CAPRI Online Manual (update)

There are two sources for interactions between activities in simulation experiments: the objective function and constraints. In the current version of CAPRI, the objective function does solve inter-activity terms for groups of arable crops, so that the major interplay is due to constraints. The interaction is best understood by looking at the first order conditions of a programming model including PMP terms:

\begin{equation} Rev_j = Cost_j+ac_j+\sum_k bc_{j,k}Levl_k+\sum_i^m\lambda_ia_{ij} \end{equation}

The left hand side (Rev) shows the marginal revenues, which are typically equal to the fixed prices times the fixed yields plus premiums. The right hand side shows the different elements of the marginal costs. Firstly, the variable or accounting costs (Cost) which are fix as they are based on the Leontief assumption. The term \( (ac_j+\sum_k bc_{j,k}Levl_k) \) shows the marginal non-linear costs, which are increasing with the activity levels. The cross effects are only introduced to let major arable crop groups interact, whereas for fruits & vegetables, permanent crops, grassland and the animal sectors, only diagonal terms are introduced. The methodology for the estimation of these terms is described in Jansson and Heckelei (2011).

The remaining term \( (\sum_i^m\lambda_ia_{ij}) \) captures the marginal costs linked to the use of exhausted resources and is equal to the sum of the shadow prices \lambda multiplied the per unit demand of resource i for activity j; the matrix A being again based on Leontief technology. The shadow values of binding resources hence are the drivers linking the activities.

The land balance plays a central role in the CAPRI supply model. The land shadow price appears as a cost in all crop activities including fodder producing ones, so that animals are indirectly affected as well. The second major link is the availability of not-marketable feeding stuff, and finally, less important, organic fertiliser.

The basic effects are best discussed with a simple example. Assume an increase of a per hectare premium for soft wheat, all other things unchanged.

• What will happen in the model? The increased premium will lead to an imbalance between marginal revenues (= yield times prices plus premium) and marginal costs (=accounting costs, ‘resource use cost’, non-linear costs). In order to close the gap, as marginal revenues are fixed, the area under soft wheat will be increased until marginal costs of producing soft wheat have increased to a point where they are again equal to marginal revenues. As the marginal costs linked to the non-linear cost function \( (ac_j+\sum_k bc_{j,k}Levl_k) \) are increasing in activity levels, increasing the area under soft wheat will hence reduce that gap. At the same time, as the land balance must be kept closed, other crop activities must be reduced. The non-linear cost function will for these crops now provoke a countervailing effect: reducing the activity levels of competing crops will lead to lower costs for these crops. With marginal revenues (Rev) and accounting costs (Cost) fixed, that will require the shadow price  of the land balance to increase.
• What will be the impact on animal activities? Again, the shadow price of the land balance will be crucial. For activities producing non-marketable feed, marginal revenues are not defined as prices times yields, but as internal feed value times prices. The internal feed value is determined as the substitution value of non-marketable fodder against other feeding stuff, and depends on their nutrient content and further feed restrictions. Increasing the shadow price of land will hence either require decreasing other costs in producing fodder or increasing the internal marginal revenues. In other words, a high shadow price of land renders non-marketable fodder less competitive compared to other feeding stuff. As feed costs are – however very slightly – increasing in quantities fed per head, feed costs for animals will increase. But as there are several requirement constraints involved, some feeding stuff may increase and other decrease. Clearly, the higher the share of non-marketable fodder in the mix for a certain animal type, the higher the effect. As marginal feed costs will increase, and marginal revenues for the animal process are not changing, other marginal costs in animal production need to be reduced, and again the non-linear cost function will be the crucial part, as the marginal cost related to it will decrease if herd sizes drop.

To summarize the supply response, increasing premiums for a crop will hence increase the cropping share of that crop, reduce the share of other crops, increase the shadow price of land, lead to less fodder production, higher fodder costs and thus reduced herd size of animals.

• What will be the impacts covered by the market? The changes in hectares will lead to increased supply of the crop with the higher premium and less supply of all other crops at given prices, i.e. one upward and many downward shifts of the supply curves. Equally, supply curves for animal products will shift downwards. On the other hand, some feed demand curve will shift as well, some upward, other downward. These shifts will move the market module away from the former fixed points where market balances were closed. For the crop product with the increased premiums, increased supply plus some changes in feed will most probably lead to lower prices, whereas prices of other crops will most probably increase. That will require new adjustments during the next iteration where the supply models are solved, with to a certain extent countervailing effects.

Table 25: Overview on a regional aggregate programming model

The definition of the supply model can be found in ‘supply\supply_model.gms’

The feed block ensures that the requirements of the animal processes in terms of feed energy and protein are met and links these to the markets and crop production decisions.

\begin{equation} \overline{AREQ}_{r,act,req} \overline{DAYS}_{r,act,req}= \sum_{feed} FEDNG_{r,act,feed} \overline{REQCNT}_{r,act,feed} \end{equation}

The left hand side captures the daily animal requirements (AREQ) for each region r, animal activity act and requirement AREQ multiplied with the days (DAYS) the animal is in the production process. Both are parameters fixed during the solution of the modelling system. The right hand side ensures that the requirement content of the actual feed mix represented by the feeding (FEDNG) of certain type of feed to the animals multiplied with the requirement content (REQCNT) in the regions covers these nutritional demands. Requirements and contents are specified in the feed calibration while production days are determined in the “COCO1” module. Total feed use (FEDUSE) in a region is defined as the feeding per head multiplied with the activity level (LEVL) for the animal activities:

\begin{equation} FEDUSE_{r,feed} = \sum_{aact} LEVL_{r,aact} FEDNG_{r,aact,feed} \end{equation}

Total feed use might be either produced regionally in the case of fodder assumed not tradable (grass, fodder root crops, silage maize, other fodder from arable land), or bought from the market at fixed prices.

The model distinguishes arable and grassland and comprises thus two land balances: