Public Capital, Private Capital and Economic Growth

A growth model is presented in which productive government expenditure takes the form of a stock. Private and public capital interact with each other in two ways. The first is related to the specification of the aggregate production function (Cobb-Douglas vs. CES). The second has to do with the rates of investment in the two types of capital, and arises from the law of motion of public capital. The share of public capital devoted to output production can be exogenous or endogenous. In this framework, we analyse how the optimal growth rate of the economy depends on the degree of complementarity/substitutability between the investments in the two kinds of capital, as well as on the elasticity of substitution between the two capital-inputs in the production of goods. Unlike Barro (1990), the relationship between optimal growth and the share of productive government expenditure in GDP is nonlinear and characterized by threshold-effects.