Solutions :
This farmer can work 2000 hours and has 100 hectares, which allows him to dedicate 20 working hours per hectare on average. Yet the crop which requires the most labour per hectare is rapeseed, with 4h/ha for the intensive or integrated pest management technologies. This suggests that the farmer will always have enough working hours and not be constrained by labour, regardless of the cropping pattern he chooses. The labour constraint is therefore never binding in this model, with this data. The land constraint, however, is binding.
Gross margins per hectare are easy to calculate automatically in GAMS by creating a calculated parameter (see Lesson 7) : yield*price – costs. In GAMS :
| parameter MB(C, mC) calculated gross margin ; MB(C, mC) = rdt(C,mC)*pxVenteInit(C)/10 – charges_tot(C,mC) ; display MB ; |
Results are as follows :
| Crop | Intensive | Sustainable | Integrated Pest Management |
| bleD | 658.4 | 667 | 636 |
| rapeseed | 407.5 | 423.5 | 383.95 |
| orgeP | 396.2 | 378 | 358 |
| orgeH | 357.5 | 405 | 405 |
The farmer chooses to grow “sustainable” soft wheat only on his land, for it is the crop with the most significant gross margin, and that it presents no constraint except for the land constraint. He therefore grows 100 hectares of “sustainable” soft wheat and has an income of 66700€.
Land is the limiting factor of the model. The marginal value of land is 667€, which means that he would be willing to rent a hectare at the maximum price of 667€.
You can download the solution and check that you wrote the model correctly and obtained the same solution : modelEco_ParisBasin_technic.gms
