Optimal price intervention policies when production is risky - chapter 19

Chapter 19 Optimal price intervention policies when production is risky* Peter B. R. Hazell and Pascuale L.,Scandizzo The authors have previously argued (Hazell and Scandizzo, 1975) that when agricultural production involves stochastic yields, then reasonable specification of the market structure leads to the result that optimally distorted prices are more efficient for social welfare than competitive market equilibrium prices. This paper provides a brief review of that finding, as well as providing a generalization to the multiproduct case within the framework of agricultural programming models. Results are also presented on the magnitudes of the optimal price distortions and associated welfare gains obtained from a linear ,programming model of agricultural production at a subsector level in Mexico. 1. OPTIMAL PRICE DISTORTIONS Consider the following market structure for a single commodity. S, = 1sj1* (1) Dr a - bP, (2) S, D, (3) *The oioionls exivessed in; tis chai)ier do0 not re[nec[ tiose or ilie %vorm 13:ink. 364 P. B. R, Hazell and P. L Scand!zzo and E (E,) =, V (cE) = c2, Cov (6,, , ) = 0 for all t, where P, is the price anticipated by producers at the time of making produc- tion decisions, E, is stochastic yield, and a, b. and X are positive constants. This model has the following key features. (i) Anticipated price, P,' is the relevant forecast of P, made by producers at the time of committing their inputs for period t. Typically, in agricultural production, there will be a lag between such decisions and the realization of production. As such, P, incorporates anticipations about both actual yield E, and about total supply S,. The assumption that Cov(c,,P,') = 0 rules out the possibility of perfect forecasts (in which case the model would collapse to a simultaneous specification) and implies that no knowledge is available about 6, other than that the parameters p and o-2 are known. (ii) The stochastic yield term c, is multiplicative. This specification is preferred to the more conventional additive model for two reasons. First, because it is the input decisions which are assumed to be price responsive (see (i) above), so that the basic behavioral relationship on the supply side is anticipated supply E(S IP,') = X/P,*. Actual supply in period t is then S, = X (tt + r,)P,* where r, is the yield deviation from the mean in the Ith period, that is, p + r, = E. Second, the multiplicative specification leads to an increasing rather than a constant variance of total output with increasing input use, that is, V(S) = X2P*2U-2 and this increases with anticipated price. However, the coefficient of variation is constant and equal to a/it If the yield term E is bounded on some positive interval E,,,< E F_., then the market structure can be portrayed as in Figure 191. The anticipated supply function E(SIP) = XuP* is linear, and passes through the origin. In the diagram, if producers anticipate P,' = p,. then they will plan production for period t so that the expected market output is S; = Xpp,. However, because 6, is stochastic, the actual supply function can rotate in a random way around E(SIP') to any position contained in the funnel defined by SIE:01 = X-P,' and Sle, = Xc,P'. Hence, if expected supply in period ( is S,', actual supply could take on any value on the line A1B. Clearly, actual market price is stochastic with E, . and the actual price in period t may take on any value between P1' and P J. An additive Specification Subsumes all the )ield stocha%icity into an intercept term for supply. Such speciricatinl i Common in the literature Masell. 1969: Oi. 196 1 Turnovsky. 1974: Waugh. 1974). Risk andlprice stabilization 365 Price SIE ,, al? o .......Quantity Figure 19.1. A market with multiplicative risk Frorn equation (3), the market must clear, hence the market clearing price each period is a B ( bb Since £, is stochastic, then P, must also be stochastic, so that we shall consider an equilibrium price, if it exists, to be the convergent mean price lim E (P,).It is not hard to show that convergence occurs if lim E(P,) =lim E(,), that is, if farmers on the average settle on the self-fulfilling expectation price (Mu th, 1961) as their anticipated price. Under this condition,2 the market equilibrium price is limE(Pt)Dbn 5 -Sufficient ardor necessary conditionis can be derived under specific