Economic Trade: a Solution to the Production Frontier of Two Economies in Trade

Abstract

It is often possible to intuit the function describing the production frontier of two economies in trade. For example, when the two individual frontiers are linear, the aggregate frontier can be rendered by an intuitive sense of the two derivatives, as will be shown below. But when the two functions are complex, no amount of judgment will suffice to sketch the aggregate production frontier. To solve this conundrum, we will employ polar coordinates and Lagrange Multipliers to yield an analytical function describing the aggregate production frontier.