ON THE COMPLEMENTARITY BETWEEN LAND REFORMS AND TRADE REFORMS

Transcription

1 ON HE COMPLEMENARIY BEWEEN LAND REFORMS AND RADE REFORMS Abhrup Sarkar Indan Statstcal Insttute Calcutta January, 1 December, 1 (Revsed) Abstract he purpose of the paper s to look at the welfare effects of trade n agrcultural goods n a less-developed country where the agrcultural market s controlled by a handful of large farmers. It s shown that the success of trade reform depends upon the dstrbuton of output between large and small farmers and the success of land reform leadng to redstrbuton from the large to the poor depends on trade reform. In other words, f undertaken n solaton, each reform mght lead to a fall n welfare, but f jontly undertaken, they wll lead to an ncrease n welfare. hus the two reforms are complementary. Acknowledgements: he author wshes to thank, wthout mplcatng, semnar partcpants at the Indan Statstcal Insttute, Calcutta and Jadavpur Unversty and especally Soumyen Skdar for helpful comments on an earler draft of the paper. Malng Address: Abhrup Sarkar, Economc Research Unt, Indan Statstcal Insttute, 3 B.. Road, Calcutta 735, Inda. Emal: abhrup@scal.ac.n 1

2 1. Introducton In recent years, a number of less developed countres are gong through a process of economc reforms. Many of these countres are stll predomnantly agrcultural and an mportant agenda n ther lst of reforms s to open up the economy to nternatonal trade n agrcultural goods. he WO has also nssted on freer trade n agrcultural commodtes among ts member countres. All ths has made free agrcultural trade among natons a very mportant polcy ssue n recent years. More so, because the current trade practces n agrcultural goods n the world s far from free. It s but natural that debates and controverses would crop up around the queston of costs and benefts of a freer agrcultural trade. Indeed, a consderable lterature has developed addressng ths polcy queston. But very few of the exstng papers wrtten on the subject address the problem n terms of a formal model. he purpose of the present paper s to fll up ths gap. Whle dong so, our focus remans restrcted to less developed agrcultural countres. In many of these countres, the agrcultural market s controlled by a handful of large sellers. rue, a large number of small sellers also coexst n the market and true, the total output produced by the small sellers s not nsgnfcant. But the small sellers do not have the power to hold stocks for long. So each year, they are compelled to sell most of ther stocks just after the harvest. As a result, every year, barrng a few busy months just after the harvest, the market s controlled by the large sellers. We model nternatonal trade n agrcultural goods n ths background.

3 What are the nature of reforms people are talkng about for these backward agrcultural sectors? Indeed, what knd of restrctons are mposed on nternatonal trade? he exstng restrctons are n the form of export and mport quotas, tarffs, restrctons on future tradng, restrcton on prvate holdng of stocks and canalzaton of exports and mports,.e. nternatonal trade only through government agences (see Pursell and Gulat (1995) for a detaled account of the restrctons mposed on Indan agrculture). he reformsts are n favour of removng these restrctons and move on to free nternatonal trade. In ths paper, we examne, theoretcally, the desrablty of free trade over autarky as well as trade wth government restrctons. In fact, there s yet another type of reform, vz. land reform, whch some economsts have been talkng about for a much longer n the context of these backward agrcultural countres. he effect of land reform s to redstrbute output from the large to the smaller farmers. Surprsngly, the proponents of economc lberalzaton have seldom talked about ths more fundamental reform. But at least n some quarters t s accepted that the success of lberalzaton depends to a large extent on certan socal reforms, ncludng redstrbuton of land (see, for example, Lpton (1995)). he hstory of Europe, Japan and that of the newly ndustralzed countres of South East Asa seems to support ths vew. Our paper provdes a theoretcal justfcaton of ths vew. In partcular, we show that free trade s better than autarky or restrcted trade only f the dstrbuton of output between the small and the large sellers s suffcently n favour of the former. We also show that the success of land reform, n ts turn, depends on trade reform. We show n partcular, that under autarky redstrbuton leads to a welfare loss and hence s costly. If, on the other hand, the economy s opened to nternatonal trade, free or 3

4 restrcted, the welfare cost assocated wth land reforms under autarky smply vanshes. So, f the prmary am s to mplement redstrbuton wthn the agrcultural sector, t s better to have the economy open to nternatonal trade. hus the purpose of the paper s to show that the two reforms are, to a large extent, complementary..1 he Envronment We consder the market for a sngle agrcultural good. Output s seasonal and s obtaned at dscrete ponts n tme. hese dscrete ponts are dentfed wth the harvest. he tme nterval, whch les between two consecutve harvests, s denoted by [,]. We focus our attenton on ths tme nterval. hough producton s dscrete, consumpton s contnuous. o meet contnuous consumpton, output has to be stored from one harvest to another. hus, storage s a very mportant actvty n the present model. here are three types of agents operatng n the market: large sellers, small sellers and consumers. Both large and small sellers own some stocks at the ntal tme pont. he problem of each seller s to decde upon the optmal sequence of sales from these stocks over the nterval [,] so as to maxmze profts. here are two dfferences between the large and the small sellers. Frst, a large seller s able to affect the market prce through hs sales decson. hus each large seller enjoys olgopolstc market power. Each small seller, on the other hand, s a prce taker. Second, the large and small sellers dffer accordng to ther storage costs. For a large seller, storage cost s n the nature of a fxed cost. Once ths fxed cost s ncurred, a large seller s able to store as much stock as he wshes at zero addtonal cost. In other words, for a large seller, the average cost of storage falls as the quantty of stocks goes up. herefore, the large sellers are specalzed 4

