**Appendix A**

*A1. Modeling the Basic Characteristics of the Firms in the Fuel Ethanol Industry in China*

(1) The Production Capacity and Output of the Firm

The production capacity of the firm is related to the fixed capital input of the firm *Fi*,*t*. The variable input of the firm is denoted as

$$m\_{i,t} = \eta\_{i,t} \cdot (a \cdot F\_{i,t}) \tag{A1}$$

where η*i*,*<sup>t</sup>* represents the capacity utilization rate of firm *i* at time *t*, and η*i*,*<sup>t</sup>* ∈ [0, 1]. A value of η*i*,*<sup>t</sup>* equal to 0 indicates that the firm stops production. α represents the maximum variable input combined with a one-unit fixed input.

We assume that the output of the firm is determined by the input and technical efficiency. The output of the firm is

$$q\_{i,t} = \varepsilon\_{i,t} \cdot (m\_{i,t})^z \tag{A2}$$

where *ei*,*<sup>t</sup>* denotes the technical efficiency of firm *i* at time *t*, and parameter *z* (0 < *z* < 1) reflects diminishing marginal productivity.

(2) Production Cost

The total cost of the firm, which consists of the fixed cost and variable cost, is

$$\mathbf{C}\_{i,t} = d \cdot F\_{i,t} + p\_t^m \cdot m\_{i,t} \tag{A3}$$

where *d* represents the depreciation rate; *d* · *Fi*,*<sup>t</sup>* denotes fixed cost; *pmt* is the price of feedstock; *mi*,*<sup>t</sup>* is the input amount of the feedstock; *pmt* · *mi*,*<sup>t</sup>* is the variable cost. Considering the relationship between a firm's input and output described by Equation (A2), Equation (A3) can also be expressed as

$$C\_{i,t} = d \cdot F\_{i,t} + p\_t^{\text{pr}} \cdot (c\_{i,t})^{\frac{-1}{\frac{1}{x}}} \cdot (q\_{i,t})^{\frac{1}{x}} \tag{A4}$$

The cost per unit of the firm is

$$x\_{i,t} = C\_{i,t} / q\_{i,t} \tag{A5}$$

The average per-unit cost of the industry is

$$\overline{c}\_{i,t} = \sum\_{i=1}^{n\_l} \mathbb{C}\_{i,t} / \sum\_{i=1}^{n\_l} q\_{i,t} \tag{A6}$$

where *nt* represents the number of firms in the industry.

(3) Profit of the Firm

Let *pbt*be the price of fuel ethanol; then, the firm's profit is denoted as:

$$
\pi\_{i,t} = p\_t^b \cdot q\_{i,t} - \mathcal{C}\_{i,t} \tag{A7}
$$

(4) Supply Function

We assume that a specific firm makes production decisions according to the profit maximization principle; then, the supply function of the firm, which is obtained by taking the derivative of the profit equation (Equation (A7)) with respect to output quantity, is

$$\eta\_{i,t} = (z \cdot p\_t^b / p\_t^m)^{\frac{\tilde{\mathbf{I}} - \mathbf{z}}{\mathbf{I} - \mathbf{z}}} \cdot e\_{i,t}^{\frac{\mathbf{I}}{\mathbf{I} - \mathbf{z}}} \tag{A8}$$

The supply function of the industry, which can be obtained by summing up the supply function of all firms, is

$$q\_t = \left(z \cdot p\_t^b / p\_t^m\right)^{\frac{z}{1-z}} \cdot \sum\_{i=1}^{n\_l} \left(e\_{i,t}^{\frac{1}{1-z}}\right) \tag{A9}$$

(5) Feedstock demand function

Substitute the relationship between the firm output and the feedstock input of Equation (A2) into Equation (A8); then, the feedstock demand function of the firm can be denoted as

$$m\_{i,t} = (z \cdot p\_t^b \cdot c\_{i,t})^{\frac{1}{1-z}} \cdot (p\_t^{\text{nr}})^{\frac{-1}{1-z}} \tag{A10}$$

*Energies* **2020**, *13*, 1034

The feedstock demand function of the industry, which can be obtained by summing up the feedstock demand function of all firms, is

$$m\_t = (z \cdot p\_t^b)^{\frac{1}{1-z}} \cdot \sum\_{i=1}^{n\_t} (c\_{i,t}^{\frac{1}{1-z}}) \cdot (p\_t^m)^{\frac{-1}{1-z}} \tag{A11}$$

(6) Average Size of the Firm and Technical Efficiency in the Industry

Let the firm's size be denoted by the firm's fixed input, so the average size of the firm in the industry is

$$\overline{F}\_t = \sum\_{i=1}^{n\_t} F\_{i,t} / n\_t \tag{A12}$$

The average technical efficiency of the industry is reflected by the average technical level of all firms in the industry; then, the average technical efficiency of the industry is

$$\overline{\mathfrak{e}}\_{t} = \sum\_{i=1}^{n\_{\ell}} \mathfrak{e}\_{i,t} / n\_{t} \tag{A13}$$

The industry's average profit to cost ratio is

$$
\Gamma\_t = \sum\_{i=1}^{n\_t} \pi\_{i,t} / \sum\_{i=1}^{n\_t} \mathbb{C}\_{i,t} \tag{A14}
$$

### *A2. The Initial Values of the Variables in the Coevolutionary Model of the Fuel Ethanol Industry*

**Table A1.** The initial values of the variables in the coevolutionary model of the fuel ethanol industry (baseline scenario).


### *A3. The Setting of the Parameters' Values in the Coevolutionary Model of the Fuel Ethanol Industry*


**Table A2.** The setting of the parameters' values of the fuel ethanol industry (baseline scenario).
