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 + 2ln m; 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 m.R 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. ANSWER THE QUESTION BRIEFLY INCLUDE ALL THE NECESSARY INFORMATION REQUIRED THIS IS A 15 MARKS QUESTION IT IS A BIT URGENT