Is exchange rate pass-through in pork meat export prices constrained by the supply of live hogs?

One option would be for the processing firm to commit its price (to a level higher than the expected value of [e.sup.a][r.sup.a] - [mu][t.sup.a]) before hog producers make their decision and thus effectively setting the quantity of hogs available in the marketing period. Even when contracting is possible, the processor's ex ante demand for live hogs may not necessarily coincide with his ex post optimal capacity choice once exchange rates are known. Under price commitment, capacity is sunk at the marketing stage unless hog producers anticipate exporting hogs to market a in the marketing period. In the spot market scenario, the processing firm can simply wait until the hogs attain market-ready weight to secure its supply of live hogs. It faces the possibility that its desired demand be higher than the available domestic supply.

The various hog-marketing mechanisms in Canada provide us with a rich and diversified economic environment to test the theoretical predictions of the model. For example, hog marketing mechanisms in Quebec address coordination issues between packers and producers by relying on some hybrid marketing schemes. In short, a marketing board has exclusive rights to market hogs to processors. An important share of all hogs available in any given period is allocated to processors at a predetermined price based on their historical market shares while the others are auctioned off (Larue et al. 2000). Hog marketing mechanisms in other provinces involve contracts between individual packers and hog producers as well as spot market transactions.

Going back to the profit maximization problem defined in (1), suppose that prior to export pricing decisions, the firm committed to buy a quantity [Q.sup.p] of live hogs. The processing firm makes pricing decisions in the foreign market subject to the constraint that [Q.sup.p] = [D.sup.a] + [D.sup.b]. Given the foreign price level of substitute goods (denoted [[bar].sup.a] and [[bar].sup.b]), the first-order conditions are

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [lambda] is the Lagrange multiplier associated with the capacity constraint. Equations (2) and (3) define the domestic firm's export prices [p.sup.a]([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]) and [p.sup.b]([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]), which can be substituted back into (1) to yield

(4) [pi](x) = TR([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]) - [r.sup.p][Q.sup.p]

where TR(x) denotes total export revenues.

In the first scenario, the price commitment of the processing firm is made before hog producers make their sunk investment decisions. In the first stage, we assume that hog producers' supply is [Q.sup.r]([r.sup.p]) with [Q.sup.r,] > 0. (2) Because of its monopsony position in the purchase of domestic hogs, a risk-neutral processing firm maximizes

(5) E[[pi](x)] = E[TR([e.sup.a], [e.sup.b], [Q.sup.r]([r.sup.p]); [[bar].sup.a], [[bar].sup.b])] - [r.sup.p][Q.sup.r]([r.sup.p]).

The first-order condition to the optimization problem in (5) yields the optimal live hog price [r.sup.p*] = [phi]([e.sup.a], [e.sup.b]; [[bar].sup.a], [[bar].sup.b]), which is a function of the various moments of the distribution of the exchange rates and the foreign firms' prices. (3)

In the second case, the domestic firm uses the spot market to purchase live hogs and [r.sup.p] is chosen when uncertainty about the exchange rates is resolved. However, the hog supply is perfectly inelastic at that point, and the processor knows it can buy as many hogs as there are available ([Q.sup.r]) as long as it offers at least [e.sup.a][r.sup.a] - [mu][t.sup.a]. Let the parameter [theta] be the Lagrange multiplier associated with the inequality [Q.sup.p] [less than or equal to] [Q.sup.r]. If [Q.sup.r] > [Q.sup.p] ([theta] = 0), the processor does not face any constraint ex post when setting export prices ([D.sup.a] + [D.sup.b] = [Q.sup.p] < [Q.sup.r]) and (1) becomes

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The processing firm maximizes (6) subject to the constraint [r.sup.p] = [e.sup.a][r.sup.a] - [mu][t.sup.a]. The first-order conditions are

(7) [partial derivative][pi]/[partial derivative[p.sup.a] = [D.sup.a]([e.sup.a] [p.sup.a], [[bar].sup.a]) + [e.sup.a]([p.sup.a] - [t.sup.a] - [r.sup.p]) x (partial derivative][D.sup.a]/[partial derivative]([e.sup.a][p.sup.a])) = 0

(8) [partial derivative][pi]/[partial derivative][p.sup.b] = [D.sup.b]([e.sup.b] [p.sup.b], [[bar].sup.b]) + [e.sup.b]([p.sup.b], [[bar].sup.b]) + [e.sup.b]([p.sup.b] - [t.sup.b] - [r.sup.p]) x ([partial derivative][D.sup.b]/[partial derivative]([e.sup.b][p.sup.b])) = 0.

