For instance, if the inputs remain the same in a factory but the existing machinery is adjusted to render greater output, the productivity of capital is said to rise. In economic studies of technical change, a concept called total factor productivity is often used. This represents the productivity that can be associated with all of the inputs involved in production. In many cases, total factor productivity is preferable for looking at the effects of technical change, because separating out productivities among inputs is often difficult or ambiguous. The traditional method for analyzing productivity in economics has been to use a mathematical construct, called a production function, to interrelate the quantity of output produced with quantities of inputs utilized - primarily capital and labor.
Productivity is said to increase when more output can be produced with the same amounts of inputs.
These studies focus on particular types of research, such as academic, government supported, and private, and on types of economic effect, such as cost reduction and quality improvement to the organization performing the research, as well as spillover effects that benefit those who did not pay for the research. He found the latter effect to be greater, on average, across all industries. It should be noted, however, that the precise magnitude of these returns cannot be measured without the use of simplifying assumptions in the analysis. This is not to say that every research project has a high, or even a positive, rate of return, but portfolios of scientific research projects selected for analysis have the rates of return cited above. These rates differ, depending on the time period being studied, the type of data, and the analytical method employed.