1. The government of Cloneland faces a long-standing constitutional...

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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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