4. Supply price elasticities are derived from a rule that defines the relationship between a set of prices and output. In supply relationships, it is normally accepted that producers who try to maximize profits will increase (decrease) the supply of a commodity in response to an increase (decrease) in the price of that commodity subject to a given technology. The technology available to the producers determines the physical response of output to the use of a set of inputs - this is what economists refer to as a production function. Producers use changes in both output and input prices to determine the expected profitability of a particular production activity. Supply price elasticities refer to the percentage change in output arising from a percentage change in prices and are obtained from supply functions.
5. Given the above, a basic problem which farmers face when they decide about output responses to price changes is that they have to base their decision on future prices. This partly results from the lagged response of agricultural production to changes in prices. This is particularly important in livestock production, in most cases, due to the relatively long period that it takes for actual output to be realised. This is further complicated by the fact that physical production responses in future depends on past decisions affecting such things as the herd/flock dynamics (e.g. herd productivity structure, composition, offtake rates etc.) Producers' expectations are also influenced by a number of other external and internal factors among which the following are important:
(i) type of market, climatic and technological information confronting farmers;
(ii) government policies (e g, input price subsidies);
(iii) farmers' own attitude toward risk-bearing;
(iv) farmers' own ability to process decision relevant information.
6. The process of estimating supply price elasticities for livestock products can be particularly complex. Consider for example the components of percentage change in the number of cattle slaughtered arising from a percentage change in the world beef price. Such a price-induced change can be decomposed into the following elements:
(i) Percentage change in the number of cattle slaughtered due to the percentage change in the type of cattle (e.g. calves, heifers, oxen, bulls) killed.(ii) Percentage change in the type of cattle killed due to the percentage change in the quantity of inputs.
(iii) Percentage change in the quantity of inputs due to the percentage change in the quality (e g, crude protein content) levels of inputs.
(iv) Percentage change in the quality levels of inputs due to the percentage change in the cattle capitalization rate (equated to the opportunity cost of a financial asset such as cash).
(v) Percentage change in the cattle capitalization rate due to the percentage change in the domestic beef price.
(vi) Percentage change in the domestic beef price due to the percentage change in the exchange rate.
(vii) Percentage change in the exchange rate due to the percentage change in the world beef price.
7. Each of the previously mentioned components involve the dynamic response of the farmer to changes in prices and technological variables. Since the components are multiplicably related, some of the items highlight the impact of government interventions on the price adjustment process. For example if the government wishes to insulate the domestic beef market from the international market changes, strict foreign exchange policies (e.g. fixed exchange rate) can be pursued in a manner which will reduce the magnitudes of items (vi) and (vii) to zero. As a result, the response of domestic cattle slaughters to changes in the world price of beef will be nil.
8. Estimates of the expected behaviour of farmers in adjusting output to price changes distinguish between short- and long-run elasticities. The long-run is distinguished from the short-run in terms of the ability of a producer to vary all his inputs in response to changes in prices. Since this ability varies according to the biological cycles and the technological process involved for different agricultural commodities it is not always possible to determine what constitutes the short-against the long-run in terms of precise time periods.
9. The expectation behaviour of farmers will vary depending on the weights they attach to a set of historical prices. This will be discussed in the context of empirical estimates for Zimbabwe. Farmers' expectation behaviour also varies with respect to their efficiency as processors of market information. In the extreme case, it is assumed that farmers may not learn from their past experience and respond to price changes in a way that sets in a process of wide fluctuations in price and output in the long-term - economists refer to this as the cobweb theorem. In other situations, farmers are assumed to appropriately use and absorb market signals to adjust output to price changes expected (subjectively) to take place - economists refer to this as the rational expectation model. Notwithstanding the above, most empirical supply elasticity studies for agricultural commodities assume that farmers will respond positively to price increases - i.e a price increase will induce farmers to increase output.
10. Cattle slaughter relationships, however, present a different situation in the short-run - i.e. an increase in the price of beef will reduce the number of cattle slaughtered. This implies that the marketable output of beef will be lower in comparison to a situation where prices did not increase - i.e. the short-run price elasticity of beef supply estimated from a given slaughter function will be negative. Disregarding the on-farm consumption effect, this situation could arise from two possible reasons. First, when beef prices increase, commercial producers will decide to build up their herd inventory by retaining the most productive animals which will increase the herd size in anticipation of still higher prices in the future. They will increase their herd size up to the point where the marginal cost of an additional input is equal to the marginal return of an additional livestock output. Secondly, subsistence - oriented farmers will sell less (now higher-priced) animals to meet a target cash demand.
11. In a commercial production setting, witholding animals from the slaughter market due to increased prices will induce beef prices to increase even more because, other things being equal, of the decrease in beef supply. When those animals which were held back reach the "appropriate" slaughter age and/or weight, producers will have to sell these animals. This would mean that increased slaughter levels will depress beef prices. Lower prices will further induce producers to sell as much as possible in anticipation of even lower prices in the future - the other side of the coin explaining the negative supply response in cattle slaughter relationships.
12. The above provides an oversimplified picture of what is usually referred to as the cattle cycle in commercial beef production. Part of the reason of why beef supply responses are said to be negative in the short-run and positive in the long-run is explained by the cattle cycle phenomena. The positive long-run response of producers is explained by the increased supply of slaughter cattle forthcoming from those retained, following a lag of a number of years. The length of this lag depends on biological as well as technological factors indicated earlier (pare 8). For example, Simpson (1979) indicates that this lag could last between 3 to 5 years in the U.S. beef industry.
13. U.S. data on prices, output and technological inputs are clearly adequate (both in terms of the period they cover and their quality) to provide a good basis for defining (and even possibly predicting) how long the long-run is or can be. Data for other countries, particularly in Africa, are far from adequate. As a consequence, in such cases, while economic theory can provide us with some guidance on whether the price elasticity of supply in slaughter relationships is either negative or positive, empirical models do not answer the following questions clearly:
(i) How long will the beef price elasticity remain negative?
(ii) When does such elasticity become positive?
14. These questions address important policy issues related to domestic production, consumption and exports. The sign switch is important in that it will allow policy-makers to determine the possible cycles in the availability of beef to domestic consumers and when beef export commitments can be met. Some of the issues related to this aspect will be discussed in the context of the Zimbabwe pricing policy experience which is briefly described in the following section.
