Part 1 - AL-Tax

Chapter 44.2 ModelFor tractability, the discrete-type setting of Stiglitz (1982) is adopted. Hence, weconsider an economy with two kinds of agents: The workers (who are also taxpayers)and two governments.4.2.1 WorkersThe workers are characterized by their identical preferences and different abilities.The preferences can be formalized by a quasi-linear utility function U (.,.):U(Z,L) Z ν(L),where Z I T(I) is the after-tax income, with I being the before-tax income, Lis the labor supply, and T (.) is the tax schedule set by the government. The functionν(.) is the disutility of labor, satisfying: ν(0) 0, ν 0, ν(0) 0, and ν 0.Ability is denoted by ω, which is also the (constant) marginal productivity. Weassume that there are two types of workers: Skilled workers who have a high productivityand unskilled workers who have a low marginal productivity. Formally:ωωω ∈ { 1, 2},with ω 1 ω 2 .Since the labor market is competitive, wages are equal to the marginal productivitiesof workers, implying I ω k L (with i 1,2). The utility can be writtenas a function of I:⎛ I ⎞Uk I T() I ν .⎝⎜ω ⎠⎟We denote by p 1 the proportion of unskilled workers in a given region and p 2 theproportion of skilled workers in a given region. Therefore, p 1 p 2 1.There are two countries denoted by i A,B. Workers can move (once) from theirnative country to the foreign country. For a worker of ability ω k , born in country A,the cost of changing country is (1 x)σ k , with x denoting a preference parameterdepending upon the individual, x∈[0,1], and σ k a preference parameter dependingupon the individual productivity. The variable x can be interpreted as a personalmobility parameter. Therefore, a worker with x 0 is the least mobile, while aworker with x 1 is the most mobile. The variable σ k can also be interpreted as amobility parameter. The higher is σ k , the less mobile is a worker with ability ω k .The variables (x, ω) are private information: They are only known by the worker.We assume that x is uniformly distributed (for either skilled or unskilled workers)on the segment [0,1]. The whole population in each country is equal to 1.k77