Knowledge = Technology + Human Capital and the Lucas and Romer Production Functions

The Lucas and Romer production functions are currently the two most popular descriptions of the new growth theories in which knowledge is endogenous to economic growth and technological change. However, in both production functions the relationship between technology and human capital is implicit, and human capital is measured as an area. The latter is inconsistent with common understanding by which knowledge can be deep and wide and evolving over and in time, meaning human capital is 3D. This paper takes human capital as being 3D and frames it in Lucas and Romer production functions. Both functions bunch knowledge together, i.e., human capital and technological knowledge are strictly inseparable. Analysis and intuition find that if we take human capital to be a volume, the Lucas production function is most appropriate for use at the micro-economic level where emphasis is on production knowledge. At the macroeconomic level the Romer production function appears more reasonable, as knowledge is far more than just production knowledge. A limitation of the paper is how to actually calculate human capital as a volume and then to estimate the production functions empirically. The limitation represents a fruitful direction for future research.