When the commodity under consideration is subject to a production quota which is binding at the level yo, there is a case for a distinction between a Decoupled PSE (DPSE) and a Supply Inducing PSE (SIE, Supply Inducing Equivalent). The former transfer does not enhance the production, i t is the quasi rent associated with the quota. The latter is the part of the PSE which is required to induce production just at level yO without the quota implemented. The variation of SIE is directly related to the notion of debit/credit in which we are interested.

As illustrated on the classical figure 1 the quota is binding i f where S(.) is the supply function of yO, pl a vector of variable input prices, and K a vector of fixed factors.

There is a virtual price level ~. which would exactly bring the production level at yO , y' = S [~O, pl, KJ

(3 ) Solving (3) for ~o defines ~o as a function of pl, K and y' and of input subsidies ISO in as much they influence pl ~.

= g (y', pl, K)

Wi th these familiar defini tions, i t is possible to decompose the PSE which is the total transfer into the DPSE which is only a domestic matter and the SIE which affects output and therefore trade. The DPSE is defined by the following equation.

DPSE = y' (p' -~. )

This is also the proportional to the output increase l .

( 5) quasi-rent due to the quota. Although level of production, it does not induce any It is not the same for the component of the PSE which is the gap between the shadow price ~. and the world price p.S IE = y' (~. _p' w) + IS'

As can be seen on figure 1, the SIE which, in the absence of a quota increased production from free trade up (6 ) is 'the income transfer restraint, would have to y' . -,----1 1 Note: In the presence 01 production quotas only one part 01 the P5E, Le. y' I~' -p',) vhere ~' is the shadov price correspondinq to the level 01 the quota has an ellect on production, It is clear from (1), ( 5) and (G) that

DPSE

PSE = DPSE + SIE (7)
The estimate of the credit to be granted for po1icy action clear1y depends on the interpretation of the notion of credit/debit. As the debate on PSE as opposed to TDE has shown, the PSE is an in come concept which is equiva1ent to the amount of transfer which indue es the same supp1y 1eve1, on1y under special cases where priees, taxes, subsidies, tariffs are po1icy instruments. From the point of view of agricu1 tural trade relations, the real issue is the impact of po1icies on ouptut, utilisation and trade. This perspective leads to correct the PSE in the case where supp1y control measures are implemented. The evaluation of credit/debit for policy changes should therefore emphasize the SIE part of the PSE rather than the whole transfer. It is clear, as a simple case, that cutting po down to po. on figure 1 will have no effect on production, and therefore on trade.

al Definition of the debit/credit (small country case d~w = 0)

The credit/debit can be measured by the variation of the SIE due to changes in the level of policy instruments, which are supposed here to be pO, yO, and/or ISO i. e. domestic support price, output quota and/or input subsidies.

The credit to be granted for effective cuts in price support can be defined as a negative variation of the SIE ; a debit being an increase in the effective support SIE. A general defini tion of credi t due to changes dyO, dISo, dpo can be defined as follows.

Debit = -Credit = d (SIE) = yOd ~o + d (ISo) + (~O-po.) dyo ( 8 )
The important variables in the determination of d~o will be examined below. Clearly, if the shadow price increases as a result of policy changes the first term is positive. That would be the case is the supply function for yO shifts to the left as a resul t of a cost increase or a cut in subsidies. As can be seen from figure 1 also, an increase in the level of the quota would increase ~o. The algebraic sum of the three terms in (8) which may or may not offset each other, de termines the eventual sign of the debit/credit.

b) Graphical illustration of credit/debit for selected policy changes

bl. An isolated reduction in the level of the quota In that case the evaluation of the debit according to equation ( 8 , uo~::' 11~ll-IZ_1:-!~i

1 1 ,
In the case of a reduction dyO of the level of allowed quota (by dyO), the shadow price falls by d~o and the PSE will decrease by area (b + c), which is an approximation of the income effect. But the equivalent income effect which would have produced the same supply reduction is gi ven by area (a+c). It is clear that the component a is just shifted from the SIE to the DPSE and is not inducing supply any more . Area a should be considered as the appropriate measure of the credit obtained from quantity restriction. Area (a + c) could also be used to follow the more traditional calculation of PSE.

Note that the presence of area c under the supply curve, which represent the cost saved when output is reduced, is an artefact of the practical implementation of PSE calculations. If the producer's surplus rather th an the PSE was used, area c would not be included in d (PSE) nor in d (SIE). In section 2. where a more rigorous approach is used in the evaluation of AMS. the contribution of the good under quota to the aggregate credit will only be area a (when only the quota level is al tered) .

b2) The credit due to a support price cut of the good subject to quota is zero Expression DPSE of yO dpo expression (6),

(5) shows tha t a change dpo has an but no effect on SIE as can be where po does not appear. impact on seen from

----------- • ----• d(PSE) • -a d(SIE) • a d(DPSE) --a 8 pO _ _ _ _ _ _ _ _ _ _ w 1 1 ---, 1 1 y Figure 3
illustrates the simple case of a price cut by dpo smaller than the wedge between po and ~o. The only effect is a cut in the decoupled transfer by area a. There is no credit to be gained from such an action if the concept of trade distorting equivalent or supply inducing equivalent is the one chosen.

If however poli tical economy considerations or inefficiencies due to the artificially created asset value of quota rights are taken into account, sorne weighted sum of (DPSE) and (SIE) might be considered, with the heavier weight placed on SIE.

b3) A change in input subsidies

From expression (7), when only d(ISo) is different from zero, the debit amounts to

Debit = d(SIE) = yO d~o + d(ISo)
where, d~o = (o~%p'). (op'/oISO).d(ISO) It can be noted in this case that the two components of d(SIE) have opposite signs under normal input conditions since one expects that o~• lop' > 0 and op' loIS• < 0, Le. a positive effect of input priees on marginal cost and a negative effect of subsidies on input priees. This change in IS• will have an effect on both DPSE and SIE. The change in DPSE is only a function of the shadow priee, which is shifted to or from SIE. But the change in SIE is the negative of the latter plus the change in input subsidies. The sum of the two components, i. e. d (PSE), will therefore be affected by the input subsidy change only as can also be seen directly from equation (1). ligure 4. iffect of a decrease in input subsidy on the credit

pO ---- --- -- - - ï - _
/ y e) Estimation of the shadow priee ehange

/

In order to use expression (8), we need to know the initial level of the quota and the gap between the shadow priee and the free trade or no policy priee p. w. We also need to estimate the change in the shadow priee d~• .

