**Appendix B**

*Appendix B.1*

$$\begin{array}{lcl}\text{Net accounting } cost\_i = & \sum\_{\substack{i}} \sum\_{j} \mathbf{\dot{r}}\_{ij} \mathbf{X}\_{ij} \\ &= \mathbf{c}\_{i,\text{Central cost of land}} + \mathbf{c}\_{i,\text{ send cost}} + \mathbf{c}\_{i,\text{ irigration cost}} \\ &+ \mathbf{c}\_{i,\text{ numre or compost cost}} + \mathbf{c}\_{i,\text{ pesticides cost}} + \mathbf{c}\_{i,\text{ fortiliary cost}} \end{array} \tag{A1}$$

+*ci*, *draf t animal cost* + *ci*, *machinery cost* + *ci*,*threshing cost* + *ci*, *hired labor cost*

$$\text{Production } value\_{i} = \sum\_{i} P\_{i} \mathbf{Y}\_{i} \tag{A2}$$

*Gross incomei* = ∑ *i PiYi* − *Inkind paymenti* = ∑ *i PiYi* − (*Ci*, *irrigation cost paid by crop* + *Ci*, *labor cost paid by crop*) (A3)

$$Net\,\,income(\pi)\_i = \,\,Gross\,\,income\_i - \,\,Net\,\,accounting\,\,cost\_i \tag{A4}$$