5 traders who nvest money to acqure large storehouses wth excess capacty. On the contrary, the small sellers ncur storage costs per unt of stocks stored per unt of tme. Moreover, ths per unt storage cost s ncreasng n the total amount of stocks stored. hus, the small sellers have a rsng margnal cost of storage wth zero fxed cost and the large sellers have a zero margnal cost of storage wth a postve fxed cost. We assume that there s a large number of small sellers and n large sellers n the market. A further mportant dfference between the large and the small sellers wll follow from our analyss. It wll be shown below that the large sellers can sometmes buy stocks from the market for future sales; the small sellers, however, wll be sellng stocks at all ponts n tme. hus we shall show that t s only the large sellers who can engage themselves n ntertemporal trade (.e. buyng cheap at one pont n tme and sellng at another future pont n tme). As compared to the sellers, the consumers are passve n ths model. hey do not, by assumpton, hold any stock for future consumpton. hey buy and consume at the same nstant. At any pont n tme they have a demand curve whch s assumed to be lnear and unform across tme. he nverse demand functon takes the form (.1) p( = a q( where p( s the prce of the good and q( s the quantty demanded at tme t. Let y( be market sales (market purchase, f y( s negatve) by the large sellers and z( be market sales by the small sellers at tme t. hen demand-supply equalty at tme pont t mples that q ( = y( + z(. Consequently, equaton (.1) may be wrtten as 5

6 (.1A) p ( = a { y( + z( } he sellers take (.1A) as gven whle maxmzng ther profts.. he Large Sellers Problem A large seller maxmzes hs ntertemporal profts by choosng hs sequence of sales (and purchases) gven the sequence of sales of the small sellers, the sequence of sales of the other large sellers and the demand equaton (.1A). Formally, a large seller s problem s to (.) max p( y ( dt - k subject to X ( ) = X, ( ) = X where y ( = X& ( In the above maxmzaton problem, X ( denotes stocks held by the th large seller at tme t. Hs ntal stocks are X and hs termnal stocks are zero. Sales at any t are denoted by y ( whch s equal to the fall n stocks at t. If y ( s negatve, then t s nterpreted as purchase. k denotes the fxed cost of storage of the th large seller. Snce these fxed costs are not gong to play any role n the subsequent analyss, we assume that k =. For smplcty, we also assume that the ntal stock X s the same for all. 6

7 Each large trader chooses hs sequence of sales (or purchases) { ( } to maxmze profts. he frst order condtons, gven by the Euler equatons are y (.3) & ( = for = 1,, n. m Here m ( denotes margnal revenue of the th large seller at tme t. Usng the demand equaton (.1A) we can solve (.3) smultaneously for all to obtan (.4) z& ( y& ( = n + 1 (.5) n y &( = z& ( n + 1 (.6) z& ( p& ( = n + 1 A few comments on the maxmzaton and the consequent solutons are now n order. Frst, a large seller chooses hs sequence of sales and purchases { y ( } to maxmze (.). We confne our attenton to the case where the path of purchase and sales s precommtted. In other words, the th large seller chooses hs optmal path at tme and stcks to ths path for the entre nterval of tme. We could alternatvely assume that the seller s able to revse hs optmal path at any pont n tme n future. hs, however, would not change the solutons (see Sarkar (1993) for a formal argumen. 7

8 Secondly, as s clear from equatons (.4)-(.5), the rate of change n optmal sales and purchases of the th large seller s ndependent of the sales or purchases of the other large sellers. he rate of change depends only on the rate of change n the market arrval of stocks from the small sellers and the number of large sellers n the market. he latter varable n s nversely related to the degree of monopoly n the market. hrdly, from equaton (.6) t follows that the extent of prce fluctuatons (as represented by the rate of change n prce at any depends only on the extent of fluctuaton n market arrval from the small sellers and the degree of monopoly. In partcular, for any gven fluctuaton n market arrval, the hgher the value of n,.e., the lower the degree of monopoly n the market, the lower s the extent of prce fluctuatons. We shall have more to say on ths pont after we compute the equlbrum paths..3 he Small Sellers' Problem he small sellers are prce takers by assumpton. A representatve small seller maxmzes hs expected profts by choosng hs sequence of sales, gven a sequence of expected prces. A small seller has a quadratc cost functon of storage gven by µ [ H ( ], where [H(] s the stock held at tme t and µ s a constant. A small seller's problem s to e (.7) max [ p ( z( µ { H ( } ] dt subject to H() = H, H() = where z( = H & ( 8

9 In words, a small seller maxmzes ntertemporal profts by choosng hs sequence of sales {z(} gven a sequence of expected prces { p e ( } and gven hs ntal stocks H. he Euler equaton representng the frst order condton s gven by (.8) p& e ( = µ H ( From equatons (.4), (.5), (.6) and (.8) we can compute the equlbrum prce sequence and the sequence of sales of the large and the small sellers. hs s done n the next secton..4 Equlbrum under Autarky Before we proceed to compute the equlbrum sequence of prces and sales, we gve a formal defnton of equlbrum. An equlbrum s defned as a collecton [{ y ( },{ z( },{ p( }] such that the followng condtons hold: () { y ( } maxmzes (.) gven { y j ( } j and {z(}, j. () { z( } maxmzes (.7) gven { p e ( }. () p e ( = p( = a y( z( t. Condton () mples that n equlbrum prce expectatons are fulflled. It also mples that ( ) p& e ( = p& ( t. Combnng condton ( ) wth (.6) and (.8) we get 9