When there is a market for quota rights or for rented quotas, the gap between support priee p. and shadow priee ~.

can be estimated on that basis, as well as changes in the level of the shadow priee over time.

In the case of Ee where a real market for quotas does not exist in most countries', we will use a different approach based on the idea that in 1983, before the implementation of the quota, support or rather market price and marginal cost (i. e. shadow pr.ice) were equal. Then the simple comparative statics of the dairy supply function will provide an estimate of the shadow price change from 1984 to 1988.

The shadow statics of the included and yO shadow price is price change is obtained from the comparative supply function (3), with technica1 change the new po1icy instrument instead of pO. [The now endogeneousl .

5S 5S 5S dyo = d~o + l dpi 1 + dt + l dKJ 1 5p' 1 5 t J 5KJ (9 )
This expression supply elastici ty Eo 0 variable input prices technica1 change can be easily wri tten in terms of own and cross elastici ties, wi th respect to Eoi = 510g Si 510g pl, ; with respect to in fonction of exogeneous variables yO, pl, dt

-1 ~o = (Eo 0 ) (Yo -l Eo' pl -Eo 1 dt -l Eo K J KJ) 1 1 J (11 )
Since the supply function is homogeneous of degree zero in prices, Eoo + l Eoi = 0 and ~o is homogeneous of degree one in variable input prices pli. If prices changes are nominal the shadow price cut is also nominal, and similarly for real changes.

This expression shows how both shifts of the supply curve and moves along this curve de termine the shadow price. As Eoo, the own price supply elasticity, is positive, a reduction in the level of the quota drives the shadow price down. Both a positive technical change bias and an input price fall work in the same direction under normal conditions. Such changes will l in section J where practical utters will be discussed further, the results of the method used will be cOlpared with the partial inforlation available on quota values. tend to give credit for policy adjustement under quota. However the flow of fixed or primary factors KJ out of the industry at ra te KJ, as one expect i t to be the case in the farm sector, will tend to slow down the fall of the sr.adow priee.

As can be seen from table l, the main contributing factors to the fall in the shadow price from 1986 to 1988 are the eut in the level of the quota and the rate of technical change. When the deflated shadow price is considered, the contribution of input priees is also significant (about -7 percent). The decrease in primary factors use works as expected in the opposite direction and has reduced the amount of credit that can be requested from the dairy quota'. However technical change bias on quasi-fixed inputs (labor and capital) more th an offsets the outflow of resources from the sector (Mahé, Guyomard 1989). These estimates will be set in wider perspective below, since policy changes carried in the EC since 1986 have not dealt only with the dairy sector. 2 -The multi-commodity case (small country)

The previous approach can be extented to the whole farm sector in order to decompose an aggregate measure of support (AMS) into two components a Decoupled Aggregate Measure of support (DAMS) and a Supply Inducing Aggregate Measure of Support (SIAMS). In the mul ti -commodi ty case, tha t is in the mu1 ti-input mu1 ti-output case, cross effects between outputs and inputs shou1d be taken into account. The AMS change must include the credit /debit on both commodities under quota and the others for which support priees have been adjusted.

The different measures of support can be defined directly from production theory, on the basis concepts of profit functions. The formulae used in the implementation, are quite understood intuitive1y without reading the of severa1 relevant which are eventually simple and can be derivations below.

For an enterprise facing exogeneous market priees (v' VO ), but with sorne netputs constrained at level qO several notions of profit functions are useful to assess income transfers due to various changes in exogeneous variables. The firs t is the uncons trained or long-run total profi t function corresponding to the case where al1 netputs are free to adjust to their optimal level.

nU(v',V O ) = Max [v'.q' + va. qO; (q', qo) E Tl (q' ,qO ) (12)
where 4 q' is the corresponding priees

inputs qO 1 V O .
vector v' and of netputs free to vary, with likewise for quota and restricted

The second is the constrained or short-run total profit function which corresponds to the cons trained profi t actually received under rationing. It is the sum of the restricted profit and the value of fixed netputs at market priees. ne (v' ,qO ,VO) = nR (v', qO) + VO qO (13 ) where n R (v' •qO) is the restricted or variable profit function defined by

n R (v' ,qO) = Max [v' q' (q' ) q' E T (qO) 1 (14 )
The third is the virtual or shadow total profit function, which is the one received by the firm if it were facing v' for variable netputs and the shadow priees iJo for the constrained ones.

n v (v' ,qO ,iJ O ) = nu (v' ,iJ O ) = n R (v' ,qO) + iJo qO (15 )
where, by Hotelling's lemma, iJo = -5n R (v' ,qO}/5qo, which defines the virtual priee as a function of variable netput priees and the level of quotas. iJo does not depend on actual support priee VO but actual profi t ne (.) does. It should be noted that when al1 netputs are in equilibrium nu = ne = n v • Furthermore, the constrained profit function ne (.) may be also written by using (15) as, (16 ) 4 Transposed vectors are not explicitel! indicated as it is clear tbat V.q is tbe inner producl. Katrix operations belol are also .ritten litbout the transpose aign.

From these defini tions, an AMS is simply defined as the difference between the constrained profit function eva1uated at this point (v' ,qO ,vol where priees are supported at v' ,vo and sorne netputs are restricted at qO and the unconstrained profit function evaluated at world priees (v', vo).

