Imputing Dairy Producers' Quota Discount Rate Using the Individual Export Milk Program in Quebec

Current Agriculture, Food & Resource Issues

M. Doyon, C. Brodeur and J-P. Gervais

converts kg of butterfat per day into hectolitre of milk produced in a year (δ ≡ 3.6/365) .2
Therefore rδp^q is the opportunity cost of holding production quotas in a period.

The current analysis differs from that of Turvey, Weersink and Martin (2003) in a
fundamental way: the timing of decisions and the assumptions about what is known to
producers when they make their decisions are different. It is assumed that the equilibrium
quota value on the auction market is the relevant short-term random variable from the
producers’ perspective, rather than the export price. Quebec dairy producers were aware
of the most profitable export contract available before making irreversible delivery
allocation decisions with respect to the export and domestic markets. Given that the
output level is predetermined in our model, the risk faced by producers stems from the
uncertain opportunity cost of one period of time of not owning the quota. Producers that
do not enter into a binding agreement to sell on the export market through the IEM
program at the beginning of a period must either sell their output in the within-quota
domestic market, if they possess a corresponding quantity of quotas, or sell in the over-
quota market at world prices.³

Numerical simulations are used to solve the optimal ratio of quota purchases (or sales)
over total output for Quebec dairy producers under the IEM program. As Tomek and
Peterson (2001) point out, three empirical issues need to be addressed before proceeding
with the simulations. First, the relevant parameters of the probability distribution of the
random variables must be estimated. The second and third steps must specify the
objective function of producers and explain the simulation algorithm. There are two
random variables in the model from the producers’ perspective: i) the equilibrium price of
the production quota and ii) the domestic price of raw milk. Suppose that the conditional
distribution of these variables can be modelled as

Pq = λo + λιp. + Λ σ²_pχ + λ_i3WTOt + ɛit and
^pt

p^d = βiT^arge^tt ^{+ l}'.'1 ^,

where ε₁₁ is a random error term distributed normally, pt represents the average price of
all export contracts offered to producers at time t, WTO_t is a dummy variable which equals
zero for the period preceding December 2001 and one onward, and σ²_x is the negative
semi-variance of all export contracts offered to producers at time t defined as
ɪF==_ι k_fw_f (px - p^x ) W . The variable wf_f is the volume of the export contract, k_f is an
index function taking the value of one if pf < p^x and zero otherwise, and F and W are
respectively the total quantity of contracts available and the total volume of export
contracts. In equation (3), ε₂₁ is a random error term distributed normally and the variable
Target is the target price of the Canadian Dairy Commission based on cost of production
estimates.

The Quebec domestic farm milk price is an average price based on a reference
hectolitre with 3.6 percent of butterfat, 3.2 percent of protein and 5.7 percent of other

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