assumptions about P1 Fgergendorff. H9ze1 .nd Scandiz m e 19wp. 366 P B. R. Hazel and P. L. Scandizzo Optimal price distortions arise because this equilibrium price does not rnaximize the social welfare function defined as the dun of the expected values of the producers' and consumers' surplus. The consumers' surplus in period t is simply the value of the area under the demand curve and above actual market price P,- Algebraically, t al (a - bP) dP. Solving, taking the expected value and simplifying, E (WV) 2 V (P*) + E (p* )2 (6) where p, denotes the second moment of I around zero, and V(P*) is the variance of anticipated price. Producers' surplus in period I is a little more tricky. since production costs depend on anticipated price P,'and not on actual price E. The surplus, which is really an ex post concept in this case, is calculated as t = P St- S/XY dS where S;= XtP; is anticipated supply in period LIIis total realized revenue (P,S,i less production costs as measured by the area under the anticipated supplh function from 0 to S,". In Figure 19.2. where it is again assumed that P; = p,and that actual supply is S, rather than S,'. the surplus is simply the area 01, CS,- OBS;. Solving, taking the expected value and simplifying, the expected producers' surplus is, a X2 12 x2 E (II) = yE )- ( p2 + -Xp) V (P')- (- 2 + - Xp) E (P)2. (7) b b 2 b 2 Adding t6) and 17) together. the chosen social measure E(SJV) is then expressed as + 1X2 I X2 £(SW) a XPE(P*)-- (- + >A) V(P) - ( p2 + Xp)E(P*). (8) b 2 b 2 b This function has its maximum hen Risk and price stabilizalion 367 Price I, C / E (SI P*) P - 1-/ I Demand 0 quantity s, s; Figure 19.2. Producer's surplus with a negative disturbance term. ap E (P*) = (9) - (9) by + X92 and I(P*) = 0. That is, when farmers anticipate the price P' =ai/bt + XA2) in each and every period. Assuming (9) is satisfied, then substituting this result into the expected value of (4), expected market clearing price becomes a (by + Xo2 E (Pt ) (10) b (by + XY2 This price is not the market equilibrium price in (5), but rather, it is an optimally distorted price for the market. It can be shown that (10) is greater than (5) while (9) is smaller than (5), so that the optimal distortion is effected when farmers produce less than an equilibrium quantity on average - corresponding to the lower anticipated price obtained in (9) - and hence realize the higher average market price obtained in (10). The percentage market price distortion T3can be exDressed as R2100% T= 1i (I d 2 + 1 3T = IE(P I/tim E JPI) - I 100% where E (PI) is obtained from (10) and fim EPI) from o). 368 P. B. R. Hazel and P. L. Scandizzo where ld I Is the absolute value of the elasticity of demand measured at market equilibrium, and R is the coefficient of variation forsE. Clearly, Twill never be negative, so that optimal distortions always imply price increases. Further, for fixed R, the distortion is seen to be larger the more inelastic the demand, but it disappears at the limit as the demand elasticity is increased towards infinity. The distortion also increases with R, so that the more risky the production, the greater the optimal market price distortion. In a deterministic market., R = 0 and the optimal distortion is 0. The existence of an optimal distortion price requires some explanation. Basically, it can be attributed to two factors in the model specification. First, because production costs are dependent on anticipated price P;and not on actual market price P,. This means that there is no fixed relationship between revenue and costs, and that for some P,', the yield c, outcome may, in conjunction with the inelasticity of demand, conspire to cause revenue to fall below costs to the extent that there is a net welfare loss to society. In itself, this cost is not sufficient to distort the market.4 However, because of a second feature of the model, the multiplicative risk term, the variance of market supply S, increases quadratically as producers move up the expected supply function, so that the possibility of costs exceeding revenue also increases. Clearly, the distortion in the market arises from the tradeoff between the surpluses from higher outputs aid the net welfare loss associated with wasted resources. The authors have explored the magnitudes of the optimal price distortions and associated welfare gains for different values of (d and R within the confines of this simple