In the analysis of the optimal level of a public good, suppose that each person's utility function is quasilinear: Ui(G) + Pi. Show that the optimal G is unique and independent of P1 and P2 if society has adequate resources. (Hint: See Solved Problem 17.3.)
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- Consider a public good, G, that is shared by Consumer A and B. Each can purchase G at the price of $20 per unit. A's marginal benefit from this public good is given by MBA-50-G. If A thinks B is getting 10 units of G, then A's optimal contribution into G will be units. On the other hand, if A thinks B is getting 20 units of G, then A's optimal contribution into G will be units. Blank # 1 Blank # 2 A/ NPublic 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.Use the general equilibrium model to derive the optimal ( efficiency ) condition for the provision of a public good. Also , discuss the constraints related to this model.
- Show the market for cigarettes in equilibrium, assuming that there are no laws banning smoking in public. Label the equilibrium private market price and quantity as Pm and Qm. Add whatever is needed to the model to show the impact of the negative externality from second-hand smoking. (Hint: In this case it is the consumers, not the sellers, who are creating the negative externality.) Label the social optimal output and price as Pe and Qe. On the graph, shade in the deadweight loss at the market output.A3) Consider production involving a positive extemality. Which one of the following statements is true? a) Without government intervention the market will produce excess supply. b) Marginal social cost is higher than marginal private cost. e) Marginal social benefit is less than marginal private benefit. d) A subsidy to producers could increase production to the socially optimum level. e) A Pigouvian tax could be imposed on the producer to achieve the socially optimum level of production.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.
- 3. Suppose the production possibility frontier for an economy that produces one public good (y) and one private good (x) is given by x*+100y =5,000 This economy is populated by 100 identical individuals, each with a utility function of the form Utility = (x,y)2 where x,is the individual's share of private good production (=x/100). Notice that the public good is nonexclusive and that everyone benefits equally from its level of production. a. If the market for x and y were perfectly competitive, what levels of those goods would be produced? What would the typical individual's utility be in this situation? b. What are the optimal production levels for x and y? What would the typical individual's utility level be? (Hint: The numbers in this problem do not come out evenly, and some approximations should suffice.)1. Consider two consumers who each choose how to split their income, m, between a private good, x, and a public good. The amount of public good consumer į buys is denoted by g, and the total amount of public good is G. The price of each good is 1 and the consumer's utility functions are as below: u, = 2 log(x,)+log(G) uz = log(x,)+ log(G) a) By referring to the utility functions, explain why goodG satisfies the definition of a public good. b) Find each individual's best-response function. c) Find the Nash Equilibrium amount of public goods purchased. d) Use the Samuelson rule to show that the level of public goods purchased in the Nash Equilibrium is inefficient. Explain your answer.Consider the market illustrated in the figure to the right. Supply curve S₁ represents the private cost of production and demand curve D₁ represents the private benefit from consumption. Suppose production of this good creates a negative externality. Show how the externality affects the market. 1.) Use the line drawing tool to draw either a new supply (S₂) or demand (D₂) curve incorporating the negative externality in production. Properly label this line. 2.) Use the point drawing tool to indicate the market equilibrium price and quantity. Label this point 'Market equilibrium'. 3.) Use the point drawing tool to indicate the efficient equilibrium price and quantity. Label this point 'Efficient equilibrium'. Carefully follow the instructions above, and only draw the required objects. Price Quantity S₁ D₁
- According to marginal analysis, in a market that experiences a positive externality, the market (private) players would ________________________ to the socially optimal output level. A. over-produce an output level relative B. under-produce an output level relative C. exactly produce an output level equal1). a).Explain why allocating property rights might help solve the inefficient outcomes generated by externalities. b).In what real-world circumstances might this approach be easier to implement and why?Consider the market illustrated in the figure to the right. Supply curve S₁ represents the private cost of production and demand curve D₁ represents the private benefit from consumption. Suppose consumption of this good creates a positive externality. Show how the externality affects the market. 1.) Use the line drawing tool to draw either a new supply (S₂) or demand (D₂) curve incorporating the positive externality in consumption. Properly label this line. 2.) Use the point drawing tool to indicate the market equilibrium price and quantity. Label this point 'Market equilibrium'. 3.) Use the point drawing tool to indicate the efficient equilibrium price and quantity. Label this point 'Efficient equilibrium'. Carefully follow the instructions above, and only draw the required objects. Price Quantity S₁ D₁ N