10 z( (.9) & = µ H ( n + 1 Equaton (.9) s a second order dfferental equaton of the form (.1) H&& ( βh ( = where H & ( = z& (, β = µ ( n +1). he general soluton of (.1) s gven by (.11) H βt ( = C1e C e βt he constants C,C 1 may be solved from the ntal condtons as (.1) C 1 He e β = = β β, C 1 e H 1 It may be verfed from (.11) that H & ( = z( >, H&& ( = z& ( <, H&&& ( = & z ( >. In vew of these, the tme paths of z (, H ( are drawn n fgures IA and IB. Fnally, the tme paths of (, y(, p( may be derved from equatons (.4), (.5) and y (.6) along wth the ntal condtons. hese tme paths are (.13) 1 y ( = [ z z( ] + y n + 1 (.14) n y ( = [ z z( ] + y n + 1 1

11 n 1 (.15) p( = a z z( y n + 1 n where y = y ( dt, y = ( ), y t dt z = z( dt. Clearly, y, y, z are average sales. he detaled dervaton of equatons (.13)-(.15) s gven n Appendx A. It s clear that once the tme path of z( s determned from equaton (.11), the other tme paths are known from (.13)-(.15). A few comments on the equlbrum tme paths are now n order. Frst, consder the optmal strategy of a large seller as gven by equaton (.13). A large seller sells the average amount y from hs own stocks at each tme t; n addton, he sells an extra amount f at any t the market arrval z( falls short of the average market arrval z. hs s captured by the frst term n the rght hand sde of equaton (.13). If, on the 11

12 other hand, the actual market arrval at t s greater than the average, he wthholds some stocks and sells less than y. In the extreme case, when the actual market arrval exceeds the average market arrval by a very large amount, y ( becomes negatve and n ths case the large seller buys from the market. Clearly, through hs purchase and sales over tme, a large seller tends to smooth out ntertemporal prces. Secondly, to follow ther optmal sequence of sales and purchases, the large sellers have to know only the average market arrval z or equvalently, the total market arrval H from the small sellers. he market arrval at any tme t can, of course, be observed by a large trader at tme t. In partcular, a large seller nether has to know the future sequence { z( } of market arrval comng from the small sellers nor the sequence of sales of other large sellers n order to follow hs optmal path of sales and purchases. 1

13 hrdly, the degree of wthholdng or over-releasng of stocks by the large sellers n response to the dfference between actual and average market arrval depends on the degree of monopoly whch s nversely related to n. he hgher the value of n,.e., the lower the degree of monopoly, the hgher s the total response of the large sellers. hs s clear from (.14) where, n the rght hand sde, n /( n +1) s ncreasng n n. In the extreme case, when n, ths total response s the hghest and s equal to unty. In ths case, whatever be the fluctuatons n { z ( }, {y(} adjusts n such a way that at each pont n tme the average amount,.e. z + y, s sold n the market and p( = p, t. Here we defne p = a z y. hus, as the number of large sellers become very large, there s perfect arbtrage leadng to perfect smoothng of ntertemporal prces. he extent of arbtrage goes down and the prce path exhbts fluctuatons as the degree of monopoly ncreases..5 Welfare under Autarky Welfare, n ths model, s taken to be equal to the sum of consumers' surplus and producers' surplus mnus storage costs. Formally, we wrte welfare under autarky, W as 1 (.16) W [ z( + y( ] dt = + )[ ( ) + p( t z t y( ] dt - µ [ H ( ] dt In the rght hand sde of equaton (.16), the frst term represents consumers' surplus, the second term represents producers' surplus and the thrd term represents storage costs over the tme horzon [,]. As shown n Appendx B, the above expresson may be reduced to 13

14 1 1 σ z µ (.17) W = [ as s ] [ H ( ] dt ( n + 1) where s = z + y,.e. the average stocks avalable n the economy, and 1 σ z = z t z dt [ ( ) ], s the varance of { z ( }. It may be verfed that welfare s ncreasng n the average stock s and fallng n the varance of market arrval σ. Let u( be the tme path of sales by the small sellers when ther total stock H = 1. From z (.11) and (.1) t follows that z( u( = and {u(} depends only on n and µ. Let the H varance of u( be denoted by σ u where 1 1 (.18) σ u = [ u( ] dt It mmedately follows that σ z = H σ u. Also, let us defne µ H µ H (.19) [ H ( ] dt = [ u( ] dt = µ c hen the expresson for welfare may be further smplfed as 14

15 1 1 (.) w = [ as s ] H Ω where W w and ] [ σ u µ Ω + c ( n + 1) In equaton (.) w s welfare per unt of tme and Ω s a constant as far as the present analyss s concerned. Moreover, s, the total stock avalable n the economy per unt of tme, s also treated as gven. Let us now talk about land reforms. In ths paper we talk about land reforms n a very smple manner. By land reforms we mean smply a redstrbuton of ntal stocks from the large sellers to the small sellers. In other words, a land reforms measure leads to an 1 ncrease n H and a fall n X, keepng H + X and hence s, whch s equal to [ H + X ], unchanged. It mmedately follows from (.) that a measure of land reforms, leadng to an ncrease n H, reduces welfare. hus we have the followng proposton: Proposton 1. A redstrbuton of output from the large to the small sellers unambguously reduces welfare under autarky. It must be ponted out that our welfare functon does not ncorporate any objectve of redstrbuton from the rch to the poor. It only gves an overall measure of effcency. hus redstrbuton can certanly come as a separate objectve. Indeed, one of the man purposes of the paper s to see whether such redstrbuton can be mplemented wthout 15

