Jones model

For a single company i According to the following modeling applies to the emergence of new ideas or design instructions:

${\displaystyle {\dot {A}}_{i}=\delta \cdot A(t)^{\phi }\cdot L_{A}(t)^{\lambda -1}\cdot L_{A_{i}}(t)}$

With

${\displaystyle L_{A}}$:: Number of employees in the research sector

${\displaystyle A}$: Technology level

${\displaystyle {\dot {A}}}$ refers to the derivation of the variables ${\displaystyle A}$ A after the time, so ${\displaystyle {\dot {A}}={\frac {\partial A(t)}{\partial t}}}$

where the parameters take the following values: ${\displaystyle 0<\lambda <1;\phi <1}$, For parameter values of ${\displaystyle \lambda =\phi =1}$ results in the Romer model (${\displaystyle {\dot {A}}=\delta \cdot A\cdot L_{A}}$). After aggregation across all companies results:

${\displaystyle {\dot {A}}=\delta \cdot A(t)^{\phi }\cdot L_{A}(t)^{\lambda }}$.

Here the parameters have the following meaning:

• ${\displaystyle \lambda }$ lambda restricts the effect of additional labor input in the research sector. Although more researchers are producing more ideas , each researcher is contributing less and less. This relationship is also called standing-on-shoes effect (step on your feet, see also yield law ). This parameter reflects a possible negative externality of the duplication. For a single company, however, this problem does not exist because within a research department, all researchers know about the work of their colleagues.
• ${\displaystyle \phi <0}$: A negative value aims at giving only finitely many potential new ideas for a given time. This case is also referred to as a fishing-out effect: over time, the relatively "simple" inventions are made first; Today, it is becoming increasingly difficult to develop a new drug.
• ${\displaystyle \phi =0}$: Here, productivity in the research sector would be independent of existing knowledge. For example, a physicist should be able to develop the same new ideas, whether he lives today or 100 years ago (an unrealistic case).
• ${\displaystyle \phi >0}$: Describes in principle a positive externality and the case encountered in reality. The current state of the art is to a certain extent involved in research. The standing-on-shoulders effect is only weakened compared to the Romer model.

In the Jones model, growth in steady state is given by:

${\displaystyle {\frac {\dot {\hat {A(t)}}}{\hat {A(t)}}}=0\quad \Leftrightarrow \quad {\hat {A(t)}}={\frac {\lambda \cdot n}{1-\phi }}}$ n for the growth rate of persons working in the research sector.

• Daron Acemoglu (2008). Introduction to modern economic growth. Princeton: Princeton University Press. pp. 488/489.

• Jones model - Article in the Gabler Wirtschaftslexikon.