There are two individuals, and each is endowed with 12 units of the private good. Let U₁ = 6x +y₁, and U₂ = 6x + y₂. If g(x) = 2x² then the Samuelson condition is satisfied by x = 12. But 12 units of the public good require 72 units of the private good as input. The economy has only 24 units of the private good. What has gone wrong with our reasoning?
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- Consider an economy with n consumers, one private good and one public good. We think of the private good as "all other goods," and measure it in terms of money. There aren individuals in the economy with utility functions Ui(xi , y) = ai In y + xi , where y is the public good, xi is the private good consumed by individual i = 1, . .., n, and 0 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.An economy consists of two individuals, A and B and two goods, a private good, which is called good 1, and a public good, which is called good 2. Each individual i = A, B is endowed with 24 units of time, which can be used to produce an amount of a private good at a labour cost of a units of time, and an amount of a public good at a labour cost of 2x units of time. Individual i's utility function is given by u(xi, x2) = (xi)¹/2 (g)¹/2, for both i = A, B and where g denotes the aggregate provision of the public good, i.e. g = x2 + x2. (a) Derive the allocation that maximises utilitarian welfare (i.e. the sum of both individ- ual's utility functions). 3 (b) Suppose both individuals decide on provision of feasible bundles (x,x) and (x,x) simultaneously and have full information about the other individual's utility function. Derive the Nash equilibrium of the noncooperative game. (c) Explain concisely (max three sentences) why there is usually under-provision of the public good (you can…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 is 1 and the price of the public good is 10. Each person has a total income of 1,000O. Find the Pareto efficient amount of G in this economy.
- )In Islandia, all goods and inputs are bought and sold at a central market where there is a single price for each product. Islandia has a large number of citizens who are all utility-maximizers and all goods are produced and sold by profit-maximizing firms, none of which is large enough to influence the prices at the market. Do you know whether the mix of goods being produced and consumed in Islandia is efficient? If so, explain whether or not it is and how the information you know guarantees that the mix is efficient. If not, identify what additional information would you need to know to tell whether the mix is efficient and explain why this information is needed.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.)How Bergson-Samuelson Social Welfare Function used in a model that considers a society's desire for both Pareto optimality and fairness, Mention all necessary assumptions and specify the conditions that ensure a general equilibrium and social welfare
- The graph below depicts a schedule of two individual marginal benefit curves (MB1 and MB2) as well as the social marginal benefit (SMB) curve. This good is non-rival in consumption and non- excludable in use, so the SMB was constructed using vertical summation of individual MB curves. Which of the following are TRUE? $20 $15 $13 a b d e Q1 Q2 Q3 SMB MB2 MBI Quantity O b. If the social marginal cost is $20 per unit, then Q2 is the output level that maximizes social net benefit. O e. None of the above are true. O d. Only b and care true OC. The social marginal benefit of the Q1st unit is $28. O a. It must be the case that Q1+02-03,Suppose there are three consumers of a public good with the following marginal benefits of consumption related to the quantity of the public good provided: Consumer 1: MB1 = 5 – 2Q Consumer 2: MB2 = 4 – Q Consumer 3: MB3 = 3 – Q Calculate and draw the total marginal benefit function of the public good in a fully labelled diagram. If the marginal cost of producing the public good is MC = 2Q, what is the efficient quantity and how much should each consumer contribute to its provision if it were to provided at the efficient level (assuming the non-rival and non-excludable problems could be resolved)?Suppose that you are president of the student government, and you have to decide how to allocate a $20,000 fund for guest speakers for the year. Conan O’Brien and Will Ferrell each cost $10,000 per appearance, Stephen Colbert costs $20,000 per appearance, and former economic advisers to the government charge $1,000 per lecture. Explain the economic problem of choice and scarcity in this case. What issues would you consider in arriving at a decision?
- QUESTION 16 16. Entering patient health care data into a database accessible to health care professionals across the medical profession and a wide region increases the ability to apply artificial intelligence to diagnostics and treatment of diseases. This is an example of a) Negative consumption externality. b) Positive consumption externality. c) Negative production externality. d) Positive production externality. QUESTION 17 17. Which of the following is an example of a negative consumption externality? a) water pollution impact of a paper plant b) honey production and pollination of fruit trees c) second-hand smoke d) vaccination against a communicable disease e) none of the aboveThe depletion of the ozone layer is attributed to the emission of Chlorofluorocarbons (CFCs). Before 1990, the use of coolants in refrigerators such as Freon released a significant amount of CFCs. Given the above scenario, is the equilibrium level of refrigerators produced prior to 1990 in the market “too much” or “too little” compared to the social optimum? Explain why this occurs. Support your answer by drawing the private and social, marginal cost and marginal benefit curves for refrigerators. Identify the deadweight loss if any exists. Identify a regulation that the government can use to achieve the socially optimal level of refrigerators. Explain how this regulation works. Explain how the Coase theorem could hypothetically work to achieve the optimal level of CFCs emissions in this context. Enumerate at least one major drawback that hinders the creation of a market for CFCs without any third party regulators in the real world. Assume that the marginal savings for refrigerator…Given a MC function and a MB funtion for a good (e.g., MC = 10 + Q, MB = 5 - Q ,how do we derive an efficient allocation for the good? What if we add a per-unit externality (e.g., set to some constant =5 per unit emissions from production)?