The Weakly Concave Production Function: Theory and Estimation

A strictly concave production function is weakly concave if the rate of decline of the marginal product of capital tends to zero in the limit. This is different from concavity that is not strict, as with a linear function. With a weakly concave function there may be no price-taking profit maximization, or no golden rule steady state. A function of this type throws light on the convergence of infinitely summed discounted utility, and on the Lucas Paradox, the tendency of capital to move from poor to rich countries. Estimation reveals a function with no technical progress, in contrast to standard growth accounting.