between the supply of C sugar and the level of the rent drawn from the production of in-quota
sugar.
• Finally, another possibility is that C sugar was produced so as to build references when
producers expected that the ongoing reforms would result in a particular allocation of future
production rights, premium rights or compensation. Again, if it is the case, this feature must
be included in the modeling of EU sugar supply.
These points may result in interactions between in-quota sugar and C sugar, and could play a role in
the response of EU sugar production to price changes. This may occur both at the beet production
level and at the refined sugar production level. In the next section, we address these three possible
cases in a more analytical way.
Cross subsidization through fixed costs. The potential cross-subsidization between in-quota and C
sugar can be modeled using a simple short run comparative static framework. The short run profit
maximizing problem of the beet producer in the presence of quasi-fixed factors can be written as (1).
Maxπ= p1y1+p2y2-CSR(y1+y2;w;z)-pz.z (1),
y1,y2
subject to y1 ≤ Quota ,
where z denotes an aggregate of quasi-fixed primary factors (capital, self-employed labor and land
owned or subject to long term leases) whose (exogenous) price is pz. The variable w denotes the price
of variable inputs; p1 denotes the price of in-quota sugar beets; p2 the price of out-of-quota beets; y1
the quantity produced in the quota; and y2 the quantity produced out of the quota (quantities of beets
are expressed in sugar equivalent, so as to adjust for the sugar content). CSR denotes the restricted or
short run cost function.
For certain levels of the marginal cost function, of the quota and of the price of C beets, the existence
of quasi-fixed inputs may result in a cross-subsidy between in-quota and C beets. This happens when
p2 and y1 are such that the production of C sugar induces a lower average cost due to a larger
production scale. In such a situation profit maximization may result in a larger output than if the
quantity y1 was not subsidized, i.e. if there was only one sugar price p2. This situation is well
described by Kopp and de Gorter (2005). Figure 1 shows a special case where the price of C sugar is
higher than the marginal (variable) cost AVC of producing at y1, explaining that a quantity y2 of C
sugar is produced, while the price of C sugar does not cover its production cost (p2 lies below the short
run average cost curve ATCSR). The fixed costs are covered by the in-quota sugar. The production of
C sugar is positive provided that the area abcd is larger than the area cefg in Figure 1. In that case, the
gains resulting from the economies of scale exceed the loss resulting from selling the extra quantities
at p2. As pointed out by Kopp and de Gorter, abcd is always larger than cefg because the fixed costs at
y1 (abhi) equal the fixed costs at y1+y2 (demk), meaning that abcd is equal to cefg + ihgfmk > cefg.