Utility = (x,y)² the individual's share of private good production (=x/100). Notice that the exclusive and that everyone benefits equally from its level of production. e market for x and y were perfectly competitive, what levels of those good ld be produced? What would the typical individual's utility be in this situa at are the optimal production levels for x and y? What would the typical vidual's utility level be? (Hint: The numbers in this problem do not come aly, and some approximations should suffice.)
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- Consider an economy with n consumers, one privategood and one public good. We think of the private good as “all othergoods,” and measure it in terms of money. There are n individuals inthe economy with utility functions Ui(xi, y) = αi ln y + xi, where y is thepublic good, xi is the private good consumed by individual i = 1, . . . , n,and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of privategood of each consumer is given by wi. We donote the aggregate endowment 1of the private good by w =Pi wi. The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.1. Suppose there is a society with two people who have the following valuations of level y of a public good: v1(y) = 1210√y and v2(y) = 410√y so their marginal benefits are given by 605/√y and 205/√y, respectively. The cost of providing the public good is given by c(y) = 10y. So we have MC(y) = 10. Suppose that their utility is given by u1 = x1 + v1(y) and u2 = x2 + v2(y) , where xi denotes person i’s money (that is not spent on the public good). Further, suppose their wealth/income levels are given by w1 = 500 and w2 = 800. (a) What is the socially optimal level of the public good?2. In this question we will combine a very simplified model of an externality that has long-lasting impacts with the model of discounted utility that we learned in our game theory topic. Consider a hypothetical environmental externality: produced as the byproduct of industrial activity, each unit of emission of a pollutant that is emitted once, today, causes $10 of external harm to society each and every year, starting immediately, forever. Let's say that policymakers apply a discount factor of 8 € (0, 1) to future gains and losses, in an analog of the discounted utility model except for cash payoffs rather than utilities. What would the socially efficient Pigouvian tax on the emission of this pollutant be if we applied a discount factor of (i) 8 = 0.5, (ii) 6 = 0.9, and (iii) 8 = 0.99? Give an intuitive explanation of how to interpret the parameter & in this context, and explain precisely but in simple terms what the goal and effect of the Pigouvian tax would be.
- Suppose the demand for standard sized bottled water in the US is Qd=120-30.5P where Qd is monthly quantity demanded in millions and P is the price per bottle in dollars and cents. If the marginal private cost (MPC) of producing the bottled water is one dollar, calculate the market equilibrium quantity. Explain what a constant marginal cost implies. Does that mean the total opportunity cost of producing bottled water is unrelated to how many are produced? Let’s assume that the marginal private benefit (MPB) of bottled water equals the marginal social benefit (MSB). Explain what that means. At the equilibrium calculated in part A, what do you know about buyers’ willingness to pay in each transaction?2.- Assume that consumers are uniformly distributed along a one-mile stretch of a beach. N ice cream vendors are pondering where to position their carts. The price that they are allowed to charge is fixed by the EACAC (Equal Access to Coolness for All Coalition). (Also, each consumer will buy exactly one ice cream.) (a) Show that there is no equilibrium (in locations) if N=3. (b) Suppose N=5 and vendors position their cart each at one of the (mile) points ( 1/6, 2/6, 3/6, 4/6, 5/6 ) is that an equilibrium?Consider the model of a rational consumer that cares about consumption of private goods and consumption of broadcast public television (a public good). Suppose that the total level of broadcast public television provided through voluntary contributions is 10 hours of programming. Then the government decides to raise money through a tax and provide 10 hours of programming to the public. What would we predict about crowd-out of voluntary contributions to broadcast public television when government does this? How would the answer change if consumers get warm glow utility from donating to broadcast public television in addition to utility from the public television itself? (Be specific.)
- 1. In the Traveler’s Dilemma, each of two people chooses a number between 180and 300. Each is paid the lower of the two numbers, but the person who choosesthe higher number must pay an amount x to the person who chose the lowernumber. In one case, x = 5, while in the other case x = 180. What differencewould you expect between choices with the two values of x?a. Higher choices when x = 5.b. Higher choices when x = 180.c. Little or no difference.d. Impossible to predict.2. Consider these statements about communication in experiments.1. Chat communication is usually more effective than written simple signals (A,B, etc.).2. Friendly appeals to mutual interest and payoff dominance are effective.3. Promises often affect beliefs and actions.4. A promise is not worth the paper it is printed on.Which of these are true?a. 1 and 2b. 1 and 3c. 2 and 3d. 1, 2, and 33. A treasure is hidden under one of the four boxes below. A person gets twoguesses to find the treasure. What do you think is the most…1a) Water filtration removes contaminants that increase the risk of plant diseases from a farmer's water sources. As a result, there is a decreased risk of consumers suffering illnesses from consuming crops grown with filtered water. Due to this, economists might suggest that the use of water filtration systems in agriculture has an associated ________ externality? 1b) Draw the private cost, private benefit, social cost, and social benefit curves in the market for water filtration systems. If any of the curves are the same, label the curve as both. 1c) Is there market failure if the market runs freely? If so, is the socially optimal quantity of farmers using water filtration systems higher or lower than the market outcome? 1d) Provide a policy suggestion that would help to correct any market failures that arise due to this externality. Explain why this would be effective. 2a) Livestock and poultry farming are some of the largest contributors of ammonia emissions. Ammonia has been…Questions for Further Discussion 1. It would seem that neighbors could easily negotiate among themselves to settle problems of local externalities such as noise and unsightly land uses. Yet most communities control these problems with local laws and regula-tions. Why? 2. Suppose courts changed rules regarding burden of proof, requiring polluters to show that their emissions are harmless, rather than pollutees to show that they have been harmed. What impact might this have? 3. Suppose a community weighed each resident's solid-waste disposal when it was picked up and published the individual totals each year in the local newspaper. Do you think this would lead to a reduction in the total quantity of solid waste disposed of in the community?
- Suppose that Sonys R. Is this a private or social benefit?(Negative Externalities) Suppose you wish to reduce a negative externality by imposing a tax on the activity that creates that externality. When the amount of the externality produced per unit of output increases as output increases, the correct tax can be determined by using a demand-supply diagram; show this. Assume that the marginal private cost curve slopes upward. Negative Externalities: The Market for Electricity in the Midwest:Assume that the marginal private costs of a film producing fuel-efficient can; is greater than the marginal social costs. Assume that the marginal private benefits of a firm producing fuel efficient cars are the same as the marginal social benefits. Discuss one wags.r that the government cans fly to increase production and sales of fuel efficient cars to the socially desirable amount. Hint: the government is flying to affect production through costs, net benefits.