market model (Hazell and Scandizzo, 1975). It was found that not only can the optimal price distortion be quite large when demand is ine!astic (more than 10% with moderate production risks), but important welfare gains (about 2% for R = 0.5) may be had from using market intervention policies to introduce the desired distortion. These results might appear to suffer from the rather stringent simplifying assumptions of the model. However, as shown below, the existence of an optimal distortion generalizes to much more complex market structures, though in these cases it is much more difficult to say anything about the size of the welfare gains without resorting to empirical situations. 2. GENERALIZATION TO AGRICULTURAL PROGRAMMING MODELS An increasing number of formal agricultural sector models are now being built using mathematical programming techniques. Many of these models are 41n an additive risk model, for example, with the same kind of lagged specification, a price distortion does not arise (see Turnovsky, 1974). Risk and price stabilization 369 also str,ctured to provide the perfect competition solution to all product mar- kets when both priVes and quantities are Cndogenous. In the deterministic case, and with suitable restrictions on demand, this is easily achieved by maxi- mi.ing an objective function defined as the sum of consumers' and producers' surpluS in all markets (Duloy and Norton, 1975; Samuelson, J952; Takayama and Judge, 1964, 1971). For example, in a simple modelof annual crop prodLuction based on a single aggregate farm facing the demand structure P = A - BhX,5 the appropriate model maximand can be written as Max II = X'W (A - 0.5BWX) - C'X (11) where X = an n x 1 vector of crop acreages grown W = an n xni diagonal matrix of crop yields per acre C = an nx 1 vector of costs per acre and A and Bare n x I and n x n matrices of demand coefficients, respectively. The term AY'W(A - 0.5BWX) is simply the sum of areas under the de- mand schedules, while CX is total production costs, or equivalently, the sum of areas under the supply functions. The difference between these two is, therefore, the sum of the consurers' and producers' surplus. The maximand assumes farmers are profit maximizers, and provides equilibrium prices and output levels such that market prices equal marginal costs. Typically, (11) is maximized subject to a set of linear programming constraints of the form DX < b. (12) The authors have generalized this model to the risk case in which yields are stochastic and farmers are risk averse (Hazell and Scandizzo, 1974). In particular, if farmers maximize the utility function U = M-OS where 0 is a risk aversion parameter and Mand S denote, respectively, the expected value and standard deviation of income, then under quite reasonable assumptions, the expected values of prices and quantities in a competitive equilibrium can be approximated by using the maximand Max U= X'W (A -'O.5BvX)- C'X- 4 (X'PX) . (13) Here, V denotes the diagonal matrix of expected yields, r is an n x n covariance matrix of crop revenues (price times quantity), and 4 is a suitable average of individual farm risk parameters. 5The procedure requires that the demand matrix B be symmetric (Takayama and Judge, 1971; Zusian, 1969). 3 70 P. 13. 1. azel and P. L. Scandizzo This maximand is iden;ical to (11) except that a new production cost, 4(XPX)", has been added. This is simply the compensation demanded by farmers for taking risks, and which is to be added to the area under the supply functions. The maximand can, therefore, still be considered as a sum of producers' and consumers' surplus over all product markets. In fact, it is LIe sum of surpluses as measured above the anticipated supply functions (Hazell and Scandizzo, 1974). That (13) provides an equilibrium solution can be shown from the necessary Kuhn-Tucker conditions of the Lagrangian function L = X'W(A -0.5BWX -C'X -(X'IX)v + v' (b-DX) where v is a vector of dual values. These necessary conditions evaluate at W(A--B WX) < C+ )PX (X'PX)-2 + D'v. (14) Since E(P) = A -BWX, the condition requires that for each crop, expected marginal revenue per acre, WE(P), be equal or less than the expected mar- ginal cost. Expected marginal cost comprises own marginal cost C, plus the marginal risk cost PPX(X'rX)" plus marginal opportunity costs as reflected in the dual values of the resodrces used by that crop D'v. For those crops