16 sgnfcant effcency loss. Our analyss suggests that under autarky there are ndeed effcency costs to be ncurred f redstrbuton s to be mplemented. Why does welfare go down f there s a redstrbuton of output from the large to the small sellers? We have already noted that welfare s ncreasng n mean output,.e. s, and fallng n the varance of market arrval σ z. hs varance ncreases as the amount of stocks owned by the small sellers go up. Hence, as H goes up keepng the mean output constant, there s a fall n welfare. Actually, the large sellers' ntertemporal buyng and sellng tend to smooth out prces. On the other hand, the small sellers contrbute to prce fluctuatons. herefore, redstrbuton n favour of the small sellers ncreases prce varance, whch, n turn, reduces welfare. Moreover, as the small sellers have postve holdng costs of stocks per unt of tme whle the large sellers do not, effcency requres that all stocks be held and marketed by the large sellers. Hence, on both counts, redstrbuton from the large to the small sellers reduces welfare. he two negatve effects on welfare are captured by the two terms wthn square brackets n the defnton of Ω. However, equty requres redstrbuton of stocks from the large sellers to the small sellers. Our analyss suggests that under autarky there s a trade off between the effcency and equty. 3.1 Equlbrum Under Free rade We now ntroduce nternatonal trade nto our model. We assume that the country s small wth respect to the rest of the world and faces a gven prce p * n the world market as trade opens up. It s also assumed that whle the large sellers have free access to the nternatonal market, the small sellers do not. In other words, the large sellers can buy and 16

17 sell freely n the nternatonal market, but the small sellers are constraned to buy or sell only n the domestc market. Frst we consder the case where the average market prce under autarky s less than the nternatonal prce,.e. p < p *. Not surprsngly, n ths case the country wll emerge as an exporter of the agrcultural commodty. We shall also consder below the other case where p p *. Now, under autarky, margnal revenue of a large seller s the same for all tme ponts. Usng the demand functon t may be easly verfed that ths common margnal revenue s less than the average market prce under autarky. Snce p < p * by assumpton, the margnal revenue of a large seller under autarky s less than the nternatonal prce. herefore, as trade opens up, the large sellers fnd t proftable, on the margn, to wthdraw stocks from the domestc market and sell them to the nternatonal market. In other words, the country wll be a net exporter of the agrcultural good. We now proceed to determne the trade equlbrum. Suppose, for the sake of smplcty, that the large sellers make all ther sales to the nternatonal market at the termnal date. hs s a harmless supposton because, for the large sellers, the varable cost of holdng stocks s zero and the nternatonal prce remans unchanged through out. hus even f stocks were sold at ntermedate dates, the profts would be the same, provded the same amount of total stocks are sold. he problem of a large seller s to (3.1) max ~ p ( ~ y ( dt + p* X ( ) subject to X ( ) = X, X ( ) s free 17

18 In equaton (3.1), ~ p(, ~ y ( t ) represent domestc prce and domestc sales (or purchase) by the th large seller at tme t ; X ( ), the termnal stock of the th large seller, represents the amount sold by hm to the nternatonal market. Clearly, ths amount has to be determned n equlbrum. he frst order condtons, gven by the Euler equatons, are, as before, m& ( =,, t and the transversalty condton s gven by (3.) m ( ) = p*,. he Euler equatons yeld equatons (.4)-(.6) as before. hese, along wth equaton (.8), yeld the same tme path of { z( } as obtaned earler. Intutvely, the small sellers' optmal path depend on the rate of change n domestc prces and not on ther levels. Internatonal trade changes the level of domestc prces keepng the rate of change of prces unchanged. Hence the optmal tme path of sales by the small sellers remans unchanged too. rade equlbrum s determned once we know how much, of the total stock avalable n the economy, s sold n the domestc market and how much s sold n the nternatonal market. he dvson of stocks between the domestc and the nternatonal markets s determned by equaton (3.). Usng the demand equaton, equaton (3.) may be rewrtten as (3.3) a ~ y ( ~ y ( z( p = * t. 18

19 n where ~ y ( = ~ y (. Summng over t and dvdng by we get = 1 (3.4) a ~ y z p* = ~ p p* = ~ y where p ~ (whch s equal to 1 ~ p ( dt ) s the average prce n the domestc market n 1 trade equlbrum, y~ ( whch s equal to ~ y ( dt ) s the average net sales of the th large seller from hs own stocks to the domestc market n trade equlbrum and ~ y ~ y. Note that ~ y ( t ) could be postve, negatve or zero. A large seller starts = wth hs ntal stocks and through out the tme horzon [, ] depletes ths stocks by sellng to the domestc market or adds to hs stocks by purchasng from the domestc market. At the termnal perod he s left wth a stock whch he sells to the nternatonal market. It s possble that the termnal stock s greater than hs ntal stocks. hs would be the case when hs ntal stocks are low. In ths case a large seller wll be sellng hs own stocks entrely to the nternatonal market and moreover he wll buy addtonal stocks n the domestc market and sell them n the nternatonal market. Consequently, y~ wll be negatve and the large seller wll be a net buyer n the domestc market. If, on the other hand, hs own stocks are large enough, he wll sell part of t to the domestc market and the remanng to the nternatonal market. In ths case, y~ wll be postve and the large seller wll emerge as a net seller n the domestc market. In the borderlne case where he s nether a net buyer nor a net seller n the domestc market, and sells hs entre 19

