## Transcribed Text

1. The government of Cloneland faces a long-standing constitutional con-
straint against levying lump-sum taxes. This is unfortunate, because
everyone in Cloneland is identical. The government must raise a given
revenue of R per person to pay tribute to a foreign colonial power that
conquered Cloneland many centuries ago. The citizens of Cloneland
consume two goods (x1 and x2) and they supply labour (L) to earn
enough to cover their consumption purchases. The Clones all have a
wage of one; producer prices of the two consumption goods are also
fixed and equal to one. The government relies on commodity taxes
on goods 1 and 2 at ad valorem (percentage) rates T1 and T2 to raise
the revenue to pay the tribute to the colonial power. The Clones have
identical utility functions given by:
= 1 1 * x I 1 * + 1 1 T2 1 , - L
where € > 0 and 1) > 0 are constant preference parameter.
(a) Determine the ordinary demand functions for the two consump-
tion goods. (10)
(b) Noting that the price of good i is (1 + Ti) because producer prices
are fixed at one, show that the own price elasticity of demand
for good 1 is and for good 2 it is -1). Show that this can
be rearranged to give
are
(1+n) x1, and similarly a(itm)
=
a(1)n)
(1+th) ? T2 for good 2. (10)
(c) We want to determine the characteristics of the relative optimal
commodity tax rates on these goods from an efficiency perspective
(i.e., which maximize V (1 + T1, 1 + T2) s.t. R = T121 + where
(-) is the indirect utility function of a representative Clonian,
and x1 and T2 are determined by the demand functions from part
(a)). To do this it is easier to determine the ratio
rather than Fif (20)
HINTS:
Have the government choose (1 +T1) and (1 + T2) (rather than
T1 and T2); this is easier and will give rise to the same insights.
From the envelope theorem note that
av
((++))
= Axc, where
X is the Lagrangian multiplier (the MU of money) from the
consumers' problem.
Use the result from part (b) that
on
a(1+n)
(1+n)
x1 for good
one, with a similar expression for good 2.
Use the two optimization conditions to determine the ratio

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