"

"

AMS = ne (v' ,qO ,V O ) -nu (v' ,vo ) " " = n" (v' ,qO) + V o qO -nu (v', V O ) " " = nu (v' ,~O) -~o qO + V O qO -nu (v' ,vo ) w " = [nU(v',~o} -no(v',v o )] + [(vo_~o) qo] " " (17)
(18 )

(19) = [SIAMS] + [DAMS] (20)
In the case of a small country, that is assuming dv'" = dvo". 0, the variation of the aggregate measure of support is obtained by total differentiation of ne (v' ,qo ,vo) This differentiation may be also written using (18) as.

d(AMS) = (on" lov' )dv' + (on" loqo) dqo + V o . dqo + qO. dvo = (on" lov') dv' + qo dv o + [v o -~o (v', qo)] dqo = q' dv' + qo dv o + [v o -~o (v', qo] dqo (22)
Differentiating the alternative expression of ne, i.e. equation ( 16), we ob tain

d (AMS) = dn e (v', qo ,vo ) = dn u (v', ~o (v' ,qo )) + d (( Vo -~O) . qo) = d(SIAMS) + d (DAMS)
The variation of the AMS is the sum of two components (i), the variation of the SIAMS which measures supply inducing Aggregate measure of support effects and (ii) ,the variation of the DAMS which has no impact on supply. The variations of both measures may be written as a function of exogeneous or control variables (v', qo, V o )

d (S IAMS) = dn u (v', ~o (v' ,qO ) ) d(DAMS)= d [(VU -~o ) qo] = (v o -~o ) dqO + qO dvo _qO [-(0 2 nR /oqo ov' ) dv' -(02 nR /oqO oqO) dqO] (24)
The importance of this decomposition is illustrated in figures 5 to 7 where only one exogeneous variable changes at a time, the other instruments variables being held constant. To make the results more transparent and easier to interpret, we consider the case of a single rationed output.

a) Change in quota level

First, let us consider the case where the quota 1evel qO varies from qO to qO + dqO (figure 5). Then the variation of the AMS, (holding dv' =dvO =dv' =dvo = O) is by ( 22 On figure 5 dealing wi th the market for output qO, the variation in the aggregate measure of support is given by the area -a ; d(SIAMS) is given by the area -(b+c+d) and d(DAMS) is represented by -a+(b+c+d). The second example is simpler and corresponds to a variation of the market price v• of the output under quota. The variations of the three measures of aggregate support are now written as

d(AMS) = q. dv• = d(DAMS) d(SIAMS) = 0 (26)
In such a case, d (SIAMS) is equal to zero since nu evaluated with v' and ~. does not de pend on v• as long as the quota is binding, i.e. as long as the shadow price ~. is lower th an the suppor price v• (see equation ( ... )). This case is illustrated by figure 6. The third particular case corresponds to a change of a market priee v' of the unconstrained output q', other instrument variables being held constant. This case results in dAMS = q' dv"

= [q' dv' + qO o~o/ov' dv'] -[qo oj,J°/ov' dv'] = d(SIAMS) + d(DAMS) (27) d (SIAMS)
is represented by the area a on corresponding to the output q' market plus the figure 3b corresponding to the output qO market represented by the area -b on figure 7b.

P ----------- / / a / / / ) pl-<ipl --- ---"1 Figure b. pO _
To conclude, a very simple expression based on expression (23) can be used to evaluate the overall debit, wh en the relevant shadow priees are estimated (see annex II). Using YI for outputs (priees p'i), x' J for inputs (priees w' J) and yO for the quota (shadow priee ~O), Debi t = -credi t = d (SIAMS) = ry' 1 dpi 1 + yO d~o -r x'.J dw' J (28)

-E.mpirical issues, terms of trade and assessment of results

The analytica1 expressions presented in the previous sections provide a simple way to calculate the debits and credits, when the effects of policy actions on priees are known. This raises at least three issues (il the actual contribution of policy action to observed changes in priees received and paid by producers (ii) the measurement of shadow priee changes (iiil the impact of po1icy action on world priees which may also contribute to a decrease in the SIAMS when support is eut and priees move up on world markets.

(i) Contribution of policy changes to observed market priees No perfect answer can be provided to this question as part of the observed changes in output and input priees is due to the reduction in priee support, but part is also due to changes in the general economic out look and in the case of tarifridden commodities world market fluctuations are the main cause for priee changes on the domestic market.

In the empirical assessment of the debi t/ credi t for EC po1icy changes we have kept in the calculation only the components of change in supply inducing income support which can be easily connected with actual EC policy changes. As can be seen in table n04, the effects of observed and shadow priee changes are included into the credit only for grains, oilseeds, beef, dairy and sugar on the output side and only for grains on the variable input side. The dramatic change in pork and poultry priees, the reduced priee of the sub aggregate "rest of agriculture", and the change in intermediate input cost are not included as they are not considered as consequences of policy adjustments from 1986 to 1988 but rather as results of the general economic situation.

It should be noted however, that when an output is regulated by a quota, the changes in cost, technica1 progress and market conditions contribute indirectly to the credit. As dairy and sugar are prevented from expanding as a resul t of e.g. technical change, there is an equivalent eut in support priee which should be included since it is due to the role of the restriction on output in preventing market conditions to influence the level of supp1y.

(ii) Measurement of shadow priee changes The method used above in the estimation of shadow priee changes depends on the parameters of the supply equa tion. In orjer to check the order of magnitude, casual or quoted informatiopns on priees of quota rights for rent or for sales were used. France' lHO p.c.

Sources '

1 Caleulated on the basis of the quoted quota priee of 1.700 S per cow and informaI inquiry. 1 personal interview , personal interview • estimates from eost funetion and frol a similar method as used here (Guyomard, Nahé 19891 1 ihen a sales priee was the data, a 10 percent discount rate was applied.

The estima tes quoted in table 2 are rather casual in most cases. Howewer the orders of magnitude are not so far away from our estimate for the whole of EC-10, which amounts to a decrease in shadow priee of about 6 p.c. from 1983 to 1986 and a further 21 p.c. from 1986 to 1988 (annex I).

(iii) terms of trade effects of policy adjustment.