20 stocks n the nternatonal market, ~ y =. It should be ponted out that f a large seller s a net buyer from the domestc market, t does not mean that he never sells anythng n the home market. he fact that he s a net buyer smply means that the total amount he sells to the home market s less than the total amount he buys from the home market. Smlarly, f he s a net seller, then hs total sales to the home market exceeds hs total purchase from the home market. o see these thngs more clearly, note that from (3.3) we get (3.5) ~ n y = [ a z *] n + 1 p In the extreme case, f z = s,.e. all stocks are ntally held by small sellers, then the expresson wthn square brackets s negatve (snce n ths case, a z = p < p * by assumpton) and consequently each large seller s a net buyer from the domestc market. At the other extreme, f z =,.e. all stocks are held by the large traders, then ~ y >, assumng, of course, a > p*. In general, gven a constant s, as the share of large sellers n total stocks goes down, they tend to become net buyers from the home market. Snce the rght hand sde of (3.4) s gven, equaton (3.4) determnes ~ y. hen the tme paths of domestc prces and sales (or purchases) of the large sellers n trade equlbrum may be determned as before usng the fact that ~ y( dt = y ~. he solutons are gven by (3.6) ~ 1 y ( = [ z z( ] ~ y n + 1 +

21 (3.7) ~ n y ( = [ z z( ] ~ y n (3.8) ~ n 1 p ( = a z z( ~ y n + 1 n + 1 he solutons mply that the tme paths under autarky and trade dffer only wth respect to ther levels. In partcular, t may be easly verfed that the autarky domestc prce les below the domestc prce level under free trade for all t. However, n vew of equaton (3.4) and (3.5), the average domestc prce n trade equlbrum may le above or below the nternatonal prce dependng upon whether the large sellers are net sellers or net buyers n the domestc market. hs leads to the followng proposton: Proposton. If the nternatonal prce s greater than the average domestc prce under autarky, then as trade opens up, domestc prce ncreases. However, the average domestc prce n trade equlbrum les above or below the nternatonal prce accordng as the large sellers are net sellers or net buyers n the domestc market. he ntuton behnd the second part of the proposton s that f large sellers are net buyers, to earn monopsony profts, they keep the domestc prce below the nternatonal prce. Smlarly, f they are net sellers, to earn monopoly profts, they keep the domestc prce above the nternatonal prce. 1

22 We end ths secton by consderng the case where p p *. Frst consder the case where the average domestc prce under autarky s exactly equal to the nternatonal prce. o determne the pattern of trade, note that the margnal revenue of a large seller under autarky s gven by (3.9) m ( = p y Snce p = p *, t follows that on the margn a large seller wll gan by wthdrawng stocks from the domestc market and sellng them n the nternatonal market. In other words, barrng the extreme case where the large sellers do not possess any stocks ntally,.e. y =, the country wll be an exporter of the agrcultural good even f the autarky prce and the nternatonal prces are the same. Clearly, ths happens due to mperfect competton n the domestc market. Next consder the case where p > p *. Even n ths case, f the two prces are suffcently close and/or y s suffcently hgh, the margnal revenue under autarky may be less than the nternatonal prce and the country wll emerge as an exporter. Only when p s suffcently hgher than p*, the country wll start mportng the agrcultural good. he basc pont to note s that even for p p*, f the dfference between the two prces s small, the country mght emerge as an exporter though comparatve advantage dctates otherwse. he determnaton of tme paths of domestc prces and sales (or purchases) may be derved n the same way as done above and wll not be repeated here. Our results regardng the pattern of trade s summarzed n the followng proposton:

23 Proposton3. If the average autarky prce les below the nternatonal prce, the country exports the agrcultural good n trade equlbrum. If the average autarky prce s equal to the nternatonal prce, the country stll exports the agrcultural good. If the average autarky prce s greater, the country wll mport the good provded the dfference between the two prces s suffcently large. If the dfference s small, the country may export the good. 3. Welfare Comparsons of Free rade and Autarky As under autarky, welfare n free trade equlbrum s gven by the sum of consumers surplus and producers surplus mnus storage costs. he only dfference s that n trade equlbrum the producers surplus conssts of proft from domestc sales as well as sales to the nternatonal market. Let us frst assume that p < p * so that the country s a net exporter of the agrcultural good. Consequently, welfare, n trade equlbrum, s gven by ~ 1 ~ (3.1) W [ ~ y t z t dt ~ p [ ~ µ = ( ) + ( )] + ( y( z( ] dt p *[ S S ] [ H ( ] dt + + where S, S ~ denote total stocks and stocks sold to the domestc consumers respectvely. ~ Clearly, [ S S ] represents total exports. Analogous to equaton (.), the above expresson may be wrtten as (3.11) ~ ~ 1 ~ 1 w = [ as s ] H Ω + p *( s ~ s ) 3

