Length : around 35 minutes
Consider the following new statement :
« A farmer in the Paris basin has a 100 ha large-scale farm. He can grow soft wheat (bleT), rapeseed, spring barley (orgeP) and winter barley (orgeH). For each crop, he can choose between three management systems :
- Intensive (written « intens ») : it is the most intensive technology in terms of chemical inputs, with a “preventive” use of phytosanitary products.
- Sustainable (written « rais ») : it involves “sustainable” practices. Phytosanitary treatments are determined following the observation of diseases or pests in the plot. The quantities used are adapted to the situation.
- Integrated pest management ( written « protI ») : such practices integrate prophylactic agronomic measures which contribute to a decrease in the pressure caused by pests. They can involve considerations concerning sowing dates, variety choices, crop successions in a plot, etc…
The farmer knows the expected yields, the variable costs, and the working time required for each technology and each crop.
He can work 2000 hours a year.
| Yields (q/ha) per crop and management system | |||
| aa Crop |
Management system | ||
| Intensive | Sustainable | Integrated pest management | |
| bleT | 72,8 | 71 | 65 |
| rapeseed | 31 | 29 | 26,3 |
| orgeP | 62,6 | 62 | 56 |
| orgeH | 71 | 70 | 64 |
| Working time (hours/ha) per crop and management system | |||
| aa Crop |
Management system | ||
| Intensive | Sustainable | Integrated pest management | |
| bleT | 3,2 | 3,1 | 3,1 |
| rapeseed | 4 | 3,6 | 4 |
| orgeP | 3,1 | 3,1 | 3,3 |
| orgeH | 3,3 | 3 | 3 |
| Total costs (€/ha) per crop and management system | |||
| aa Crop |
Management system | ||
| Intensive | Sustainable | Integrated pest management | |
| bleT | 652 | 611 | 534 |
| rapeseed | 724 | 635 | 576 |
| orgeP | 668 | 676 | 594 |
| orgeH | 746 | 680 | 587 |
The selling price of soft wheat is 180€/ton, that of rapeseed is 365€/ton, that of spring barley is 155€/ton, and that of winter barley 155€/t.
The objective of the farmer is to maximize his income. »
The data come from : Ecophyto R&D vers des systèmes de culture économes en produits phytosanitaires – Volet 1. Tome II : Analyse comparative de différents systèmes en grandes cultures. Janvier 2009. INRA et le ministère de l’écologie, de l’énergie, du développement durable et de l’aménagement du territoire.
i. Writing the model
Before you begin, consider the following questions :
How many constraints does the model present ? What can you say about the labour constraint ?
Calculate the gross margins of each crop for each management system. Can you anticipate the crops and cultivation methods which the farmer will choose ?
Write the model in GAMS and calculate the optimum cropping pattern for a farmer who maximizes his income. Check that your thoughts on the labour constraint and the chosen crops are confirmed.sont confirmés.
ii. Analysing a technological change 
You will carry out several simulations in order to study the influence of an increase in cereal prices on crop and technology choices. For that purpose, you will modify the price parameter in the model. Two scenarios will be simulated :
Price decrease (Simulation 1) : 110€/t of wheat, 210€/t of rapeseed, 85€/t of spring barley and 70€/ha for winter barley.
Price increase (Simulation 2) : 230€/t of wheat, 400€/t of rapeseed, 195€/t of spring barley and 160€/ha for winter barley.
Once you have modified the model and checked the solutions, answer the following questions (click on “Start quiz”)
