Length : around 40 minutes
The following statement introduces a model which helps analyse the change in land use, between forest and agriculture. You may write the model with or without the help page in which we put forward names of data, variables and equations.
« A group of farmers and foresters of a region in Cameroon, that we represent as one single entity in the model, has 300 ha of land on which they can :
- Have a non-exploited forest
- Have a forest that they maintain and log in order to sell wood (exploited forest)
- Grow cassava or oil palm.
It is assumed that the use of the exploited forest cannot be changed. The non-exploited forest can be used as an exploited forest or torn up in order to grow cassava or oil palm. Once land has been deforested, it is not possible to go back. Deforestation costs 10$/ha.
The table below summarises the possible changes (1 indicates a possible change, 0 that it is not possible to change the use of the land) :
| Initial use of land | Change to | |||
| Forest | Exploited forest | Cassava | Oil palm | |
| Forest | 1 | 1 | 1 | 1 |
| Exploited forest | 0 | 1 | 0 | 0 |
| Cassava | 0 | 0 | 1 | 1 |
| Oil palm | 0 | 0 | 1 | 1 |
Data are as follows :
| Use | Yield (unit/ha) | Price ($/unit) | Cost ($/ha) | Carbon storage (ton of carbon/ha) |
| Forest | 325 | |||
| Exploited forest | 7.25 | 125 | 25 | 163.8 |
| Cassava | 13 T/ha | 195 | 50 | |
| Oil palm | 2,5(thousand L/ha) | 1230 | 35 | 30 |
The initial distribution of land area in the region is as follows : 100 ha of non-exploited forest, 100 ha of exploited forest, 50 ha of cassava and 50 ha of oil palm.
Due to poor infrastructure in this region, farmers must produce at least 1200 tons of cassava and 800 tons of palm oil per year in order to feed local populations. The population of the area goes up by 2% every year.
An environmental sustainability index is measured using the total quantity of stored carbon.
The group of farmers maximizes its profit in every period. »
Build a recursive model which covers a period of 20 years in which you will calculate environmental sustainability, using an indicator that measures the carbon stored.
Observe the .lst file and answer the following questions :
Why does the model not succeed in obtaining a stable solution over the years ?
How do the simulation results evolve over 30 years ?
The marginal value of the chgtTerreBal(mngFor) equation is negative (-2158.75) : what does this evoke ? And why this value of -2158.75 ?
What can you say about the carbon stored ?
Analyse the solution, and check 