The general decomposi tion of the AMS gi ven in section 2 was

ANS = [nu (v', ~u) -nu (v' w, VU w ) J + (vu -~u) qU = SIAMS + DAMS
Up to now we have discussed the effect of policy changes on nu (v' ,~O). If there are policy instruments gu (n = 1, N), this effect can be written as the total differential of the virtual profit function around domestic and shadow priee 1evel, dn u (v', IJO) = l (~nu (.) / ~g.) dg• • 20 Likewise the terms of trade effect of policy changes in EC, has increased the level of the virtual profit function at world market priees, dn u (v' w ,v o w) = l (~nu (.) / ~g.) dg•

•

In order to discover the magnitude of the second effect, the MISS model (Mahé, Tavéra et Trochet, 1988 ;Guyomard, Mahé, Tavéra et Trochet, 1988) was used to assess the impact of policy changes on world priees. Table 3 summarizes the outcome of implementing theses changes in support priees (grain, oilseeds, beef) and in the dairy quota.

  ), letting d(ISo) = 0, gives Debit = yO d~o + (~O -pO.) d yo where d~o = (~~o/~YO)dyo is calculated along the supply curve given by (3).

Figure 2 -

 2 Figure 2 -Change in SIE and credit/dehit estimate (case ni a change in queta levell

Figure J -

 J Figure J -Credit a.d suppcrt priee eut under a constant level of quota

  5LogSI5t = Eol 5Log SI5Log KJ and with respect to quasi-fixed inputs EOJ = Denoting by x = d log x a relative change yO = Eoo ~o + l Eol p'+ Eol dt + EoJ KJ 1 1 (10) Since the shadow price ~o is now endogeneous, (10) must be sol ved for ~o and K.

  ) = (v o -~o (v' ,qo) )dqO = d(SIAMS) + d(DAMS) = [-(02n R /oq O oqO).dqo.qo] + [(VO-~O(v',qO)) dqo + (02n"/ oqO oqo). dqo. qO] (25)

Figure 5 .

 5 Figure 5. A~5, SIAM5 and DAMS iariations in the case of a decrease in the leiel of the production quots (di' :dv' edit ,dv' w =0)

Figure 6 .

 6 Figure 6. AM5, SIAMS and DAKS variatinns in the case of a change in the nrket priee nf the output under quota Idi' : dq' : dv',: dv', : 01

  figure area b d (DAMS) Ga on is

  1

  MAHE L-P., TAVERA C., TROCHET T., 1988, An analysis of interaction between EC and US agricul tural policies wi th a simp1ified world trade model : MISS. Background paper for the report to the Commission on Disharmonies on EC and US Agricultural Policies, INRA, Rennes. 10 0 + --------+ --------+ --------+ ----------;-

Tabl! 1 -Provisicnal 3stiaace of Mil! shadoJ priee change ~nd

  credit ~ue te quotas in oC-10 11987-881 Isingle coolodity -soall country case) .here the cUlulative evolutions of nominal. shado. and observed, priees of Iii! are plotted.

					12
	1. Estioation of shadow priee variation (per cent)
	Contributinq	chanqe in	impact in	ilpact in
	factor	factor	nooina! tens	real teros
		Iper centl	(per centl	Iper mtl
	quota	-8.5	-9.4		-9.4
	technical
	chanqe	J.l	-3.45		-).4
	variable
	inputs priees		+ 1.13		-6.3
	quasHixed
	inputs quantities		-0.46		-O. 46
	!otal shadow priee variation
	nominal		-lU
	deflator		J.9
	deflated		-10.1		-la .1
	1. Estilation of credit in terls of SIE decrease
	1986 quota Ilillion tonnes)	99
	1986 priee' (ECU/tonne)		178
	1986 shadow priee IEcu/t)	lJJ
	credit Ilillion ECU)
		Y'd~'	4613
		1~•-p•.ldy•	733
		Total	5m
	credit imillion ECUI
	, see annex 1

Table n

 n

	'l. InformaI estimates of leasinq or sellinq priees of quota riqhts 119881
		rentaI sales	support	rate of quasirent
		priee priee	priee	as per cent of
					support priee'
	Uni ted Kingdom 1fll.l 0.06	0.034'	0.16	ll-J7 p.c.
	iBurrel. 19891
	Ireland 1If/1.1	0.036		UO	18.0 p.c.
	[Com!, 1989)
	Netherlands'lHfl/1. 1			0.75	40.0 p.c.
	Denmark' ID. Kr Il. 1		4.5	l.O	lU p.c.

Table l .

 l Terls of trade effeets and in crea se in fara incoae at lorld lariet priees. Sugar concribution to the credit vas judged to be sial! and neg igible ..BURREL A. ed, 1989, Mi1k quotas in the European Community. C.A.B. international, 214 p. BURREL A., 1989, The microeconomics of quota transfer BURREL ed., chapter 8, pp. 100-118. H., MAHE L-P., 1989, Théorie du producteur en présence de rationnements : application aux quotas lait en Europe.

			21
	4 -Summary of credit for policy measures in EC from 1986 to
	1988 (million ECU, 1986)
	actual or shado.'	support or shadov	inclusion
	priee variation	price eut	in the dehit
	funetion dn'iv'.,v'.1 grains oilseeds heef dairy sugar pori and poultry rest of agriculture Total agriculture • unconstrained ontpnts lorld priee change Iper centl + l.1 + 0.6 +1.9 + 1.9 + O.l nOlinal deilated (per centl (per centl grains J.J -11.6 oilseeds -15.5 • lU beef + 7.4 -0.5 park and poultrJ . lU • 10.5 rest of agriculture J -U . outpnts under qnota dair,' -13.1 • li sugar' inputs grains J.7 -11.6 proteins 5.9 • 13.8 lin feed 6.4 -1.5 other feed -0.8 -8.7 other int. consulpt + 1.9 -6 Debit' total change in SIAKS (sul! coun tryl iorld price change effect Debit' total change in SIAKS lIarge countryl CONWAY A.G., 1989, The exchange value change in profit at lorld priees laillions 8CO,I9861 llO II 19l 860 1 Il! (sillion ECU, 1,861 J', dp' 1 -1 850 -1 l7l !J6 -4 6n Ils l' 1d~" -4 844 •x t 1 dv', + 1 462 + 464 + 20 + 12 + 144 Repub1ic of Ireland and some future allocation, in A. BURREL ed., chapter 9, GUYOMARD H. , MAHE L-P . , TROCHET agricultural trade policy interactions between the EC and US : seasure Jes Jes yes 00 no Jes yes 00 no no no -7 540 -1 519 -9 069 of milk quotas issues for EC pp. 119-129. in the quota T. , 1988 . Mode 11 ing comparative projection. International Agricultural Trade Consortium, San-Antonio, 25 p. Paper presented at Societé Française d'Economie Rurale, 27-28 September 1989. MAHE L-P., GUYOMARD H., quotas and quasi-fixed 1989, Supp1y behavior with production factors. Paper presented ~t 6èmes , in A. journées de microéconomie appliquée, Orléans, June 1989.	..

