Describe and explain Samuelson’s general equilibrium model with one pure public good and one private good using the diagrammatic framework. Derive the efficiency condition which emerges.
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Describe and explain Samuelson’s general equilibrium model with one pure public
good and one private good using the diagrammatic framework. Derive the
efficiency condition which emerges.
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- Use the Lindahl Equilibrium model and discuss how this approach can be used to provide public goodsConsider 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?Define a public good and, using a graph, explain the equilibrium of a pure public good.
- 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.Suppose the marginal cost of a pure public good increases as more is purchased by a community. Prove that the Lindahl equilibrium will result in a budget surplus at the efficient annual output of the pure public goodThe accompanying table relating to a public good provides information on the prices Young and Zorn are willing to pay for various quantities of that public good. These two people are the only members of society. Determine the price that society is willing to pay for the public good at each quantity of output. If the government’s marginal cost of providing this public good is constant at $7, how many units of the public good should government provide? Why not less? Why not more?
- Illustrate the efficient provision of a public good regarding partial equilibrium analysis.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.Can you answer with explanation and show formula. The accompanying table relating to a public good provides information on the prices Young and Zorn are willing to pay for various quantities of that public good. These two people are the only members of society. Determine the price that society is willing to pay for the public good at each quantity of output. If the government’s marginal cost of providing this public good is constant at $7, how many units of the public good should government provide?
- Consider an economy consisting of three people – A, B, and C. Person i (where i is A, B, or C) has the utility function where z is the quantity of public good provided and ci is person i’s consumption of private goods. Person i’s income yi is divided between consumption of the private good and his contribution to the financing of the public good. Person i’s contribution is the product of his “tax price” ti and the quantity of the public good, so Person A’s income is 90, person B’s income is 120 and person C’s income is 150. Twenty units of private good must be given up to produce each unit of public good. Find the Lindahl equilibriumSuppose you wish to reduce a negative externality by imposing a tax on the activity that creates that externality. On a supply-demand diagram, please show the tax needed to correct the externality if the amount of externality produced rises as output rises. Assume that the marginal private cost curve slopes upward.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.