, y) = 1/3 ln x2 +2/3 ln y.The endowment of consumer 1 is w1 = 2, and endowment of consumer 2 is w2 = 3, both in units of private goods. The production of public good uses the linear technology y = z. 1. Find Lindahl equilibrium.
- Scenario 4 Suppose there are two residents in a neighborhood, Tana and Jason. Tana's demand for clean streets is Q = 100 – 4P. Jason's demand for clean streets is Q = 80 – 2P. If your answer is not a whole number, please make sure to round to the nearest hundredth. Refer to Scenario 4. Find the social demand curve for clean streets in this neighborhood. What is the y-intercept of the social demand curve? (Do not enter a dollar sign in your answer)Consider an economy with a private good and public good. The economy consists of two consumers whose utility functions are: u1(x1,y)=1/2 ln x1 + 1/2 ln y and u2(x2,y)=1/3 ln x2 + 2/3 ln y (better written equations attached) The endowment of consumer 1 is w1=2, and the endowment of consumer 2 is w2=3, both in units of private goods. The production of public good uses the linear Technology y=z. Find Lindahl equilibrium.Suppose there are two consumers A and B, and two goods x and y. A’s utility function has the following form UA = xA – (xB)-1. Which of the following is true? Consumer B's consumption of good x exhibits a negative externality. Consumer A's consumption of good x exhibits a negative externality. Consumer B's consumption of good x exhibits a positive externality. Consumer A's consumption of good x exhibits a positive externality.
- Consider a two-good economy with one private and one public good. There are four consumers in this economy who contribute to public good provision. The price of the private good is $1 and the demand function of the public good for each consumer is as follows: p1 = 20 - 2G, p2 = 30-(5/10)G, p3 = 100-(G/2) and p4 = 60-G where G is the number of units of the public good and p^i is the price of each unit for consumer i in dollars. The cost of providing one extra unit of the public good is (alpha). (a) With 170 < alpha < 210, what is the optimal level of provision of the public good? Show the optimal point on a graph. (b) Is there a possibility that the public good is not supplied at all? Why? (c) If the public good is not supplied at all, what is the size of the deadweight loss due to this market failure? (d) If at least one person contributes, for what values of the public good will be supplied?In experiments in which participants voluntarily contribute to the provision of a public good, we often find a reduction in contributions in successive rounds of the experiment. We can explain this as Group of answer choices Evidence of participants reaching satiation and not wanting such high levels of the public good. Evidence of participants working out the Nash equilibrium outcome of the voluntary contribution game. Evidence of participants reducing cooperation to punish free riding. Evidence of participants learning how to play the game more effectively.Scenario 3 Suppose there are one hundred residents in a neighborhood, and each resident has an identical demand for a public good. The demand for each resident is given by P = 2 - .01Q. If your answer is not a whole number, please make sure to round to the nearest hundredth. Refer to Scenario 3. Find the social demand curve for the public good in this neighborhood. What is the y-intercept of the social demand curve?
- Chris and Dana live in an exchange economy with two goods: good Q and good R. Chris starts off with an endowment of 6 units of Q and 10 units of R. Dana starts off with an endowment of 8 units of Q and 8 units of R. Suppose that the price of good R is pR=1 and the price of good Q is pQ=2. a )At these prices, does the market clear? Yes or no? Explain your answer. b) What relationship must hold between the consumption of each agent and the price of the two goods at the market clearing equilibrium? Write the equationEvaluate the following statement: "When it comes to public goods, individuals do not reveal their true preferences because it is not in their self-interest to do so."A century ago this month, the Addison Act was passed in the UK placing a duty on local authorities to take up the gauntlet of providing 500,000 new homes within three years. Typically, housing had been built by private developers with an eye on turning a profit, but the Tudor Walters Report recommended that new homes were not to be cramped terraced houses packed into available space, but rather open and airy, low-density garden suburbs. The report mandated several designs and layouts of generous proportions, with gardens attached to all. In the last decade the number of homes built by both public and private providers combined has averaged only a paltry 159,000 each year. Most new homes are built by about a dozen big housebuilding firms, such names as Persimmon, Bellway, Barratt and Taylor Wimpey. Chasing financial returns tends to lead to a short-term view of shareholdings, seeking immediate gain over longevity and loyalty. The nine key housebuilding firms had a combined turnover of…