GUYOMARD

least in a rather static point of viel, the OPS! has no effect on the level of production. Hevertheless, as it affects incole, it lay eventually affect the output of ressources frai the farl sector and therefore prnduction capacity. The label 'Oecoup1ed' given to the quasi rent is a1so sOlelhat too strong in as luch as the producer does have ta produce y' to receive the quasi rent.

ANNEX II.

This appendix is based on Mahé Guyomard Guyomard, Mahe (1989). (1989) and 24 When a11 priees are given and produeers are free to adjust immediate1y, the familiar produeer problem is :

where q is the veetor .of (n + m) netputs quantities, v the veetor of eorresponding priees and nu (v) the (uneonstrained) profit funetion. The feasible set T is assumed striet1y eonvex so that optimal quanti ties are uniquely determined and weIl behaved funetion of priees. The veetor q is parti tioned into two subveetors of quantitities q' always variable and quanti ti ties qO susceptible of being eonstrained. A similar subdivision app1ies to the veetor of priees v. Problem (a) may then be written as

The complete system of supply response ean be written in terms of the Jaeobian of this uneonstrained profit funetion

When

quantitites are pegged at say qO by poliey instruments (production quotas, set-aside, ... ), variable quantities do not behave in the same way with respect to exogeneous priees v', sinee they are also a funetion of fixed quanti ties qO. Define ~o the veetor of virtual priees, whieh ensure that the uneonstrained quanti ties qO U as funetions of priees will stay at level qo, by :

Solving (d) for the virtual priees ~o as funetion of v' and qO, we ean define the relationship between the restrieted behavioral funetions' q" ( .) and the uneonstrained funetions q' U ( • ) 5 When sOIe netputs q' are fixed at q', the constrained producer prohles is written as : lax Iv' q' ; q' ! T Iq' ~I • n' Iv', q' J. Supply and deaand equations for variable netputs q' are then given by q" Iv" q,l • on' Iv', q'l/ov'. q'R (V', qO) = q'a [V', !Jo (V', qO)] Differentitating (d) and (e) yields

The cross partial derivatives of na are evaluated at the point (v' ,qO), i.e. (v' ,!Jo (v' ,qO)). The comparative statics of the constrained regime is obtained by solving (f) for the actual endogeneous variables (dq' a, d!J°) wi th respect to the new set of exogeneous ones which are (dv', dqO), that is

The virtual priee changes are analysed using the second row of (g) : these changes may equivalently be written in terms of unconstrained price elasticities.


P Poquillon

Maurel

published or not. The documents may come


Hervé Guyomard

Louis P Mahê

IMPACT OF A GRAIN PRICE CUT ON INCOME OF CROP FARMS AN EXTENDED PARTIAL EQUILIBRIUM APPROACH

SUMMARY

The paper stems frorn the apparent very large impact of a 10 % price cut on the farrn incorne o~g rain growers rneasured by traditional producer's surplus or orther sirnilar "static" rneasures. In the context of French specialized farrns it would be around -24 per cent. Can we conclude that these farrns are not resilient and cannot sustain a significant price cut ?

The paper atternpts to identify the various induced effects triggered by the output price cut on input prices due to derived dernand effects, including a land co st effect. Even under pessirnistic assurnptions, the induced effects are not negligible (2 to 5 percent).

The effects considered above are once and for all shocks.

However, trend effects due to technical change in both agriculture and the farrn input industry do bring offsetting contributions which are both large and obtained every year (about 6 per cent).

As a result, in spite of the pessimistic static measure, specialized farrners need onlY 2 to 3 years to recover the original farrn incorne per head. Due to land price fall however, they would feel poorer .. or less rich.

Introduction

The Common Agricultural Folicy, as the farm policies of man y other industrial countries, has been caught under increased pressure to curtail priee supports since the earlY eighties. Even if the budget has recently received some relief A Quick measure of the static impact of an isolated grain output price change in percent of the base period is obviously given by the coefficient of the share

(5 q )
of the corresponding output (Oq) in income R (b) dR/R = (OqPq/R) (dPq/P.) = 5. (dPq/P.).

In the lower part of table 1, the 5. coefficient is reported for three definitions of income. The perception of the impact of a grain price cut wi 11 clear l y depend on the degree of specialization of the farms in grains and on the assumption made on which inputs will support the effects. If all inputs except raw materials participate proportionally in the burden, the impact is modest on any one of them.

R(p,w,Z,t)

= max v. x N [PY -r "'iXi i == 1 (Y, X) c T(Z,t)]
Via Hotteling's lemma, restricted ouptut SUPply and input demand eouations are obtained by first differentiation of R(p,,,,,Z,t) ",ith respect to p and", respectivelY.

Y(p,,,,,Z,t) = SR(p,,,,,Z,t)/Sp Xi(P,,,,,Z,t) = SR(P.""Z,t)/S"'i Vi = l, ... , N

Therefore, using (2a) and (2b), the farm income function may be ",ritten as N R(p,,,,,Z,t) = P.y(p,,,,,Z,t)-r "" X,(p,,,,,Z,t)

i == 1

(3)

The This can be written with more concise usual notation as

Short

(8)
Assuming that the second-or der effects are small, the impact of the induced variation in land use cost is measured by the term R,,",,~( -(Rws"",~)-1. RW!3P). dD, which, as one would expect, works as an offsetting factor on incame in the context of an out ut price cut.

-Effect due to the induced variation of variable input priees

The previous analysis applied to rented land which has an inelastic aggregate supply can be generalized to other variable inputs. In this case we make a further step toward the "general equilibrium" repercussions of the output priee eut on other market priees.

