3.2.4. Industrial Dynamics

(1) Entry of Production Firms

Production firms in the fuel ethanol industry are divided into two types: one is the traditional technology firm which mainly uses traditional production technology and the other is the new technology firm which mainly uses new production technology. Let <sup>Δ</sup>1*n<sup>t</sup> f t* denote the number of traditional technology firms entering in period *t*. According to the previous section, it is related to Γ*t f t*−1 and *nt f t*−1, which indicate the cost to revenue ratio of traditional technology firms and the number of firms in the industry of the last period respectively, as well as the random distribution function *ps*. In addition, in the fuel ethanol industry, the entry of traditional technology firms is also restricted by the shortage of feedstocks. Then, we can describe the number of traditional technology firms as follows:

$$
\Delta\_1 n\_t^{tf} = f\_1(\Gamma\_{t-1'}^{tf}, n\_{t-1'}^{tf}, m\_{t-1'}^{t}, p\_s) \tag{10}
$$

where *m<sup>t</sup> t*−1represents the demand for traditional feedstocks in the last period.

There are two kinds of new technology firms entering in period *t* in the fuel ethanol industry: one is transformed from R&D firms, which is denoted by <sup>Δ</sup>1*n<sup>n</sup> f t* ; the other includes newly established firms that use new technology, denoted by the parameters' values <sup>Δ</sup>2*n<sup>n</sup> f t* . According to the above definition, <sup>Δ</sup>1*n<sup>n</sup> f t* is related to the number of R&D firms in the last period, *nrd t*−1, its production costs in the last period, *crd i*,*t*−1, and the highest production cost in the last period, *Max*{*c<sup>t</sup> <sup>i</sup>*,*t*−<sup>1</sup>}, which can be shown as:

$$
\Delta\_1 n\_{t}^{nf} = f \natural (c\_{i, t-1}^{rd}, \,\,\, \text{Max} \{c\_{i, t-1}^t\}, \,\, n\_{t-1}^{rd}) \tag{11}
$$

<sup>Δ</sup>2*n<sup>n</sup> f t* is related to the cost of new technology firms in the last period, Γ*<sup>n</sup> f t*−1, to the revenue rate, the number of new technology firms in the industry, *nn f t*−1, and random distribution function, *ps*, so:

$$
\Delta\_2 n\_t^{nf} = f\_3(\Gamma\_{t-1'}^{nf}, n\_{t-1'}^{nf}, p\_s) \tag{12}
$$

(2) Exit of Firms

According to the above rules, when a firm loses money in a continuous k-period, it will exit from production. If the number of withdrawing traditional technology firms in period *t* is denoted by <sup>Δ</sup>2*n<sup>t</sup> f t* , and the number of withdrawing new technology firms in period *t* is denoted by <sup>Δ</sup>3*n<sup>n</sup> f t*, then there are

$$
\Delta \Delta n\_{t}^{tf} = f\_{4}(n\_{t-1'}^{tf} \left\{ \pi\_{i,t-1'}^{tf} \cdot \cdots \cdot \pi\_{i,t-k}^{tf} \right\}) \tag{13}
$$

$$
\Delta\_3 \mathfrak{n}\_t^{nf} = f\_5(\mathfrak{n}\_{t-1'}^{nf}, \{\mathfrak{n}\_{i,t-1'}^{nf}, \dots, \mathfrak{n}\_{i,t-k}^{nf}\}) \tag{14}
$$

(3) Change in the Number of Firms in Production

Then, the number of traditional technology firms in period *t* is

$$\begin{array}{lcl} n\_t^{tf} &= n\_{t-1}^{tf} + \Delta\_1 n\_t^{tf} + \Delta\_2 n\_t^{tf} \\ &= f\_6(n\_{t-1'}^{tf}, \Gamma\_{t-1'}^{tf}, m\_{t-1'}^{t}, p\_{s\prime}, \{\pi\_{i,t-1'}^{tf}, \dots, \pi\_{i,t-k}^{tf}\}) \end{array} \tag{15}$$

The number of new technology firms in period *t* is

$$\begin{array}{lcl} n\_t^{nf} &= n\_{t-1}^{nf} + \Delta\_1 n\_t^{nf} + \Delta\_2 n\_t^{nf} + \Delta\_3 n\_t^{nf} \\ &= f\_7(n\_{t-1}^{nf}, c\_{i, t-1}^{rd}, \text{Max} \{c\_{i, t-1}^t\}, n\_{t-1}^{nf}, \Gamma\_{t-1}^{nf}, p\_{s\cdot} \{\pi\_{i, t-1}^{nf}, \dots, \pi\_{i, t-k}^{nf}\}) \end{array} \tag{16}$$

The total number of firms involved in the production in the industry at period *t* is

$$n\_t^f = n\_t^{tf} + n\_t^{nf} = f\_8(f\_{6\prime}f\_7) \tag{17}$$

According to Equations (15) and (16), the entry or exit of firms in an industry is influenced not only by the industrial system itself but also by the evolution of the market system and technology system.

### **4. Results and Discussion**

### *4.1. History Replicating Runs*
