Endogenous Growth and Publicly Funded Knowledge Accumulation

We investigate a centrally planned, infinite horizon, single good economy in which new knowledge is generated in a separate R&D sector with government subsidy. The rate of growth of new ideas is assumed to be linear in the amount of labor devoted to R&D. Perpetual growth in per capita output and consumption is sustained by the spillover effects of knowledge creation. Using an isoelastic social welfare function and a general production function, the unique balanced growth path is characterized and the conditions for balanced growth to take place derived. In analyzing standard balanced growth, we demonstrate that so long as physical capital and knowledge grow at some arbitrarily constant rates along an optimal time path, the two rates must necessarily be equal. Using a Cobb–Douglas production function, the dynamic evolution of the economy is explicitly described in closed form for each state and control variables. In particular, it is shown that the economy either (i) attains the balanced growth path from the initial time, or (ii) converges monotonically to the balanced growth path. An asymptotic balanced growth path along which labor input in manufacturing tends to zero in the long run is ruled out by the tranversality condition on knowledge.