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

Two random shocks are drawn from a univariate normal distribution N ( 0, σ2 ) using the
variance of the estimated residuals in (2) and (3). The random quota price and domestic
price are computed using the random forecast errors in the prediction model in (2) - (3),
conditional on a set of predetermined variables. This procedure is repeated 50,000 times
to compute that many realizations of the random profit function defined in (1).

A non-linear optimization algorithm is used to maximize expected utility of profit
over the choice variable
a in (1). Solving the optimization problem requires calibrating
the annual discount rate
( r), the risk aversion parameter ( γ ) and the marginal cost ( c).
The empirical strategy is thus to build a grid search over the potential values of the annual
discount rate for given values of
γ and c such that producers will choose to sell
production exclusively on the domestic market
( a = 1). This is achieved by averaging out
the utility realizations of the 50,000 random draws and optimizing over the variable
a.
That optimization procedure is repeated ten times and the average optimal proportion is
used to determine the iso-utility lines relating the price of export contracts and the
discount factor of production quotas. The grid search procedure is assumed successful
when the optimization procedure yields a value within 0.01 of the desired level
(a = 1).

Results

Two different optimization scenarios were computed. The first one relates to export milk
deliveries occurring in May 2001, and the second relates to May 2002, a period of higher
quota price. Estimates of marginal costs are not readily available, but average variable
costs have been estimated for the province of Quebec in Levallois and Perrier (2001).
They report that average variable costs range from $16.30 per hl to $25.05 per hl
depending on various factors that are farm-specific. Based on these estimates, the
portfolio model solves the optimization routine for three different levels of marginal costs:
$16, $20 and $24 per hl.

Simulations for May 2001

Figure 1 illustrates various iso-utility lines for a producer with an average variable cost of
$20 per hectolitre, according to his/her coefficient of relative risk aversion. The horizontal
axis lists the different prices of export contracts available in May 2001. The iso-utility
lines plot the maximum value of the quota discount rate for which the producer would not
be willing to participate in the export market. For example, a producer with marginal
variable costs of 20$ per hl and a coefficient of relative risk aversion of two will not
participate in the commercial export milk program if his/her discount rate is lower than
8.7 percent, given that the most profitable export contract available is priced at $35.09 per
hl (figure 1). If that producer accepts to supply milk for export at $35.09 per hl, it implies
that he/she discounts the production quota at a higher rate than 8.7 percent. The same
producer will accept an export contract priced at $29.03 per hl if his/her discount rate of
the quota is greater than 10.9 percent on an annual basis. The positive slope of the iso-

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