24 where w~ 1 ~ 1 1 ~ = W, s = S, ~ s = S and Ω s defned as before. o analyze gans from trade, we have to compare (3.11) wth (.). Frst note that from (.) dw dh = HΩ < so that autarkc welfare as a functon of the stocks held by the small sellers may be represented as a downward slopng straght lne as shown n fgures IIA and IIB. Next note that from (3.11), dw~ ~ p p * (3.1) = HΩ dh ( n + 1) Clearly, at H =, the rght hand sde of (3.1) s postve. On the other hand, at H = S, the large sellers are net buyers n the home market and hence by proposton, ~ p < p * so that the rght hand sde of (3.1) s negatve. hus, there s an H* such that at H = H*, the rght hand sde of (3.1) s zero. Next, subtractng (3.11) from (.) we get 1 (3.13) w w ~ = ( s ~ s )[( ~ p p*) ( s ~ )] s Now suppose that z s close to s,.e. almost all the stocks are ntally owned by the small sellers. In ths case the large sellers wll be net buyers n the home market and by proposton, ~ p < p *. From (3.13) t then follows that w < ~w. In other words, when the small sellers ntally own most of the stocks, autarky welfare wll be less than welfare 4

25 under trade. hus, around H = S, the w ~ ( H ) curve wll le above the w(h) curve as shown n fgures IIA and IIB. hs leads to the followng proposton: Proposton4. If output s suffcently redstrbuted,.e. the small sellers hold a suffcently hgh proporton of the total stocks, then free nternatonal trade s better than autarky. Next, note that around H = S, dw~ dh > dw dh so that f the w(h) lne ntersects the w ~ ( H ) curve at all, the pont of ntersecton les to the left of H* (fgure IIA). Or else the two curves do not ntersect at all Hε [,S] (fgure IIB). Presently we wll show that ether the trade curve les above the autarky curve for all H or they ntersect only once. We wll also derve the condton under whch the two cases occur. 5

26 he sgn of the rght hand sde of (3.13) depends on the sgn of the term wthn square brackets as long as the country s an exporter,.e. ( s ~ s ) >. In Appendx C we show that the sgn of the term wthn square brackets on the rght hand sde of (3.13) depends on the sgn of [ y ( n + ) δ ] where δ = p * p. In other words (3.14) w w ~ [ y ( n + ) δ ] where the equalty sgn prevalng n one expresson mples that equalty prevals n the other. Clearly, f the two welfare curves ntersect, as n fgure IIA, they ntersect at y = ( n + )δ whch gves a specfc value of H denoted by H n fgure IIA. hs means 6

27 that the pont of ntersecton, provded there s one, s unque. It s also clear that f δ, the dfference between the nternatonal prce and the domestc prce under autarky, s large, then the welfare curve n trade equlbrum les above the welfare curve under autarky for all values of H. hs case s depcted n fgure IIB. hus, to conclude, for small values of δ the two curves ntersect and for suffcently large values the trade welfare curve les above through out. It may also be verfed that as long as δ >, t s not possble for the trade welfare curve to le below the autarky welfare curve for all H. It follows from our analyss that the trade welfare curve les above the autarky welfare curve for all H (fgure s s IIB) f δ > and the two curves ntersect at some H f δ (fgure IIA). n + n + We are now n a poston to talk about gans from trade. Frst consder fgure IIA. Suppose land dstrbuton s such that H < H. hen, openng up of trade reduces welfare. On the other hand, f trade s not opened up, but there are land reforms leadng to an ncrease n H, welfare unambguously goes down (.e. the country moves along the w(h) curve). In other words, when mplemented n solaton, ether trade reform or land reform reduces welfare. However, f the two reforms are mplemented smultaneously, the country moves along the w ~ ( H ) curve to H* where welfare s maxmzed. Welfare at ths maxmzng pont may very well be greater than that under autarky. Indeed, f the dfference between the autarky and the nternatonal prce s not very small, welfare under trade at H* wll be greater than welfare under autarky for any H. We say that the two reforms are strctly complementary f the two welfare curves ntersect and ntally H < H. If H < H < H *, then free trade ncreases welfare ndependent of any land reforms. But f the am s to mplement land reforms, then ths am can be mplemented wthout any welfare cost f the country opens up to trade. hus, n ths case, successful 7

28 mplementaton of land reforms would depend upon trade reforms,.e. the openng up of trade. he same comments apply to the stuaton n fgure IIB where the trade welfare curve les above the autarky welfare curve for all H. In ether case, we gnore the stuaton where H > H* because our concern s restrcted to less developed countres wth suffcently skewed dstrbuton of ncome n the agrcultural sector. We summarze our fndngs n the followng proposton: Proposton5. Suppose the dfference between the autarky and the nternatonal prce s s not very large,.e. δ <. hen f the ntal share of output of the small sellers s not n + very large,.e. less than H, then the two reforms are strctly complementary. If s δ n +, land reforms lead to welfare gans f trade reforms are smultaneously mplemented, provded the ntal share of output of the small sellers does not exceed the optmum H*. We may now consder the case where p* p. Frst consder the case where the two prces are equal. We have already seen that n ths case the country wll be an exporter of the agrcultural good provded H < S. Consequently, from (3.14), w > w ~ (snce δ = ) for y >. Only at y =, or alternatvely, H = S, the two welfare levels are equal. Hence, f the nternatonal prce s equal to the autarky prce, the trade welfare curve les below the autarky welfare curve for all H < S and only at H = S the two curves ntersect. hs s shown n fgure III. 8

