Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively. a) Derive her utility at the optimal consumption point as a function of prices and income. b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for? c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy? d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?
Suppose a consumer’s preferences over two goods x_1 and x_2 are given by u = Square root (X_1,X_2). Her income is M and the two goods cost p1 and p2 per unit respectively.
a) Derive her utility at the optimal consumption point as a function of prices and income.
b) Now suppose the government imposes a proportional tax t on the value of the good x_1 (such as VAT). If the consumer approaches the government for income compensation to remain as well off as before the tax (i.e. compensating variation in income), how much money would she ask for?
c) If instead, the government decides to maintain consumer’s utility level not through lump-sum transfer but by introducing a proportional subsidy S on the price of good 2, then what should be the size of the subsidy?
d) Based on your answer in part c) discuss how much would it cost for the government to introduce both a tax and a subsidy at the same time? Can you think of any situation when this policy would make sense?
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