A General Equilibrium Expression of the Paradox of Thrift

A model is presented which is derived from some observations of Keynes on the nature of capital. The allocation of investment is analyzed in two economies with random demand shocks which are identical except for the types of markets. In the first, the combination of an asset and forward markets realizes the complete set of markets. In the second, the forward markets are replaced by spot markets. Consumers and entrepreneurs are rational and markets clear. A clear definition of the paradox of thrift is proposed and its existence is proven. The substitution of spot markets for forward markets generates fluctuations of the aggregate variables. The equilibrium with fluctuations is not always a constrained Pareto optimum.