the WTO panel that EU exports of C sugar should be considered as subsidized. However, such a
cross-subsidization cannot hold in the long run. If quasi-fixed factors can adjust to their optimal level
for production y1, then there is no point producing C sugar at loss as in Figure 1, for example. The
simple expression of the long run producer's profit maximization problem (3) and Hotelling's lemma
shows that such a cross-subsidy is not optimal.
MYaxπ = p1y1+ p2y2 -CLR(y1+y2;w;pz)
(3),
= p1y1+ p2y2-CV(y1+y2;w;z*)-pz.z*
*
with z
* ∂π
≡ z (У1 + У2) = Arg -
∂pz
Because z can freely adjust, there will be no production of y2. The reason is that there is no cost
saving due to increasing returns to scale (caused by a non-optimal level of fixed cost at y1 in the short
run) that can offset a loss in the out-of-quota market. Obviously, there might be production of C sugar
in efficient firms where the long run marginal cost is lower than p2 at the production level y1, but in
such cases, the difference between p1 and p2 is a simple rent, and there is arguably no cross subsidy.
As pointed out by Witzke and Kuhn (2003), the quota regime has been in place for many decades
almost without modification, and it is difficult to believe that the situation that has been taking place
during the last years is merely a short run equilibrium. Major non-convexities (indivisible inputs)
could prevent firms from adjusting their production structure to the optimal input level corresponding
to the quota as in (3). However, in the beet sector, there are many opportunities to share machinery, to
buy second hand machinery, and to purchase contract work. Contract harvesting or planting costs are
only slightly decreasing with the size of operation. The fixed component in the cost of contract work
is not large enough to provide a significant incentive for producing C beets so as to spread this fixed
cost on a larger output. Overall, the argument that the fixed costs of C sugar are covered by the quota,
and that this explains the production of C sugar in the EU is not compelling.
However, a recurrent problem in production economics is to define how long is the "long run". In
Europe, there is evidence that some equipment has a long service life (Ball et al, 1993). In addition, in
the processing sector, some equipment might be less divisible, or less easily adjustable than in
agriculture, and fixed costs in refineries could be a reason for sugar processors to encourage farmers to
produce C sugar. For this reason, we keep open the possibility that the production of C sugar benefits
from the high price of in-quota sugar, i.e. that there is some form of cross-subsidy, when we model the
EU sugar sector.
Quota overshooting as insurance. Because of the high price received for in-quota sugar beets,
producers may overshoot so as to make sure that they will capture the rent in case of poor harvests. A