To determine how the variable input priees will change, we solve the system of supplY-demand equations on factor markets :

-6R(p,w,Z,t)/OWi = Xi(P,W,Z,t) = Edwil i = l, .. , N-l (9) where Ei (Wi) represents the supply function of input Xi .We

where : a

= [ai] = [510g E,/510g Wi] Cxw = CCxi w~] = [510g X,(p,w,Z,t)/ 510g Wj] Cxp = [CXiP] = [510g Xi(P,W,Z,t)/ 510g p] Mx = (Mxi) = (510g R(p,w,Z,t)/ 510g Wi]

Trend e""ects

Direct and indirect effects of an output price cut on farm incarne must be corrected by trend effects. As a consequence, the time necessary to cancel the impact of an output price decrease can be deri ved. We f irst deal wi th the effects of technical progress. Then structural effects related to trends in other costs and family labour out-migration are analysed.

Technical progress effect

This effect is se en more clearlY by total differentiation of the farm Equation ( 16) shows that the growth rate of the "unit" supply function can be decomposed into three components a substitution effect, a fixed input effect and a technical change effect (given respectively by the first plus second terms of ( 16), by the third term and by the fourth term of ( 16)). Furthermore where MNt reoresents the share of family labour in farm incarne and Ms, the share of owned land in farm income (MN'+ Ms, = 1).

Cvt = Slog(Y/S,)/St = SlogY/St -SlogS,/St = CVt -CS,t (18)
4. Empirical illustration impact of' a ten percent output price cut on farm income of' specialized grain growers

The previous approach is apolied ta sDecialized grain growers (France. FADN, Otex 11, year 1984). The different effects of a ten percent output priee eut on farm incarne defined by FIR of these producers are presented in table 2, according to the sequence followed in sections 2 and 3.

  Most studies which deal with the impact of priee support on incarne use the concept of Producer Surplus or the closely related Producer Subsidy Equivalent (PSE) which has become popular in the context of the OECD trade mandate (OECD, 1987) and the GATT negotiations. The paper attempts to go beyond the static equilibrium approach and tries to identify the actual impact of price support (or price cut) policies. partial long-run First the producer surplus concept is related to the restricted (or short-run) profit function in a multioutputmul t i input framework. Key factors exp laining the short on the farm and are to get their returns from whatever is left from the rewards to variable inputs due to the working of factor markets. The impact of a change in the price of one output wi 11 depend, f irst of all, fixed factors (i.e. family inputs self employed labour and own capital) is important in that context since the definition of the farm income function depends on the partition of inputs into fixed (i.e., more precisely, fixed for an arbitrary analysis period) and variable subsets. Value-added may be then a poor indicator of farrn incarne in arder ta assess the impact of a priee support

  As an example a 10 percent grain price cut would have a 8 percent static effect on Value-Added. But if the onlY factors bearing the consequences of the price cut are family workers, then the impact is Quite large 19 percent in OTEX 12 and up to 30 percent in OTE X Il. incarne relevant te any assessment of a priee change impact de pends on the time horizon of the analysis. In the very short-run (i.e. within the year or sol, all purchased factor costs (including wages, caDi tal deoreciation, interest payments, rentals), taxes and related costs have to be payed by the operator at the prevailing prices which are unlikely to adjust immediatel y. Value-Added i s not an adeQuate concept covers the rewards to all non paid factors which are supplied by family operators. As the owned land is afairly small share, the static impact of a grain price cut is likely to be large percentage wise in OTEX 11 and 12, as it is the price cut in percent multiplied by a factor of 1.5 to 2.4.

2.

  Restricted profit, income function and producer's surplus 2.1. The income t'unction Let the farm' s inputs X = (Xl, •.. , set XN) of technologieally feasible variable and output Y be denoted bY T(Z,t)or restricted profits, in other \Nards ta maximize the farm income ",hich must re"'ard family labour and the land o",ned by the operator. The producer' s farm income function can then be defined as the solution to the problem N of maximizing variable profit DY-r WiX~, subject te the 1. = 1 constraint imposed by the technology T(X,Z,t,Y) = O.

  farm income function accounts explicitly for the fixity of familY inputs, self employed labour and o",n land. As a consequence, the impact of a decrease in the priee of the output on this farm income can be analysed. Key factors in the short-run and in the long-run are identified fram the exogeneous varaibles in (3). First, it may be useful to relate the familiar producer' s surplus concept ta the farm incarne function as defined bY (1) or equivalentlY by (3).

Figure l .

 l Figure l . Producer's surplus and short-run direct ellect, 01 an output priee change

  note e, = oEi (. )/OWi the magnitude of the slope of the [Rww + a]-l Rwp. dp where a is a diagonal matrix of terms ai.

  that Z = t = w~= 0, to keep the analysis simple) . dR = Rp dp + 1/2 Rpp d p 2 + R'w dw + 1/2 dw' Rww dw + 1/2 dw' Rwp dp = Rp dp + 1/2 Rpp d p 2 + R'w (-(Rww + a)-l Rwp) dp + 1/2 dw' (-Rw p dp -a dw) + 1/2 dw' Rw p dp = Rp dp+1/2 Rpp d p 2+R'w(-(Rww+a)-lRwp)dp-1/2 dw'adw (12) Finally, the variation in % may be written in terms of familiar parameters. R = My (1+1/2 Cyp p)p -M'x(-cxw + a)-l Cxp P -1/2 w'a 1,,1

  effect corresponds to the rate at which the restricted profit function shifts. Nevertheless this effect is not eQual to the total factor productivity growth rate in the grain sector since a total factor productivity representations of the technology (long-run isoQuants, longrun cost or profit curves). The following analysis proposes an approximation of this technical change effect. First, let us introduce a Tarrn incarne function bY unit of owned land ares. p,w,n,t) is the supply function by unit of owned land x,(p,w,n,t) is the demand function by unit of owned land for the ith factor (i = 1, N) and n is familY labour 16 per unit of owned land. By total logarithmic differentiation of supply and demand functions, at first order, we obtain

