The Atkinson-Stiglitz Theorem

Equality-Efficiency Tradeoff

Governments intervene all the time to push the market towards outcomes they deem favorable. In general, such steering falls into one of three categories

  • Strategic Interventions - Most governments have certain strategic goals. A common one is a desire for the country to be self-sufficient in "essential" industries so that the country can support itself during crises (wars, pandemics, famines, etc).
  • Efficiency Interventions - Government frequently intervenes to correct or mitigate market failures. For instance, they might tax or regulate pollution and prevent monopolistic corporate mergers. Likewise, law enforcement fits here since its a public good that free markets can't adequately supply.
  • Redistributive Interventions - Governments typically also engage in policies to redistribute resources from some groups to others.

I don't have much to say about strategic interventions.

Assuming they follow economic theory, interventions to boost efficiency are generally uncontroversial among economists since they rely only on the assumption that people can rank possible outcomes.

This contrasts with redistributive interventions, where you need to assume (1) that people can assign numbers to outcomes and (2) that you can compare these numbers between people. I personally accept both these conditions (and assume them going forward), but many economists and philosophers do not.

Atkinson-Stiglitz

The Atkinson-Stiglitz theorem Atkinson-Stiglitz theorem assumes utilitarian logic and proves

where the utility function is separable between labor and all commodities, no indirect taxes need be employed

Put in english: given the authors' assumptions, the government need only tax labor income, though this tax can be negative (i.e. welfare) and can be based on other characteristics that predict one's ability or need (more on that later). The main point is that there is no need to tax things that aren't labor-income - that is no need to tax capital gains, corporate profits, consumption, etc.

The obvious question, of course, is what assumptions Atkinson and Stiglitz made. Let me list them:

  • Everyone has the same preferences.
  • People are rational.
  • People have utility functions.
  • Wages are fixed.
  • With regards to labor and consumption, the utility function is linearly separable. To put this another way, it assumes everyone's utility functions can be represented as $f(L) + g(c)$.

These assumptions are obviously false and there has been significant work examining what violations of these assumptions end up implying about optimal taxes and transfers. In principle, all non-excise non-labor-income taxes should be justified on violations of the above assumptions.

We'll cover these issues below.

TODO: cite 2019 United States federal budget.

TODO: Kaplow

TODO: Laroque

Exceptions to Atkinson-Stiglitz

TODO

  • separability Hellwig
  • homogenous preferenceBoadway
  • human capital Naito
  • Add a small tax on goods that higher earners wants more of (controlling for actual income). This includes savings The desirability of commodity taxation.
  • Add a small tax to goods whose consumption positively correlates with leisure The desirability of commodity taxation.
Wikipedia contributors. (2019, October 20). Atkinson-Stiglitz theorem. In Wikipedia, The Free Encyclopedia. Retrieved 01:12, April 18, 2020, from https://en.wikipedia.org/w/index.php?title=Atkinson%E2%80%93Stiglitz_theorem&oldid=922185884 Kaplow, L., 2006. On the undesirability of commodity taxation even when income taxation is not optimal. Journal of Public Economics 90, 1235–1250. https://doi.org/10.1016/j.jpubeco.2005.07.001. Laroque, G., 2005. Indirect taxation is superfluous under separability and taste homogeneity: a simple proof. Economics Letters 87, 141–144. https://doi.org/10.1016/j.econlet.2004.10.010. Wikipedia contributors. (2020, March 28). 2019 United States federal budget. In Wikipedia, The Free Encyclopedia. Retrieved 01:58, April 18, 2020 , from https://en.wikipedia.org/w/index.php?title=2019_United_States_federal_budget&oldid=947842888 Hellwig, M. F. (2010). A generalization of the Atkinson–Stiglitz (1976) theorem on the undesirability of nonuniform excise taxation. Economics Letters, 108(2), 156–158. https://doi:10.1016/j.econlet.2010.04.035 Boadway, R., & Pestieau, P. (2003). 21 Indirect Taxation and Redistribution: The Scope of the Atkinson-Stiglitz Theorem. Economics for an imperfect world: Essays in honor of Joseph E. Stiglitz, 387. Naito, H. (2007). Atkinson-Stiglitz Theorem with Endogenous Human Capital Accumulation. The BE Journal of Economic Analysis & Policy, 7(1). https://doi.org/10.2202/1935-1682.1516. Saez, E. (2002). The desirability of commodity taxation under non-linear income taxation and heterogeneous tastes. Journal of Public Economics, 83(2), 217-230. https://doi.org/10.1016/S0047-2727(00)00159-6.