Part 1 - AL-Tax

International Taxation Handbook4.2.2 GovernmentsThe governments are both benevolent. 3 They have the same preferences over theutility space represented by the same welfare function W (U 1 ,U 2 ). We will consideronly two particular cases, the Rawlsian case:WU ( , U ) min{ U, U }1 2 1 2and the ‘quasi-utilitarian’ case:WU ( , U ) αU U,1 2 1 2where α is an exogenous weight such that α p 1 /p 2 .Therefore, we restrict our analysis to welfare functions which do not dependon the proportion p 2 . The governments are only interested in gross inequalitiesbetween workers. Note that if we include p 2 in the welfare function some undesirableeffects may result: Attracting skilled workers may increase the total welfareeven if utilities remain the same.The second welfare function is not exactly the utilitarian social welfare function,it will be used to test the robustness of the results obtained in the Rawlsiancase. Introducing a real utilitarian welfare function would complicate the technicalanalysis of the model. Moreover, assuming that α p 1 /p 2 , governments havea clear behavior: Their preferences are biased towards the unskilled workers.Thus, without ambiguity, they want to redistribute wealth from skilled to unskilledworkers.The governments choose their income tax schedule noncooperatively under abudget constraint. The taxation has a unique purpose: Redistribution from the‘rich’ to the ‘poor’. The governments do not need to finance public goods.Given the two income tax schedules, T A (.) and T B (.), a worker from country Achooses to move if and only if:max⎡I maxI TA()I I TIν ⎛ ⎞⎤⎡⎝⎜ω ⎠⎟⎣⎢⎦⎥ I⎣⎢We denote by P 1 [T A (.),T B (.)] the proportion of unskilled workers who choose tolive in country B, given the two tax policies. In the same way, we denote byP 2 [T A (.),T B (.)] the proportion of skilled workers who choose to live in country B,given the two tax policies.B() II ν ⎛ ⎞⎤⎛ 1⎞x ⎝⎜ω ⎠⎟⎦⎥ ⎝⎜2⎠⎟ σ 1 .78