29 Fnally consder the case where p * < p. If the dfference between the two prces s suffcently large, the country wll be an mporter at all H and n (3.13) ( s ~ s ) would be negatve. hs, along wth the fact that δ <, y > mply that the trade welfare curve les above the autarky welfare curve for all H. So we are n a stuaton smlar to fgure IIB. If, on the other hand, the dfference between p and p* s small, then for low H, the country wll be an exporter and w ~ < w. So, n ths case, we are n a stuaton smlar to fgure IIA. In other words, n the case where p * < p, the welfare curves ntersect f the dfference between the two prces s not very large; the trade welfare domnates autarky welfare for all H f the dfference s large. Hence our earler comments regardng the complementarty of the two types of reforms apply n ths case as well. 9

30 We may now dscuss the ntuton behnd our results. Frst note that under autarky, redstrbuton from the large to the small always reduces welfare n our model. In a standard model, as a market gets more olgopolstc, there s a loss n welfare. But ths loss n welfare s due to the fall n output resultng from the shrnkage of the compettve frnge and an expanson of the monopolstc frnge. In the present model, snce total output s gven, such effects are absent. On the other hand, n the present context, the large sellers smooth out the prce through ntertemporal trade and ths ncreases welfare. hus the net effect of redstrbuton from the large to the small ncreases the varablty of the prce path whch s welfare reducng. As trade opens up, the standard monopoly effect comes nto play. he olgopolstc large sellers act as dscrmnatng monopolsts sellng at a hgher prce n the domestc market whch s acheved by restrctng domestc sales below the optmum level. So, on one count, welfare falls as the share of output of the large sellers ncreases. On the other hand, the large sellers stll smooth out ntertemporal prces and on ths count a redstrbuton from the large to the small reduces welfare lke under autarky. he two opposng effects lead to an optmum dstrbuton denoted by H* n fgures IIA and IIB. 4. Government Interventon We had so far been talkng about free trade and autarky. We shall now talk about optmal nterventons by the government. In partcular, we shall dscuss the desrablty of the knd of nterventons, e.g. export quotas or nternatonal trade through government agences, that have been crtczed by the proponents of free trade. Not surprsngly, t 3

31 turns out that some government nterventon s optmal, gven the dstorton created by the exstence of olgopolstc traders. Let us consder equaton (3.11) whch represents welfare after nternatonal trade opens up. For any gven H, suppose the government chooses the optmal ~ s,.e. domestc sales, to maxmze welfare. he actual choce of domestc sales may be mplemented through approprate polces whch we shall dscuss later. he frst order condton, mpled by ths maxmzaton, yelds dw~ (4.1) ~ ~ = p p* = ds hs s what we should expect. Welfare s maxmzed at the pont where the domestc prce s equated to the nternatonal prce. he government, through an approprate polcy has to fx ~ s n such a way that the correspondng ~ p s equal to the nternatonal prce. Suppose the government makes the optmal choce at all levels of H. We know from equaton (3.1) that at ~ dw~ p = p *, <. dh hus, f the government makes the optmal choce of ~ s for all H, the functon wˆ ( H ), whch represents welfare for dfferent levels of H wth optmal government nterventon, wll le above the free trade welfare curve whenever under free trade ~ p p *. Now, notng that ~ p = a z ~ y and usng (3.5), t s straght forward to verfy that ~ p = p* z = a p *. In other words, under free trade, the domestc and the nternatonal prces are equal only at a unque value of H, say H. At ths level of H, welfare under free trade and welfare under trade wth optmal government nterventon wll be the same. At all other ponts, the wˆ ( H ) curve wll le above the 31

32 w ~ ( H ) curve. hs s shown n fgure IV. he H pont wll le to the rght of H* because at the later pont ~ p > p * and the domestc prce falls as H ncreases. Also the slope of the wˆ ( H ) curve s Ω and so the wˆ ( H ) curve and the w(h) curve wll be parallel. Now suppose that we start wth a skewed dstrbuton of agrcultural output so that H < H. Clearly, free trade wll not be optmal n ths case and optmal government nterventon wll be desrable. In other words, free trade wthout any government nterventon can be advocated only f we have suffcent land reforms to start wth,.e. only f we have H = H. It should also be ponted out that the welfare loss due to free 3

33 trade, as measured by the vertcal gap between wˆ ( H ) and w ~ ( H ), goes down as output s redstrbuted from the large to the small sellers. Proposton 6 s mmedate. Proposton 6. If dstrbuton s not at the optmum, government nterventon s superor to free trade. Gven that t s optmal for the government to choose domestc sales, the queston arses as to what specfc polces should be adopted to fx ~ s? We concentrate only on the case where dstrbuton s suffcently skewed,.e. H < H. Frst, consder the case where the country s a net exporter and the large sellers sell postve amounts to the domestc market from ther own stocks. Of course, ths wll be the case when H s low. In ths case, under free trade, ~ p > p * and to acheve the optmal domestc sales have to be ncreased. Clearly, ths can be acheved through an approprate export quota. he sze of the requred export quota wll go down as there s land reform leadng to an ncrease n H. Also, f the country s a net mporter and ~ p > p *, once more a hgher output has to be sold n the domestc market than under free trade. Snce the large sellers wll not be wllng to undertake ths addtonal mport, the government would have to undertake ths mport through ts own agences. In other words, as long as there are dstortons n the trade of agrcultural goods, we need to have precsely those government nterventons whch have been crtczed by the proponents of free trade. Before endng ths secton, let us pont out that lke under free trade, t s easer to pursue land reforms under restrcted trade than under autarky. Suppose the ntal dstrbuton s denoted by H, as shown n fgure IV, and the government wants to mprove t to H 1. Under autarky, ths measure leads to a welfare loss. But wth optmally restrcted trade, 33

