Bridging Micro- and Macro-Analyses of the EU Sugar Program: Methods and Insights

rational beet producer will accept losses on the C sugar, or on a share of the C sugar, in order to
maximize expected profit. The non-linearity in prices caused by the quota and the asymmetry between
gains and losses caused by the dual price system result in kinked marginal returns, showing
similarities with the classical concavity of the expected utility function. In such a case, even a risk
neutral producer will overshoot as prevention.

A defendable assumption is that all costs are experienced by the time of harvesting. In such a case, if
the output harvested is one unit lower than the target quantity y1, the loss is p1. If it is one unit larger,
the extra profit is p2. Let us call q the subjective probability that the actual yield exceeds the expected
one by one unit. The expected profit of the producer targeting a production y₁ is
p1.y1-C(y1)-q.p1+(1-q).p2. Here, C denotes the long run cost function (rather similar behavior can be
derived with a restricted cost function) and Cm denotes the marginal cost. The expected profit of a
producer targeting one unit of production above y1 (i.e. overshooting) is
p1.y1+p2-C(y1+1)+(1-q).p2-q.p2, with C(y1+1)-C(y1)≈Cm(y1)). That is, overshooting is rational
provided that Cm(y1) -p2 < q(p1-p2). The higher the difference between the two prices, the more
likely the overshooting.

More formally, the introduction of an "insurance" behavior modifies the standard marginal conditions
that characterize optimal production. Following Roumasset (1977), the producer's expected profit
maximization problem takes the form of a discontinuous function as in equation (4), where δ denotes
the Kronecker symbol, and μ_r is the expected yield (unit sugar content times quantity of beets per
hectare), under the assumption that variable costs are experienced before climatic conditions affect the
final yields. L denotes the quantity of land (acreage), r denotes the actual yield and the bar over y₁
denotes the quantity under quota.

MaxE⁽p2. (r.L ^-y_λ )+ Pi.y ₁ ^-C(μ_r.L;w)^{- δ}_rL≤- (p2 ^- Pi).(r.L ^-y_i ))                      (4),

or

MaxP2.(pr.L -У1 )+P1∙У1 - C(μ_r.L;w)-(p2 -pɪ) .Prob[rL ≤ y ]. E(r.L -y₁ ; r.L -y_λ ≤ 0)

The first order conditions involve

Three conclusions can be drawn from equation (5) and from the fact that the bracketed term is
positive, and therefore the right hand side of (5) is negative. First, producers will overshoot and
produce C sugar, since the determination of the optimal supply behavior responds to the condition that
marginal costs equals the price p2 plus a positive term. Second, this term depends positively on the

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