The first-order conditions in (7) and (8) can be manipulated to yield the standard elasticity pricing formula of Knetter (1989). The equilibrium prices defined by (7) and (8) are pa([e.sup.a]; [[bar].sup.a], [r.sup.p]) and [p.sup.b]([e.sup.b]; [[bar].sup.b], [r.sup.p]).

However, if the processors' demand for live hogs is equal to the (perfectly inelastic) supply of hogs ([Q.sup.p] = [Q.sup.r]), the optimization problem of the processor when selecting export prices reduces to (2) and (3). As Larue, Gervais, and Lapan (2004) argued, if the processor does not commit its output price, it has no incentive to raise prices above the net marginal revenue that hog producers can obtain in the export market once hogs attain ready-to-market weight. Producers are rational and fully anticipate that outcome, thus leading to a potential "low-price, low-capacity trap."

Based on the previous theoretical set-up, the empirical model needs to distinguish between two general cases. In the first instance, production of live hogs will impact ERPT because hog supplies are predetermined (i.e., inelastic hog supply). For example, consider a favourable movement in the exchange rate that was unexpected when the processor's price commitment was made. The variation would normally induce additional sales in the export market but additional purchases on the spot market may not be possible due to the inelasticity of the short-run hog supply. Similarly, commitments made in the first stage can also influence ERPT when there are unfavorable movements in the exchange rate because the domestic firm's purchases of live hogs are sunk at this stage. In the second general situation, the domestic firm relies exclusively on the spot market and the supply of live hogs does not constrain the domestic firm's behavior; i.e., there exists an excess supply of live hogs at the observed domestic price.

Comparative static exercises can be carried out on the set of first-order conditions in (2) and (3) or (7) and (8), which define the equilibrium price. The latter first-order conditions are independent of each other and, provided that the export demand in country j is negatively sloped and not too convex, it can be shown that

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (9) illustrates the standard result that depreciation (appreciation) of the domestic currency will increase (decrease) the export price, albeit in a lesser proportion. In the linear case, manipulating (9) shows that the pass-through impact is equal to -(1 + 1/[[epsilon].sup.j])/2 where [[epsilon].sup.j] is the export demand price elasticity. Zero pass-through occurs when the demand elasticity is -1.

The comparative static exercise for case of a binding capacity constraint is a little more involved. Assume for simplicity that the demand in each market is linear in its arguments. Totally differentiate the set of first-order conditions in (2) and (3) and the constraint to obtain

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The system in (10), (11), and (12) can be solved using Cramer's rule to obtain [partial derivative][p.sup.j]/[partial derivate][e.sup.j] < 0 and [partial derivative][p.sup.j]/[partial derivative][e.sup.i] < 0; i [not equal to] j. A depreciation (appreciation) of the domestic currency with respect to country a's currency will increase (decrease) the export price in market a. Incomplete pass-through will increase (decrease) sales in market a and will decrease (increase) sales in market b because supply is sunk at this stage. The decrease (increase) in sales to market b must necessarily be induced by an increase (decrease) in the export price in market b. It is, however, difficult to directly compare the pass-through coefficients under the standard elasticity pricing formula and the case of predetermined supplies because, in the latter case, the demand elasticity of both markets affects the degree of exchange rate pass-through.

Data

Hog marketings, slaughters, and exports from January 1988 to November 2003 in Manitoba, Ontario, and Quebec were obtained from the Red meat market division of Agriculture and Agri-food Canada. The three provinces accounted for more than 75% of all hogs marketed in Canada in 2003. There are in some instances some significant differences between total hog marketings and hog slaughterings within a province. Processors in Quebec almost always slaughter all available hogs in the province while a significant portion of total hog production in Ontario is sold to Canadian packers outside Ontario. The relationship between slaughterings and production in Manitoba is less stable over the sample, but Manitoba can generally be considered a net exporter of live hogs.