34 the welfare level actually goes up f land reform and restrcted trade are mplemented smultaneously. 5. Concludng Remarks In ths paper we looked at the effects of two types of economc reforms on the level of welfare of a less developed agrcultural economy whch s characterzed by an olgopolstc product market. he frst s land reform redstrbutng output from the large to the small farmers; the second s trade reform leadng to the openng up of the domestc agrcultural market to the rest of the world. he man conclusons we drew from our analyss were as follows. Frstly, we showed that f ntal dstrbuton of output s suffcently skewed and the dfference between the average autarky prce and the nternatonal prce s not very large, then there s a strct complementarty between the openng up of free trade and redstrbuton of output. Undertaken n solaton, each leads to a loss n welfare, but f undertaken jontly, welfare unambguously ncreases. Secondly, f the dfference between the autarky and nternatonal prces s large, then free trade welfare s always greater than welfare under autarky. Indeed, the hgher s the dfference between nternatonal and autarky prces, the hgher s the gan from free trade for any gven dstrbuton of output. Moreover, the trade off between redstrbuton and welfare loss dsappears once free trade s opened up. hus f the economy s open, t becomes easer to pursue land reforms. hrdly, restrcted trade wth optmal government nterventon n general domnates free trade; government nterventon can be totally removed only f dstrbuton attans a 34

35 certan optmum level. On ths count, too, proper land reform s a prerequste for the optmalty of free trade. Fourthly, as compared to autarky, restrcted trade also makes land reforms easer, for the latter ncreases the welfare level and hence reduces the welfare cost of land reforms. o make our model tractable, we made a number of smplfyng assumptons. Frstly, we assumed that whle the small sellers have a postve and rsng margnal cost of holdng per unt of stock per unt of tme, the large sellers have zero costs. he analyss, however, goes through, though at the cost of complcatng the algebra, f both types of sellers have postve costs but the cost of holdng for the large sellers s lower. Smlar smplfcatons were made by assumng that demand s lnear and that the dscount rate s zero. Once more, non-lnear demand or postve dscount rates could be brought n, but only at the cost of makng the analyss messy. 35

36 References Cassen, Robert and Vjay Josh, edted, Inda: he Future of Economc Reform, Oxford Unversty Press, Cassen, Robert and Ashok Gulat, Lberalzng Indan Agrculture: An Agenda for Reforms, n Cassen and Josh edted Inda: he future of Economc Reform, Oxford Unversty Press, Josh, Vjay and I.M.D. Lttle, Inda's Economc Reforms: , Oxford Unversty Press, Kamen, Morton and Nancy Schwartz, Dynamc Optmzaton, North-Holland, Lpton, Mchael, Lberalzaton, Poverty Reducton and Agrcultural Development n Inda, n Cassen and Josh edted, Inda: he Future of Economc Reform, Oxford Unversty Press, Sarkar, Abhrup, On the Formaton of Agrcultural Prces, Journal of Development Economcs, 41: 1-17, Sarkar, Abhrup,On the Relatonshp Between Prce and Output Seasonalty n Backward Agrculture, Indan Economc Revew,

37 Appendx A Dervaton of equatons (.13)-(.15): We have, by defnton, (A.1) (A.) Hence z( = z() + z& ( τ ) dτ y ( = y () + y& ( τ ) dτ t t t n y ( = y () + z& ( τ ) dτ [usng equaton (.5)] n 1 n (A.3) = y ( ) [ z( z()] [from (A.1)] n + 1 Hence, ntegratng over, and dvdng both sdes by, we get 1 n 1 n y ( dt = y () z( dt + z() n + 1 n + 1 Substtutng the value of y () from (A.3) and usng the defntons of y, z the above expresson becomes (A.4) y n = y ( + [ z( z n + 1 whch s nothng but equaton (.13). Summng (A.4) over n we get equaton (.14). Fnally, from (.14) and the demand equaton we get (.15). 37

38 Appendx B Dervaton of equaton (.17): From equaton (.14) we have (B.1) n 1 y ( + z( = z + z( + y n + 1 n + 1 Now, consumers surplus = 1 [ y( + z( ] Smlarly, producers surplus = [ a { y( + z( }][ y( + z( ] dt Hence consumers surplus + producers surplus dt = a [ y( + z( ] dt [ y( + z( ] dt 1 (B.) = as [ y( + z( ] dt where S = X + H, the total stocks avalable n the economy. Usng (B.1), we may wrte, after some straght forward algebrac manpulatons, (B.3) where σ z [ y( + z( ] dt = + s ( n + 1) S 1 s = and σ z = [ z( z] dt. Equaton (.17) follows drectly from (B.) and (B.3). 38

39 Appendx C Dervaton of equaton (3.14): he sgn of ( w w ~ ) depends on the sgn of {( ~ p p*) ( s ~ s )}. Now from equaton (3.4), ( ~ p p*) = ~ y and by defnton, ( s ~ s ) = ( y ~ y). Hence t s suffcent to look at 1 the sgn of { ~ y ( ~ y y)}. Usng equaton (3.5) and the fact that y = a z p, t s straght forward to show that the requred sgn depends on the sgn of [ y ( n + ) δ ], where δ = ( p * p). 39