  the function r(p,w,n,t) is Cobb-Douglas with respect to the ratio n, then Cyn is simply equal to the family labour share MN'. Finall y, the part ial logari thmic deri vat ive of the supply function y(p,w,Z,t) with respect to time may be lNritten as N -1 Mx • . Slog w(t)/St i ::: 1 (23) The second structural effect measures the impact on farm income per unit of family labour of the decrease in the longrun of self-employed labour. From equation (2), this impact is equal to : Slog(R/N.)/Slog N•. Slog N./St + Slog(R/S.)/Slog S •. Slog S,/St = [(MN, -1) Slog N,/St + Ms, . Slog S,/St]

  decrease) which occur each year. Technical progress within and out of the farm sector must now be included in order to assess the resilience of specialized farms faced with decreasing priees. The total of these trend effects is estimated to 6 % per year. The impact of yield growth rate, which is eoual to about 3 % per year, is measured according to eouation (22) 22), observed past evolutions of relevant variables are used in arder to calibrate necessary parameters the share of output in farm income is equal to 2.4, the SUffi of shares of variable inputs in farm incarne i5 equal te -1.4, the share of family labour is equal to 0.9 and the growth rate of family labour is estimated to range between -1 % and -2 % per year. Using these estimates, the technical change impact on farm income is equal to 5.1 % per year. Structural effects, which measure the consequence on farm incarne of variable input priee and family labour trend evolutions, are smaller but far from being negligible from 0.8 % to 0.9 % per year. The sum of these trend effects lies between 5.9 % and 6 % per year and, consequentlY, three years only are necessary in arder ta cancel direct or indirect effects of the output priee cut on farm incarne, in spite of the quite large impact as measured by the static producer' s surplus or by the very close static or accounting effect.

direct impact of a ten percent price cut is very large, only

	policy.	As	exoeeted,			the	larger	the	share	of	output	in
	restricted prof i t, the		lar<i/er the short-run direct impact of
	an output priee change	on the reward of the factors remaining
	fixed.
	Induced or indirect effects on purchased variable input
	markets are then emphasized. These effects depend on demand
	response	but	also	on	the	elasticity	of	factor	supply
	functions. Following Schumway, Pope and Nash, 1984	Mahé and
	Rainelli, 1987	Guyomard, 1989	rented land is assumed to be
	more or less fixed at the aggregate level. For other variable
	inputs, supply is assumed to be less than infinitely elastic
	so that their prices fall somewhat, dampening the impact of
	the output price cut on income. We compare the fairly high
	impact		of	a	ten	percent	price	cut	on	farm	income	of
	into	account	particularly	in	order	to	assess	the	time
	necessary to actually cancel	the impact of a	lower price
	three years at most are sufficient to restore income per head
	at the initial level.
	The organization of the paper is as follows.

specialized grain growers, when variable factor supplies are perfect l y elast ic, wi th the lower ones obtained when factor supplies are not assumed to be perfectly elastic. FinallY, trend effects (i.e., technical progress, variable input price and family labour level trends) are also taken support policy. As an example, for French specialized grain growers (FADN, Otex 11), we show that, although the short-run

section, the relevant concepts of farm incame

	and	discussed.	In	the	second	section,	the

framework is derived and the producer's surplus

	1	Impacts of a priee change under different definitions of
	farm income
		The evaluation of labour earnings is a well known problem
	in farm management due to the difficulty to distribute rewards
	to the various fixed	inputs supplied by the owner.	This
	situation is typical for self employed operations since other
	fixed inputs as capital cannot in general be priced neither at
	their opportunity cost	(which may be Quite small) nor at
	market priee	levels.	Many	examples show that	using	some
									In the first
									are oresented
									theoretical
									is related to
	the farm	income	function.	Induced	and	trend	effects	are
	analysed in section three. Empirical results are	presented in
	section four.

average profit rate for capital or sorne imputed wage for non ooerator familY labour may lead in sorne cases ta zero or negative operator's incarne.

		Table 1 exhibits an average FADN account for French
	specialized cr op farms in 1984. (OTEX 11 and 12). It first
	shows	a	different	output	mix	according	to	grain

specialization. Various measures of income are shown. They are

	Qui te di fferent in magni tude according to which factors they
	are supposed to reward. Family Labour Income (FLIl is ~of
	course much smaller (139 000 francs).	than gross operat ing
	income (225 657 francs) or Gross Value-Added.
		change it is important
		to	be	included	in

are supposed te be and which ones have In assessing the impact of a priee to define clearly what is supposed producer's surplus, i.e. which factors

	payed at market priees (variable inputs)
	to be content with what is left.

Table 1 .

 1 Main ite.s 01 an ayerage operation account and grain output 'share in inco.e -(FAON, 1984,

French farls, in francs).

	OTEX 11 OTEX 12
	1. Gross revenue grains
	2. Other cash crops
	3. Inter.ediate co.su.ption
	4. Gross Yalue Added
	5. Operating costs
	6. Land rentaI costs
	7. Land taxes
	8. Yages
	9. Social security P8yments on wage earners
	9'. Land interests
	10. Gross operation inco.e (4-51
	11. Depreciation
	12. Net operation inco.e (10-11)

13. Loan rep8Ylents 14

				407 821 231 471
				148 025 272 760
				224 786 121 129
				331 060 292 102
				105 403 95 422
				30 492 25 698
				4 341	4 115
				7 106 10 680
				2 480 3 501
				6 982 4 545
				225 675 196 680
				73 662 57 727
				151 995 136 953
				42 564 28 751
				109 431 102 202
				13 004 12 392
				138 991 124 561
				43 496 38 090
				171 981 153 890
	ratio	inco.e concept	cOIPutation
	51,	GYA	1/4	1.2	0.8
	S',	FIR	1/18	2.4	1.5
	SI,	FU	1/16	2.9	1.9

. Ayailable lar. inco.e (12-13) 15. I.puted land costs 16. Fa.ily labour inco.e (12-15) 17. Land returns (6+15) 18. Fa.i!Y input returns (12+15+9') 1.1. St:at:ic or account:ing impact: ot' a pric~change One aim of the paper is to illustrate how measuring the impact of a priee change is sensitive te incorne definition. Simple calculations based on table 1 will illustrate this point. In the very short run, the input/output coefficients are fixed and a static measure of impact is readily obtained from expression (a) (a) R

