- The Town Of Khatmal Has Two Citizens A Rich Citizen R And A Poor One P It Has A Road That Leads To The Neighbourin 1 (84.17 KiB) Viewed 27 times
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.
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INFORMATION AND STEPS REQUIRED IT IS A 15 MARKS QUESTION DIVIDED
INTO TWO PARTS AB AND CDE IT IS A BIT URGENT
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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 = ln xR + 2lnm; Up = ln xp + ln m 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 mr and mp to be equal or different, and give two reasons for your answer. B.Solve mathematically for m² 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.