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

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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
xi 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=lnxR+2lnm;
UP=lnxP+lnm
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 BREIFLY INCLUDE ALL THE NECESSARY
INFORMATION AND STEPS REQUIRED THIS IS A 15 MARKS QUESTION DIVIDED
INTO TWO PAERTS AB AND CDE. IT IS A BIT URGENT.