The Infeasibility of Free Trade in Classical Theory: Ricardo's Comparative Advantage Parable has no Solution

Abstract

In this paper, formal models of Ricardo's comparative advantage parable, which include general forms of consumer price response behavior, are constructed from a detailed textual exegesis of Ricardo's story. Using these models, the comparative advantage parable is shown to be mathematically over-determined and therefore generally unsolvable. To reinforce this conclusion, a numerical solution is derived for a constant elasticity version of the model. A necessary condition for the existence of a solution to the constant elasticity model is that two price elasticities of demand must be functions of the other two price elasticities of demand. General formulas are derived expressing this dependency. When realistic elasticities for wine are set, the model can only be solved if Portuguese demand for English cloth is unrealistically elastic. This demonstrates that sustainable and mutually beneficial trade between England and Portugal can only be realized through managed trade.