### 1. Introduction

### 1.1. Outbreak of Foot-and-Mouth Disease in 2010/2011

### 1.2. Purpose and Method

### 2. Materials and Methods

### 2.1. Model

#### 2.1.1. Derivation of willingness to pay

*i*reply for the 1st amount

*A*

*suggested as “yes” or “no”. The 2nd amounts suggested for “yes” respondent and “no” respondent are denoted as A*

_{i}_{i}

^{H}and A

_{i}

^{L}. Like this, we can add more notations.

##### (1)

$$\begin{array}{l}{I}_{i}^{YY}=1({i}^{\prime}s\hspace{0.17em}answer\hspace{0.17em}is\hspace{0.17em}yes-yes)\\ {I}_{i}^{YN}=1({i}^{\prime}s\hspace{0.17em}answer\hspace{0.17em}is\hspace{0.17em}yes-no)\\ {I}_{i}^{NY}=1({i}^{\prime}s\hspace{0.17em}answer\hspace{0.17em}is\hspace{0.17em}no-yes)\\ {I}_{i}^{NN}=1({i}^{\prime}s\hspace{0.17em}answer\hspace{0.17em}is\hspace{0.17em}no-no)\end{array}$$*I*

_{i}*is 1, if the responses of respondent*

^{YY}*i*are “yes-yes”, and 0 if not. If we suppose respondents who seek the maximization of utilities, we can set a log likelihood function based on respondent

*i*’s reply.

##### (2)

$$\begin{array}{l}\text{lnL}=\sum _{i=1}^{n}{I}_{i}^{YY}\hspace{0.17em}\text{ln\hspace{0.17em}}\left[1-{G}_{C}({A}_{i}^{H})\right]+{I}_{i}^{YN}\hspace{0.17em}\text{ln\hspace{0.17em}}\left[{G}_{C}({A}_{i}^{H})-{G}_{C}({A}_{i})\right]\\ +{I}_{i}^{NY}\hspace{0.17em}\text{ln\hspace{0.17em}}\left[{G}_{C}({A}_{i}^{H})-{G}_{C}({A}_{i}^{L})\right]+{I}_{i}^{NY}\hspace{0.17em}\text{ln\hspace{0.17em}}\left[{G}_{C}({A}_{i})-{G}_{C}({A}_{i}^{L})\right]\\ +{I}_{i}^{NN}\hspace{0.17em}\text{ln\hspace{0.17em}}{G}_{C}({A}_{i}^{L})\end{array}$$*F*

*(·) as a logistically accumulated distribution function and combine with Δ =*

_{η}*a*−

*bA*, then the accumulated distribution function of WTP becomes (3).

#### 2.1.2. Spike model

*G*

*(·;*

_{C}*θ*), and supposing it as logistic type, then we can draw the average amount of WTP.

##### (5)

$${G}_{C(A;\theta )}=\{\begin{array}{ll}{[1+{e}^{(a-bA)}]}^{-1}\hfill & \text{if\hspace{0.28em}}A>0\hfill \\ {[1+{e}^{a}]}^{-1}\hfill & \text{if\hspace{0.28em}}A=0\hfill \\ 0\hfill & \text{if\hspace{0.28em}}A<0\hfill \end{array}$$##### (6)

$$\begin{array}{l}\text{lnL}=\sum _{i=1}^{n}{I}_{i}^{YY}\hspace{0.17em}\text{ln\hspace{0.17em}}[1={G}_{C}({A}_{i}^{H})]+{I}_{i}^{YN}\hspace{0.17em}\text{ln\hspace{0.17em}}[{G}_{C}({A}_{i}^{H})-{G}_{C}({A}_{i})]\\ +{I}_{i}^{NY}\hspace{0.17em}\text{ln\hspace{0.17em}}[{G}_{C}({A}_{i})-{G}_{C}({A}_{i}^{L})]+({I}_{i}^{NY}+{I}_{i}^{NNY})\\ \text{ln\hspace{0.17em}}[{G}_{C}({A}_{i}^{L})-{G}_{C}(0)]+{I}_{i}^{NNN}\text{ln\hspace{0.17em}}{G}_{C}(0)\end{array}$$*e*

*) and it means the ratio of zero response. The average amount of WTP is estimated by Eq. (7).*

^{a}