A model of growth with living capital

Acknowledging the economic role of knowledge, education, training and health, can preserve and make them thrive without assuming that preferences depend on any of them. In this paper we will define living capital as the aggregate of all these factors, and then, total capital as the sum of physical and living capital.

In a planned economy, we find that the optimal sequence of total capital is always monotonic. Depending on the productivity of total capital, three different regimes hold: bounded growth; asymptotically balanced unbounded growth or unbalanced unbounded growth.

At the early stages of development the economy optimally devotes all its investment effort to increase the stock of physical capital and only physical capital. As the economy develops, it will start involving living capital in production. In the first regime, total capital converges to a steady state with a positive stock of total capital, which is larger than the one without living capital. In the second regime, growth becomes unbounded, and consumption grows at a constant rate. Total capital grows at the same rate but only asymptotically. In the third case, living capital is used increasingly from the beginning. Once the economy is sufficiently rich, physical capital starts growing faster than living capital.

To close, we consider a market economy with externalities from the living. In this scenario, if the government levies taxes to finance the accumulation of living capital and implements exactly the optimal sequence of living capital as in the planner’s program, then the equilibrium market prices exactly decentralize the planner’s solution.