Consider an economy with three people and two goods: private good (x) and public good (y). Suppose that marginal rate of transformation is 1. (one unit of private good is needed for the production of one unit of public good). The utility functions of the individuals are given below: U₁ = 2y¹/2 + x₁ U₂ = 4y¹/2 + x₂ U₂ = 6y¹/² + x3 What is the optimal level of public good?
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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 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.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.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.
- 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.Which of the following is true if good x is an externality exhibiting good. If consumption of good x by person 1 exhibits a positive externality, then consumption of good x by person 2 must also exhibit a positive externality. Consumers consume too much good y relative to what is socially optimal. Consumers consume too much good x relative to what is socially optimal. Equilibrium consumption of the good is not Pareto efficient.Which of the following statements is correct? Select one: a.In models of network goods with positive externalities, no consumption is always an equilibrium. b. The equilibrium in the hotelling model when both firms have the same location is for the firms to set their prices equal to their (constant) marginal cost even if their marginal costs are different. c. If all firms start wiht the same techonology, under both minor and drastic innovations the inovator firm is only one firm producing after the innovation. d. The Schumpeter hypothesis establishes that competitive firms have higher capacity to produce R&D than monopolies.
- Consider two consumers (1; 2), each with income M to allocate between two goods. Good 1 provides 1 unit of consumption to its purchaser and units of consumption to the other consumer. Each consumer i, i = 1; 2, has the utility function is consumption of good 1 and is consumption of good 2. a. Provide an interpretation of α. b. Suppose that good 2 is a private good. Find the Nash equilibrium levels of consumption when both goods have a price of 1. c. By maximizing the sum of utilities, show that the equilibrium is Pareto-ancient if α = 0 but incident for all other values of α. d. Now suppose that good 2 also provides 1 unit of consumption to its purchaser and a, 0 ≤ α ≤ 1, units of consumption to the other consumer. For the same preferences, find the Nash equilibrium and show that it is ancient for all values of α. e. Explain the conclusion in part d.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?Consider agent A with (inverse) demand curve for the public good Pa = 60 - 2Qa and agent B with inverse demand Pb = 90 - 5Qb , where prices are measured in £ per unit. The marginal cost of producing the public good is £10 per unit. What is the Pareto efficient level of the public good? Explain. Illustrate in a graph.
- which statement is true In the absence of market power and externalities, efficiency is achieved in a market when the sum of producer surplus and consumer surplus is maximized. The benefit received by sellers in a market is measured by producer surplus and producer surplus is calculated as the amount sellers receive for their product minus the cost of production. In a market, the marginal buyer is the buyer who would be the first to leave the market if the price were any higher. Moving production from a high-cost producer to a low-cost producer will decrease total surplus. Suppose the United States changed its laws to allow for the legal sale of a kidney and the government allowed a free market in organs for transplant then there would be a decrease in the price of a kidney and an increase in the shortage of kidneys for transplant. Total surplus in the market is the summation of consumer surplus and producer surplus and it is maximized at the market equilibrium in the absence of…Public Goods. Suppose a neighborhood in Segovia’s central business area is deciding how many fountains they want to see in the main avenue. There is a first group of 20 neighbors and each has a demand Q = 20 − P for fountains. There is a second group of 5 people, and each has a demand Q = 20 − 2P for fountains. The cost of building each fountain is 225. How many fountains are socially optimal? Fountains are public goods. Hint: To obtain the SMB, please first transform the demand functions into “public goods’ valuations” (“isolate P”) and then multiply them by the amount of neighbors per group. Then you can proceed with the vertical summation.(Optimal Provision of Public Goods) Using at least two individual consumers, show how the market demand curve is derived from individual demand curves (a) for a private good and (b) for a public good. Once you have derived the market demand curve in each case, introduce a market supply curve and then show the optimal level of production.