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A suppl .y function based on j nventor.y- sales interaction
Both Reut’linger and Tryfos sfrecified a model with a high level of aggregation over time by using annual data. I use a model where the production 1ag is defined more accurately. At one point in time, we may -1sdefine the state of the herd by a vector Xa.whose components are the numbers of individuals jn each properly defined age and physiolog’ical classes.
Then there is a dynamic relationshio between the state vectors at successive points in tjme, name’lY, (2.r).
Where the matrix M, ‘includes both demographic parameters (fertility, survival rates ) and control variables corresponding to farmers deci sions.
Now if we can’t use this detailed framework because of incomplete data, we may still consider the dynamical relationship between some components of the state vector. Consider the age group of individual s which may be either bred or sold for slaughter at time t, its number depends on the number of females bred w unjts of time before. Then ure may write (1), (2.2) H t =mBt-w.
Partial adj ustment and adaPtive expectations
Since decisions are basically made on breeding stock it is natural to define the « slow adjustment » at this’level. The behavioral equation (2.4) becomes now, (2.12) oo + partial adiustment hypothesis means, (2.13) Bt – Bt_1 = I (tT – tr-r) , o.< 1r< 1 adaptive expectations imp1y, Bi OPT (?.r4) (Pi – PT_r) = o (Pt – PT_l) ,0<û-<1 As urell known when either one of the two assumptions is introduced alone (e.g. ç + L, û = 1) the estimab’le equation takes the same form.
If both are introduced, then one cannot identifycp and rp. Assuming Û = 1′ we get the equation expressed in observable variab’les, (2.15) Br =1o0 + (1 – f) Br-1 + ?oPr Again, in Tryfos’case the coefficient of Pt (in 1.15 as in 15) is what js usually ca’lled short run e’lasticity when multiplied by E . The long run elastjcity is obtained by dividing byct. The equation .15) may easily be expressed in terms of available supply or production, 2. p/ (2 -22- H, = mBr-* gives (2.16) Ha = mtgo’ + m (1 – ?) Bt_*_l + mgaPr_*.
Supplv in numbers, supplv in weiqhts
All the previous models have been specified in numbers. But the relevant variable on market equilibrium is the IiVeweight marketed. Current prices have a positive effect on average carcass we’ights, as well known, ê.g. Harlow [15, p. 40]. More recently, Myers, Havliceck and Henderson [34 , 35 ] have provided us with a more sophisticated model of short run (1) supply behavior. Basically, they consider the problem of theprofitabilityofdelaying the sales of fattened animals when prices are changing. They expect total ‘live weight at time t to depend positively on current price and negatively on the pnice expected for the next unit of time, where the available animals at t will still be in the suitable weight range for slaughter. The difficulty is that expected prices depend heavily on current prices, as the authors were avare of, making impossible to separate the two effects. It seems to me that they could have introduced in their model one more function based on the relationship between hogs’age and their average weight ; they could have then sorted out the two components of supply: numbers and weight per head. What they rea11y tended to show is that when price go up, farmers anticipate further jncrease and delay the sales. This is the same as saying that average weight increases with price, at least this seems to be the only way to verify their hypothesis. Using total liveweight as they clid leads to a misleading interpretation of their results. The.v found a negative current price effect jn a model very close to (2.10) with liveweight instead of numbers as dependent variable, which may be stated with some simplifjcatjon as, Q1 = 9H1 – oO – oP, , Qt (2.1E) total liveweight.
Simultaneous or recursive cobweb ? Bjases resulting from unappropriate estimation procedure
Quite a few workers have used simultaneous equat’ions methods jn livestock and hog supply research. Some were’looking for an estimate of « short run supply » elasticity which they expected to be positive [8, 35 ]. Others justifying this approach by the inventory-supply interactjon [ 44, 11 ]. Hildreth and Jarret were probably the first to interpret comect’ly the negative sign they obtained on the current price parameter. Fox ftt, p. 73] was interested in the possible bias on demand elasticity resu’lting from the wrong assumption that supply is predetermined, i.e. assuming recursiveness instead of sjmu’ltaneity. His results are of interest and are presented below since they illustrate the analyt’ica1 discussion of the biases given in this section.
Table of contents :
Chap. 1 – A SHORT REVIEW 0F LIVEST0CK CYCLES THEORY
1 – Periodicity
2 – Reversibility and the nature of the supply function
3 – The relationships between breeding
stock and supply
Chap. 2 – INVENTORY-SUPPLY INTERACTION AND ITS C0NSEQUENCES 0N THE SUPPLY FUNCTIoN
1 – A supply function based on inventorysales interaction
2 – Partial adjustment and adaptive expectations
3 – Supply in numbeis, supply in weights
4 – Dynamics and stability conditions
5 – Simul taneous or recursive cobweb ?
Biases resul t’ing from unappropriate estimation procedure
Chap. 3 – AN ECON0METRIC MODEL 0F THE HOG SUBSECTOR IN FRANCE
L – General setting of the French hog j ndu stry
11 – Production
1,2 – Consumption, prices i3 – Trade, EEC and pol icy
2 – Data available, implications for specification and possible biases
21 – The supply block
22 – Denand block
23 – Trade equation
3 – Empirical results
3i – Compl ete model
32 – Prel iminary work on supply
33 – Structural changes and supp’ly el a stic i ti es
Chap. 4 – WTLFARE ANALYSIS 0F THE HOG CYCLE IN FRANCE
1 – tlelfare loss in a simple cobweb
2 – Distribution effects
3 – l,lelfare effects of fluctuations . in a more general model
3L – Consumers’surp’lus and marketing margins behavior
1 – constant margins
2 – proportional margins
3 – non reversibility of retail price fluctuations
32 – A first appl ication to the hog market
Conclusion
Appendix 4.
CONCLUSION
