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The Capital Asset Pricing Model as Modern Austrian Business Cycle Theory

According to Austrian macroeconomic theory, capital accumulation today generates supply tomorrow. Will that supply match tomorrows demand? In this paper we study this question in a multi-good and risky environment with an efficient financial system. Towards this end we develop a model based on the Capital Asset Pricing Model (CAPM), Rational Expectations, and Linear Homogeneous Production Functions. Within this framework we show how the financial system in the form of CAPM allocates resources across the different sectors in the economy so as to maximize the ratio of expected returns to a measure of risk like the standard deviation of returns for some initial time period t=0. In t=1 a Linear Homogeneous Production Function subject to a random productivity shock determines actual output and the structure of production. The link between t=0 and t=1 is Rational Expectations, the assumption that the subjective probability distribution in t=0 on which real investment decision are made is equivalent to the objective distribution generating the actual output/income in t=1. If total output is more (or less) than expected in t=0, we have a cyclical expansion (or recession) the magnitude of which depends on the spread of the subjective probably distribution in t=0. With this model we discuss: 1) monetary policy under a full reserve banking system with Central bank digital accounts for all; 2) an all-inclusive transaction tax to substitute for the U.S. present tax system; 3) the trade-off between economic growth and the cyclical volatility of the economy; and 4) the advantages and disadvantages of trade deficits.