Part 1 - AL-Tax
Part 1 - AL-Tax Part 1 - AL-Tax
Chapter 44.3 AutarkyThe results presented in this section have been obtained by Stiglitz (1982). Tocharacterize the optimal tax policy, we derive a ‘revelation mechanism’. For ourpurpose, a mechanism consists of a set of specific after- and before-tax income.The government maximizes the welfare function with respect to (I 1 , Z 1 , I 2 , Z 2 )under the two incentive constraints and the budget constraint:s.t.This program can be written as:s.t.⎡ I Imax W Z1 ν⎛ ⎞1, Z2ν⎛ ⎞⎤2⎝⎜ω1⎠⎟⎝⎜ω 2 ⎠⎟⎣⎢⎦⎥ZZ12⎛ I ⎞ ⎛1I ⎞2ν Z2ν⎝⎜ω1⎠⎟⎝⎜ω1⎠⎟ ,⎛ I ⎞ ⎛2I ⎞1ν Z1ν⎝⎜ω⎠⎟⎝⎜ω⎠⎟ ,2p ( I Z ) p ( I Z) 1 1 1 2 2 2 0.max W(U 1 , U 2 ),2UU12⎛ I⎞⎛1 I⎞1ννU⎝⎜ω⎠⎟⎝⎜ω⎠⎟⎛ I⎞⎛2 I⎞2ννU⎝⎜ω⎠⎟⎝⎜ω⎠⎟⎡ ⎛ I ⎞⎤⎡p 11 I1 U1ν p I U⎝⎜ω 1⎠⎟⎣⎢⎦⎥⎣⎢12212 2 22 01 0,,⎛ν I ⎞⎤2 0.⎝⎜ω2⎠⎟⎦⎥(4.1)(4.2)(4.3)The government maximizes with respect to (U 1 , I 1 , U 2 , I 2 ). We denote by δ 1 theLagrangian multiplier associated with constraint (4.1), by δ 2 the Lagrangian multiplierassociated with constraint (4.2), and by λ the multiplier associated withthe budget constraint (4.3).79
International Taxation HandbookTo clarify and simplify the notation, we will adopt the following definitions.We define I 2 fb and I 1 fb as the two before-tax incomes that would be optimalwithout asymmetric information. Formally, they are defined by the followingequations:⎛ν⎝⎜ωI 2fb2⎛ν⎝⎜ωI 1fb1⎞ω2,⎠⎟⎞ω1.⎠⎟Proposition 1 (Mirrlees, 1971; Stiglitz, 1982). If we consider a pure Rawlsiangovernment or a quasi-utilitarian government with α p 1 /p 2 at the optimum,constraint (4.1) is binding, the labor supply (or the before-tax income) of theskilled workers is not distorted, I 2 I fb 2, and the labor supply of the unskilledindividuals is distorted: I 1 I fb 1.The assumption α p 1 /p 2 guarantees that the government wants to redistributewealth from skilled to unskilled workers. If we assume α p 1 /p 2 , then thelaissez-faire is optimal and thus fiscal competition is not an issue. If α p 1 /p 2 ,government’s preferences are biased towards skilled workers and redistributionoccurs from the ‘poor’ to the ‘rich’. Since we want to model interactions betweenredistribution and tax competition, the former assumption seems to be the mostappropriate.It must also be noticed that the optimal taxation exhibits an important feature.The labor supply of the less skilled individuals is distorted in order to reduce theincentives for the skilled to misreport their type. It shapes the form of the tax function,which cannot be convex everywhere. International mobility affects this propertywhen the moving cost is sufficiently low, as is shown in the following sections.4.4 Rawlsian governmentsFirst, we consider two Rawlsian governments. Moreover, each governmentchooses its tax function taking the tax function of the other country as given andanticipating correctly the migration induced by taxes. Equilibrium is a fixedpoint at which no worker wants to move and no government wants to change itsredistribution policy (given the policy of the other country):80
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International <strong>Tax</strong>ation HandbookTo clarify and simplify the notation, we will adopt the following definitions.We define I 2 fb and I 1 fb as the two before-tax incomes that would be optimalwithout asymmetric information. Formally, they are defined by the followingequations:⎛ν⎝⎜ωI 2fb2⎛ν⎝⎜ωI 1fb1⎞ω2,⎠⎟⎞ω1.⎠⎟Proposition 1 (Mirrlees, 1971; Stiglitz, 1982). If we consider a pure Rawlsiangovernment or a quasi-utilitarian government with α p 1 /p 2 at the optimum,constraint (4.1) is binding, the labor supply (or the before-tax income) of theskilled workers is not distorted, I 2 I fb 2, and the labor supply of the unskilledindividuals is distorted: I 1 I fb 1.The assumption α p 1 /p 2 guarantees that the government wants to redistributewealth from skilled to unskilled workers. If we assume α p 1 /p 2 , then thelaissez-faire is optimal and thus fiscal competition is not an issue. If α p 1 /p 2 ,government’s preferences are biased towards skilled workers and redistributionoccurs from the ‘poor’ to the ‘rich’. Since we want to model interactions betweenredistribution and tax competition, the former assumption seems to be the mostappropriate.It must also be noticed that the optimal taxation exhibits an important feature.The labor supply of the less skilled individuals is distorted in order to reduce theincentives for the skilled to misreport their type. It shapes the form of the tax function,which cannot be convex everywhere. International mobility affects this propertywhen the moving cost is sufficiently low, as is shown in the following sections.4.4 Rawlsian governmentsFirst, we consider two Rawlsian governments. Moreover, each governmentchooses its tax function taking the tax function of the other country as given andanticipating correctly the migration induced by taxes. Equilibrium is a fixedpoint at which no worker wants to move and no government wants to change itsredistribution policy (given the policy of the other country):80