David Cass: Economic theorist

In this issue of JET, we celebrate Dave Cass’s remarkable scientific career with two symposia: (1) “Economic Growth” organized by Daron Acemoglu, and (2) “General Equilibrium” organized by Yves Balasko and John Geanakoplos. Dividing the issue into two parts should not obscure the fact that Dave recognized only one economic science, one that includes growth, general equilibrium (GE), and more. Dave might begin the analysis of a problem in growth theory using the simplest (macro-style) model, but he invariably followed up in proper GE style with a general model that allows for many goods. Sometimes the results from the simple model would be confirmed, sometimes not. For example, in [6] it is shown that the analysis of optimal growth in the 1-sector model [2] is not robust to generalizations of the technology. Full disclosure: Dave and I were good friends from grad school. At Stanford, I introduced Dave to Serra House, and Dave introduced me to the Uzawa seminar. Dave’s first job was at Cowles. Mine was at MIT. We visited each other regularly for the seminars that we initiated in New Haven and Cambridge. We were Penn colleagues for more than 15 years. Dave and I worked separately and together on growth theory. We teamed up on overlapping-generations (OG) and sunspot equilibrium (SSE), which we then saw as a single project. We worked closely on several other subjects. Dave was a charter member of the JET editorial board. Dave’s first two publications were drawn from his dissertation on optimal growth. The RES article [2] is Dave’s most cited. The technology is 1-sector, neoclassical. The time-horizon is infinite. The planner maximizes the integral over time of discounted utilities. Utility is an increasing, strictly concave function of per-capita consumption. A sufficiently well-endowed economy initially consumes all of its gross output. By assuming positive discounting, Dave generalizes Ramsey [11] while also side-stepping technical problems arising from the no-discounting case. If the discount rate is positive, then the Cass planning problem is well defined. Like the Solow [14] descriptive economy, the Cass planning economy is globally stable: the capital–labor ratio tends to its modified-golden rule (MGR) value, defined (by Dave) as the capital–labor ratio at which the interest rate is equal to the labor growth rate plus the discount rate. Hence the MGR is a generalization of the Golden Rule (GR) of Phelps [10]. Dave’s companion article [3] in Econometrica is equally important. The model is the same as in [2] except that the planning horizon is finite. The discount rate can be positive, zero, or negative for the finite-horizon case. On the terminal date, a target capital–labor ratio must be met or exceeded. The optimal trajectory of the capital–labor ratio exhibits a Dorfman–Samuelson–Solow [8] turnpike property: as the timehorizon is increased, the capital–labor ratio is near its MGR value most of the time. The constraint on the terminal capital–labor ratio is the basis for the necessary transversality condition: either