Hayek's Triangle, General Equilibrium, and Keynesian Folly: a first step in bridging the gap between the Spanish-Austrian school and mathematical formalism

Abstract

Although this model builds on the work of Roger W. Garrison, it is quantifiably more rigorous and perhaps more useful as a result. Like Garrison’s general equilibrium model it shows the overwhelming weakness of the Keynesian macroeconomic approach, as well as the need for the re-introduction of sound money as a practical policy solution to today’s relentlessly reoccurring global financial and economic crises. If this paper makes a useful intellectual contribution to the field of economics, then it is its derivation of Hayek’s triangle from a perhaps estimable, value-added, cost function and its strengthening of Roger Garrison’s effort to bridge the theoretical gap between mainstream mathematical formalism and the Austrian business cycle developed by Ludwig von Mises, Friedrich August Hayek, and others.

Specifically, the model is divided into three components including a profit-maximization problem with a constraining value-added cost function, a utility maximization problem with a national budget constraint, and a private sector investment market whose demand and supply functions are derived from the solutions to the aforementioned optimization problems. In particular the model focuses on the term structure of capital as the key to sustained, long-term, economic growth in the absence of environmental concerns, as well as the trade-off between current and future real consumption and the effect of uninvested savings on each. After a thorough discussion of each component all three components are combined to form the general equilibrium model whose presentation is the ultimate goal of this paper.

This is part one of a two-part paper. The second part models the effects of the introduction of bank money and lays the foundation for the introduction of central banking.