Distributing the Gains from Trade With Incomplete Information

We argue that the incomplete information which the government has about domestic agents means that tariffs become an optimal instrument to protect them from import competition. We solve for the optimal government policies. subject to the political constraint of ensuring Pareto gains from trade, the incentive compatibility constraint, and the government's budget constraint. We find that the optimal policies take the form of nonlinear tariffs, so that both buyers and sellers of the import face an effective price which exceeds its world level. We find that the tariffs are never complete, in the sense of bringing prices (or all individuals back to their initial level. Rather, it will always be possible to make some individuals strictly better off than at the initial prices, while ensuring that no persons are worse off.

Negotiated Trade Restrictions with Private Political Pressure

In this paper we consider a home government with political pressure to restrict trade, at the expense of foreigners. The foreign country is compensated with an income transfer, which can be thought of as a portion of the tariff revenues or quota rents. In this setting the two countries should negotiate over the level of tariff and transfer of rents, depending on the level of political pressure at home. However, if this pressure cannot be directly observed abroad, then the home country may have an incentive to claim arbitrarily high political need and seek corresponding high trade barriers . We resolve this problem by determining incentive compatible trade policies, in which the home government has no incentive to overstate (or understate) the political pressure for protection.

Designing Policies to Open Trade

In this paper we consider recent proposals to auction U.S. import quotas. using the funds so obtained to encourage relocation out of the protected industries. We argue that the information available to the government, or lack thereof, is a critical factor in understanding these policies. In a world or full information, it makes little sense to use auction quotas rather than tariffs. Similarly, it is unclear why an elaborate program of temporary protection is needed, rather than immediately opening trade and compensating people with an income transfer. When the government has Limited information, however, these policies become quite sensible and may even be optimal.

Formalizing the Solution to the Cap Set Problem

In 2016, Ellenberg and Gijswijt established a new upper bound on the size of subsets of F^n_q with no three-term arithmetic progression. This problem has received much mathematical attention, particularly in the case q = 3, where it is commonly known as the cap set problem. Ellenberg and Gijswijt\u27s proof was published in the Annals of Mathematics and is noteworthy for its clever use of elementary methods. This paper describes a formalization of this proof in the Lean proof assistant, including both the general result in F^n_q and concrete values for the case q = 3. We faithfully follow the pen and paper argument to construct the bound. Our work shows that (some) modern mathematics is within the range of proof assistants