Models of Energy Use: Putty-Putty versus Putty-Clay

In this paper, we build a version of the putty-clay model in which there is a large variety of types of capital goods which are combined with energy in different fixed proportions. Our principal contribution is to establish easily checked conditions under which the problem of solving for the equilibrium of the model economy reduces to a dynamic programming problem with only two endogenous state variables, regardless of the number of different types of capital goods that are allowed. In appropriate applications, this result allows us to avoid the 'curse of dimensionality' that typically plagues attempts to analyze the dynamics of economies with a wide variety of capital goods and binding non-negativity constraints on investment. We apply these results to study the equilibrium dynamics of value-added, investment, wages, and energy use in a simple model of energy use with putty-clay capital.