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

Implications and Conclusions

Different assumptions about production quotas’ discount rates are used in different trade
policy simulation models (e.g., Cox et al.
, 1999, and Meilke, Sarker and Le Roy, 1998).
Meilke, Sarker and Le Roy use a discount rate of 20 percent and state that it is “... in the
mid-range of discount rates estimated by . economists.” As they note, estimates of
discount rates in the literature vary wildly. The current article estimates that annual
discount rates range from approximately 8 percent to 12.5 percent in May 2001 and May
2002. These estimates are conditional on the producers’ degree of risk aversion,
producers’ cost efficiency and the non-stochastic return on the export market. The
estimates of the discount rate are relatively greater than the commercial risk-free interest
rate on government bonds or returns on other risk-free assets sometimes used to discount
quota values; however, they are also smaller than previously computed discount rates
(e.g., Chen and Meilke, 1998).

Background

A ruling of the WTO Dispute Settlement Body in October 1999 forced the Canadian dairy
industry to reform dairy export mechanisms in the fall of 2000. An electronic marketplace
for exports of dairy products, known as the Individual Export Milk (IEM) program, was
implemented in Quebec (and in other provinces). Under this program, export milk was
sold directly to processors without the intervention of the national supply management
system. The IEM program was subsequently successfully challenged by New Zealand and
the United States, and the program ceased to exist in early 2003. The current analysis
seizes the opportunity created by the existence of the IEM programs to produce iso-utility
lines that determine threshold values for the discount rate conditional on risk preferences,
cost efficiency and a given export price.

The Economic Model

A portfolio model is built to derive optimal purchases of export contracts and domestic
production quotas by dairy producers. Let
a and 1 - a represent the shares of milk
allocated to the domestic and export markets respectively under the existence of the IEM
program. Assuming that output of dairy producers is pre-determined and that variable
costs are constant, the per-unit profit function is

π = ( pd - rδpq ) a + px (1 - a ) - c,                                            (1)

where pd , px and pq represent the domestic price of milk, the export price of a contract
offered to a producer and the auction equilibrium price of production quotas, respectively.
The symbol ~ denotes randomness in a variable,
c is the constant average variable cost of
production,
r represents the annual discount rate and the parameter δ is the factor that

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