Part 1 - AL-Tax

International Taxation HandbookTedious but straightforward computations show that:● If σ 2 σ, the countries adopt the following policy: I 2 I fb 2, I 1 I fb 1,UI2 2 fb 2σ fb 2 ω1 I ν () ,andIt implies that skilledworkers pay an income tax T 2 σ 2 and unskilled workers receive a transferp2T1 σ 2.p1● If σ 2 σ, the equilibrium policy implies that T 2 σ 2 .Appendix C: Proof of Corollaries 1 and 2Proofs of Corollaries 1 and 2 are similar to the proof of Proposition 2.Appendix D: Proof of Proposition 3The program of government B:max αU B1 U B2 ,s.t.⎛ I ⎞ ⎛B I ⎞1 B1UB1ννUB2 0,⎝⎜ω1⎠⎟⎝⎜ω2⎠⎟ ⎛ I ⎞ ⎛B2I ⎞B2UB2ννUB1 0,⎝⎜ω2⎠⎟⎝⎜ω⎟1⎠⎡ ⎛ ⎞pP U U U I B11 1( A1, B1)B1ν ⎝⎜ω 1⎠⎟ ⎤ ⎡⎛ I BIB1 p2P2( UA2, UB2)UB2ν ⎣⎢⎦⎥⎝⎜⎣⎢ωThe Lagrangian of the problem:UI1 1 fb 1σ fb 1 ω1 I ν () .⎡ ⎛ I ⎞ ⎛ I ⎞B BL αUB UB δ1 11 2 2 UB1ννU⎝⎜ω1⎠⎟⎝⎜ω2⎠⎟⎣⎢⎡ ⎛ I ⎞ ⎛ ⎞ ⎤B2δ1 UB2ν ν I B2U⎝ ⎜B1ω2⎠⎟⎝⎜⎠⎟⎣⎢ω1⎦⎥⎛⎡ ⎛ I ⎞ ⎤ B1pP 1 1( UA1, UB1)UB1ν IB1⎢ ⎝⎜ω 1⎠⎟⎝⎜⎣ ⎦⎥⎛I B2pP 2 2( UA2 , ⎡UB2)UB2 ν ⎞ ⎤⎞ I ⎝⎜ω 2⎠⎟ B2 ,⎣⎢⎦⎥⎠⎟where λ, δ 1 , and δ 2 are the multipliers associated with the constraints.22⎞ ⎤I ⎠⎟B2 0.⎦⎥B2⎤⎦⎥92