This paper contains a brief review of the recent literature on economic applications of optimal control theory. It is not a comprehensive review, rather it serves to illustrate the assertion made in the title. Pursuit of an analytical solution confines the economic theorist to a narrow class of problems : termed here as the ' single differential equation model world '. Empirical economists searching for linear decision rule3 are also restricting themselves to a narrow class of problems. The adoption of general numerical algorithms would liberate both groups and this may yet prove to be the major contribution of systems theory to economics.