This paper is an exploration of numerical optimization as it applies to the consumer choice problem. Suggested algorithms are intended to compute solutions to the Marshallian problem, and some can extend to the dual given the suggested modifications. Each method seeks to either weaken the sufficient conditions for optimization, converge to a solution more efficiently, or describe additional properties of the decision space. The purpose of this paper is to explore constrained quasiconvex programming in a less complicated environment by design of Marshallian constraints.

This paper provides a revised accounting system for the U.S. current account that accounts for the U.S. foreign intangible capital stock, capitalizes U.S. intangible investments, and applies a constant average real 4.2% return on both quarterly tangible and intangible investments. This system also adjusts the net foreign asset position for transfer pricing and considers economic net exports rather than misreported accounting net exports. The 2 primary implications of our system is that the U.S. is in a trade surplus, and that the U.S. net foreign asset position is large. Applying a 4.2% constant average real return on foreign investments and considering economic profits instead of accounting profits eliminates the discrepancy between U.S. and foreign returns on foreign direct investment. This system solves how the U.S. can appear as a large net debtor while receiving positive income from foreign factors. The answer is that the U.S. is not a large net debtor.