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Consider a world economy composed of two countries, A and B. There is a fixed world population of size H that allocates between countries on the basis of the utility levels offered. Each consumer is characterized by a parameter x that measures their attachment to country A (and by 1 – x, which is their attachment to country B). The parameter x is distributed uniformly across the population with values from 0 to 1. Let the utility level in country A of a consumer with attachment x be equal to M – x – tA, where tA is the tax rate in country A (and so utility in B is M – [1- x] – tB). Assume that there always exists a value of x that partitions the population between those who choose country A and those who choose country B.
a. For given tax levels in the two countries, determine the value of x at which the population partitions.
b. For a given partition of population, state the budget constraint for the government in each country.
c. Using the answers to parts a and b, state the decision problems of the two governments when they act as independent ‘‘leviathans’’ and attempt to maximize revenue. What is the equilibrium level of taxes?
d. What are the ancient taxes that maximize the sum of tax revenues?
e. What are the implications of these findings for tax policy?