Quality-adjusted productivity gain in the propagation of innovation

We introduce a class of production function whose inputs and outputs constitute multiples of quality and quantity. Under the efficiency unit approach, we precisely reduce innovation regarding qualitative and quantitative improvements of production to the measurement of quality-adjusted productivity gain. We then consider a system of compatible unit cost functions inclusive of such productivity improvements in any industry, for which we can solve for the ex-post equilibrium to examine the technological structural propagation. In this way, we can evaluate any given innovation with respect to its social welfare gain. We use this framework of multi-industry multi-factor production to study effective industry-wise research and development investment allocations.