Simulations

Indicators

You can observe four graphics which describe the evolution of the industry.

1. Evolution of the market price in time ;

2. Innovation and the diffusion of the technologies (the ratio of Average Productivity to Maximal Productivity$\,\leq1$) ;

3. Herfindal concentration index for the allocation of capital in the industry (in equivalent firm number) ;

4. Herfindal concentration index of market shares (in equivalent firm number);

5. Total capital stock of the industry;

6. Total profits of the period (comparison of innovators with imitators).

Only the concentration of capital needs some explanation:

$$\mathcal{K=}\frac{\sum\limits_{j}K_{j}^{2}}{\left( \sum\limits_{j} K_{j}\right) ^{2}},$$ (3)

where $K_{j}$ is the capital stock of firm $j$.

This indicator gives an equivalent number of firms as if each of them had the same part of capital stock.

We have $1\leq\mathcal{K}\leq N$ where $N$ is the number of active firms in the industry.

The higher is this indicator, the more evenly balanced is the distribution of capital stock between firms.

This is an application of the Herfindall index to the capital stocks and summarizes the inequalities in the distribution of the capital stock.

Initialisation of the original model

The initial capital stock of firms is fixed in order to imply zero net desired investment.

Only an innovation in the industry can incite firms to modify their capital level at this stage.

The initial level of productivity is fixed high enough to let firms have positive profits and invest in R&D.

Initial values of $r_{in}$ and $r_{im}$ imply a probability of imitation of $5\%$ and a successful innovative draw has a chance of $2\%$.

Investment increases the capital stock, and hence, the probabilities of successful draws.

We have also $\delta=0.03$ and two cases for $b:$ $b=1$ and $b=2.5.$

These elements correspond to the following values:

$$%% \begin{tabular}[c]{ccc}\hline & \multicolumn{2}{c}{{\small Num... ...all0.16}\\ $\mathcal{D}$\ & {\small 67} & {\small 67}\\ \hline \end{tabular}$$

Java version

$\longrightarrow$ http://yildizoglu.u-bordeaux4.fr/nworig/nelwin.html
           or
$\longrightarrow$ http://cournot.u-strasbg.fr/yildi/nworig/nelwin.html

for the Java version of the model.

The parameter table can be used to setup different elements of the model:

• Unit capital cost $\left( c\right)$;

• Coefficient of the demand function (Dem. coeff. $-\mathcal{D}$)

• Elasticity of demand $\left( \eta\right)$;

• Initial productivity (initial prod.$-A_{0}$) of firms in the industry;

• Depreciation rate of the capital $\left( \delta\right)$;

• Initial probability of an innovative draw (Pr. innovation)
  $\rightarrow r_{in}$;

• Initial probability of an imitative draw (Pr. imitation)
  $\rightarrow r_{im}$;

• Standard deviation of the normal distribution from which a new productivity is drawn after an innovation (Dispersion $-\sigma_{2}$);

• Credits from the banking sector (Bank$-b$);

• Number of periods;

• Number of innovating firms;

• Number of pure imitators.