= Q9 p~+ Qo Po -X1C Wic -Xo Wo where Qg P g is the grain revenue in FF terms, 00 Po is other crops revenue, Xie Wic is total intermediate consumption cost

and Xo Wo other variable costs.

priee eut are carried over soecified period of time and technical progress gives on at a more or less exogeneous

  This static measure leads to a pessimistic vie ... on the eapabi 1 i ty of speeialized farms to bear signi f icant reduct ion variable inputs ean adjust to some extent to the ne... input output priee ratio so that a second order effeet can be added to the stat ie effect. Thi s effect ... i 11 tend to attenuate the estimate given by the static point of vie ....

	in	priee support.	What does the pieture looks like ...hen
	adjustments are allo ... ed to take place both on input mix and on
	factor markets ?
	1.2. Second-order, induced and long-run impact
		Even in the short-run,	where input priees are given,
		A	third	effect,	the	indueed	effect,	must	also	be
	eonsidered as the deerease in the demand for inputs,	as a
	resul t of the priee eut, ... i 11 impact farm input markets and
	therefore	input	priees.	By	assuming	some	reasonable	(or
	pessimistic) levels of input supply elasticity, the dampening
	effeet of cheaper inputs to the priee support reduetion can be
	evalued.
	Last, pace. By	taking		into		aecount	produetivity	gains,	it	is
	possible to find out the aetual impact of a given priee eut on
	ineome in the long-run.

It may also allo... to evaluate the magnitude of priee eut that even sDecialized farmers can stand ...hen all adjustments are ineluded in the analysis.

:-run dir~t: errect:s and producer's surplus

	The short-run	direct effect of	an output price	cut	is
	derived	from	a	second-order	Taylor	approximation	of	dR,
	holding variable	input priees,	fixed	input levels	and	time
	constant.
										p)	(5a)
	= My (1 +									(5b)
	where My	is	the	share	of	Y in	farrn	incarne	and	Cyp	the
	restricted oINn price elasticity of output Y.
	This short-run direct effect includes the adJustment of
	variable input and ouptut levels in response to the ouptut
	price	cut.		This	effect	corresponds	to	the	variation	of
	producer's

dR = ô R (p, IN, Z, t ) / ô p. dp + 1/2. Ô 2 R (p, IN, Z, t ) / ô P 2 • (dp J2 = y(p,IN,Z,t).dp + 1I2.ÔY(p,IN,Z,t)/ôp.(dp)2 Noting dR/R = Rand dp/p= p, this effect in % is equal to R = My.p + 1/2.ôlogy(p,IN,Z,t)/ôlogp. My. (

surplus which is represented by ares A on figure 1.

	Taking only a first-order Taylor approximation of dR, the
	measured effect	INill	be equal to My.p. 5ince this first
	order ef fect is represented by are a A + B in figure 1, i t
	overestimates the surplus variation in the case of a priee
	eut. In the case of a priee increase,	a first-order Taylor
	approximation of dR (area Al) underestimates the real surplus
	variation (area Al + B1).

Table 2 .

 2 ropact ot a ten percent output priee eut on taro inco.e ot specialized gain growers[Frence, FAON, OTEX Il, ,ear 1984) second induced effect lies between 1.8 % and 5.1i. %. Detailed results are presented in table 3. rable 3 incole lndueed etteet related to variable input priee deereose ot a 10 , priee eut ot 9rains on for.

	Short-run direct effets
	'accounting' or tirst-order short-run direct ettect				-24 \
	second-order-direct ettect						+ 0.5 \
	Indirect or induced effects
	ettect due to the induced variation ot rented land cost				+ 2.1 \
	ettect due to the induced wariation ot wariable input priees		troo 1.8 \ to 5.3 \
	(1) , Sua ot direct and indirect ettects tro.			-19.6 to -16.1 \
	1Nnd effects (per year)
	technical progress ettect						+ 5.1 ;
	structural ettects
	trends ot variable input real priees					+ 0.7 ;
	trend ot taoil, labour evolution			trol 0.1 ; to 0.2 \
						+5.9\	t06;
	Recuperation dela, ' (1)/[2)				2.6 to 3.2. ,ears
	Short-run direct effects are very large and equal to -24 %
	because the output share in farm income is 2.4. It is clear
	that the more specialized is the farm,	the larger is this
	impact. The second order effect is estimated to	0.5 % with an
	own price supply elasticity of 0.4. ConsequentlY using either
	the short-run	direct	effect,	up	to	second-arder,	or	the
	"accounting" effect give an impact of the price cut of same
	order of magnitude. Induced or indirect effects are equal to
	2.1 % for the user cost of rented land effect and lie between
	1.8 % and 5.3 % for the variable input price effect. The first
	induced effect is obtained assuming that the	cross priee
	elasticity of land with respect to grain price is equal to 1.

(2) , Suo ot trend ettects

[per ,ear)

Using macroeconomic data for France, it was found that this cross elasticity is equal to 1.12 whereas the elasticity of land priee with respect ta crop intermediate input priee i5 only 0.12.

BIBLIOGRAPHY DRONNE Y., GUYOMARD H., MAHE L-P., TAVERA C., TROCHET T., VERMERSCH D., 1989, L'impact d'une baisse de prix des céré-

CYt = Cv, + C =' f t N = Y -Cyp P -r Cywj lN, -Cyn n + C =s f t J =1 N = (Y/s)-k r Cy""j (lNjp) -MNf n + C:sft

In the same lNay, the partial logarithmic derivative of the demand function Xi(p,lN,Z,tl for the ith factor lNith respect to time may be written as :

Structural effects

These structural effects represent the impact on farm income of trend evolutions of variable input priees and familY labour level.

The long-run decrease of raw material real priees, which

is essentially the result of an increasing productivity in the above sector, leads te an increase of the farm incarne. Since income is defined according to the fixity of tamily inputs, self-employed labour and owned land, the long-run trends of other variable input prices (hired labour, rented land and capital) must also be taken into account. The variable input price vector is then a function of time : w(t