Problem 1 [15 points] The town of Khatmal has two citizens: a rich citizen (R) and a poor one (P). It has a road that le

[answerhappygod]

Problem 1 15 Points The Town Of Khatmal Has Two Citizens A Rich Citizen R And A Poor One P It Has A Road That Le 1 (66.33 KiB) Viewed 40 times

Problem 1 15 Points The Town Of Khatmal Has Two Citizens A Rich Citizen R And A Poor One P It Has A Road That Le 2 (40.75 KiB) Viewed 40 times

Problem 1 [15 points] The town of Khatmal has two citizens: a rich citizen (R) and a poor one (P). It has a road that leads to the neighbouring town; however, this road needs to be cleaned everyday, otherwise ash from the neighbouring thermal power plant settles on the road and makes it impossible to use it. Cleaning the road costs 1/- every day. R has to go to work in the neighbouring town and has to use this road, whereas P works in Khatmal and therefore do not use this road much. The daily income of R is 15/- and that of P is 10/-. Let X, denote the private good consumed by each citizen and m denote the amount of cleaning service provided. The cost of the private good is also 1. The utility functions of the two citizens are given by: UR = InxR + 2lnm; Up = Inxp + Inm a. Set up the maximization problems for R and P. Let me and mp denote the amount of road cleaning demanded by R and P, respectively. Without doing any math, describe whether you expect me and mp to be equal or different, and give two reasons for your answer. b. Solve mathematically for me and mp. What is the resulting utility of R and P? What is therefore the social surplus in the economy? The government of Khatmal is concerned that there is a market failure in the provision of road cleaning services and is considering a public provision option financed by taxes on R and P. However, the tax collector is unable to distinguish between R and P as it is each for R to disguise as P. Hence, the government is restricted to taxing everyone the same amount to finance the cleaning. I.e., if m units of cleaning are provided, everyone is charged m/2 in taxes. Page 1 of 3 c. What amount of daily cleaning should the government provide to maximize social surplus (assume the government maximizes the sum of the utilities of R and P)? What would be the
c. What amount of daily cleaning should the government provide to maximize social surplus (assume the government maximizes the sum of the utilities of R and P)? What would be the resulting utility of R and P under this level of provision? Discuss any differences from the utilities in part b above, and also comment on any changes in social surplus. d. Does the sum of the individuals' marginal rates of substitution equal the price ratio? Why do you think? e. Now suppose that it is possible to distinguish between R and P, thus allowing differential taxation. Now how much of m does the government provide, and how is the tax burden divided? Calculate the sum of the individuals' marginal rates of substitution, and compare with part d above. Also calculate resulting individual and social surplus.