Question

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 (21 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 71 and T2 to raise the revenue to pay the tribute to the colonial power. The Clones have identical utility functions given by: ;- 1-I* 1 IT*X2 where e > 0 and n > 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 + i) because producer prices are fixed at one, show that the own price elasticity of demand for good l is-and for good 2 it is -1. Show that this can be rearranged to give a = - 43*1, and similarly atz) = -(+) 32 for good 2. (10)

Answer 1

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tha the Picc of goal iis C+) beaaue b Nothng Praduco ane Aud . Ahe oun Pice clahciy ot demand for gd is-E and fo garl at 9-n. shoo the ea rangid and simikay to give C) 2 foq good a. (0). Heu Noco -E Pa n г GR1 Prom C1 144 FYom (a) n tJ2