Search

Formula apportionment as a way to attribute taxable profits of multinationals across jurisdictions is receiving increased attention. This paper reviews existing literature and discusses experiences in selective federal states to evaluate the economic properties of formula apportionment relative to the current international tax regime that is based on separate accounting. It highlights major advantages, such as the elimination of profit shifting within multinational groups; and it discusses new distortions and the impact on tax competition. The analysis exploits different datasets to assess the direct revenue implications for individual countries under alternative formulas. The distributional effects across countries are found to be large, reflecting major discrepancies between where profits are currently attributed and where factors of production are located or sales take place. The largest losses appear in investment hubs (i.e. countries with a disproportionate ratio of foreign direct investment to GDP), while several large advanced countries are likely to gain. Developing countries gain most likely if employment receives a large weight in the formula; they also tend to benefit, on average, from a formula based on sales by destination.

This collection of six papers provides a valuable source of material on the real-world problem of allocating objects among competing claimants. The examples given show how mathematics, particularly the axiomatic method, can be applied to give insight into complex social problems. Originally presented as an AMS Short Course, these papers could serve as a suitable text for courses touching on game theory, decision sciences, economics, or quantitative political science. Most of the material is accessible to the mathematically mature undergraduate with a background in advanced calculus and algebra. Each article surveys the recent literature and includes statements and sketches of proofs, as well as unsolved problems which should excite student curiosity. The articles analyze the question of fair allocation via six examples: the apportionment of political representation, the measurement of income inequality, the allocation of joint costs, the levying of taxes, the design of voting laws, and the framing of auction procedures. In each of these examples fairness has a somewhat different significance, but common axiomatic threads reveal broad underlying principles. Each of the topics is concerned with norms of comparative equity for evaluating allocations or with standards of procedures for effecting them; it is this focus on normative properties which suggests that a mathematical analysis is appropriate. Though game theory provides a useful tool in many of these allocation problems, the emphasis here is on standards rather than strategy and equity rather than rationality, an approach which more accurately mirrors real-world social problems.