which are nonzero (A,> 0), then by the complementary slackness conditions, (14) holds as an eqUality, in which case the expected values of marginal revenues and cost are equated. Despite the specificity of this model, it does provide a good forum for generalizing the optimal distortion results, as well as providing a framework for empirical experimentation. Theoretically, the model is appealing because it assumes the multiplicative yield structure: - output = yield multiplied by area planted, where area planted (the X variables) are price responsive. Further, since the supply structure is embedded in the model through a set of choice variables and resource constraints, the mxlel incorporates nonlinearities, as well as such multiproduct considerations as covariances between crop revenues (the off-diagonal elements of I) and stIstitution in demand (the off-diagonal elements of B). Before considering these generalizations, it is worth noting, that in as much as (13) can he interpreted as a welfare function,6 it is an ex ante welfare measure, The producers'surplus, in particular, issimply the excess of expected utility as measured by the fUnction U = M- 0S.This type of welfare function has frequently been used to analyze intervention policies in risky markets 6A welfare interpretation of (l3) is not necessary for obtaining a competitive Cquilibrium solution. Rather (13) can be viewed sim[ a,, a computational device or trick, Risk and price stabilization 371 (Massell. 1969; Oi. 1961: Tirnovsky, 1974; Waugh, 1974), but it is not the relevant welfare measure when production is lagged and yield risks are multiplicative. For this Situation, we must return to the welfare measure used in (8). That is, to the sum Of expected values of realized (ex post) consumers' and producers'surplus. The appropriate welfare function can equivalently be expressed as the sum of expected values under the demand curves, minus the sum of areas under the anticipated supply functions. In the context of the sector model notation, this becomes E(SW) = E[X'N(A-0.5BNX)]-C'X- 4(XTX) () (1 5) SX'WA - 0.5X'E (NBN)X- CX-4(XTPX) where Ndenotes the diagonal matrix of stochastic yields such that E(N)= W. This welfare function leads to a set of optimally distorted prices. To prove this, consider the Langragian function L = E (SW) + v'(b - DX). Apart from the feasibility conditions in (12), the necessary Kuhn-Tucker conditions are = WA-E(NBN)X-C-4PX(XTX)- -D'v 0. (16) Now, E(NBN)X = V(NBN)X + WBWX where V is the variance- covariance operator. Substituting this into (16), and rearranging terms, W(A -BWX)<C +4rX (X'TX)~ + D'v +V(NBN)X. Using the demand equations E(P) = A - BWX, we finally obtain WE(P)<C + 4X(XIX)-V + D'v + V(NBN)X. (17) This relationship between marginal revenue and cost is very similar to that obtained in (14) for the market equilibrium case. However, a new cost V(ABN)X appears on the marginal cost side, which gives rise to optimal price distortions. Using complementary slackness conditions, it can also be shown than (17) holds as an equality for all crops entering the solution at nonzero levels. The cost V(NBIN)Xis highly interesting because it is a social rather than a private cost. The ith element of this cost vector can be written as cov (Et I) b x. 372 P. B. R. Haze/ and P. L. ScandizZo Thus, the price of the ith crop is distorted from its equilibriun price by a term which depends on the variance of the yield of that crop and its covariances with the yields of all other crops. Thfi variance-covariance effects are, of course, measured in physical units, but are converted into money costs through the demand coefficients b,. Since the signs of the covariances and the b;j coefficients may be positive or negative, the distortion effects are indeterminate in sign. It is likely that some prices should be increased above equilibrium prices, but that others should be reduced. However, the size of these distortions and the associated welfare. gains, is a purely empirical question, and to this we now turn using a specific agricultural model of Mexico. 3. ILLUSTRATIVE APPLICATION IN MEXICO 3.1. The Model An agricultural sector model, CHAC,7 already exists in Mexico and provided a suitable basis for this study. CHAC is a linear programming model which encompasses the supply -- domestic and imported - and all demands - domestic and export - for 33 short cycle crops. It does not include livestock, forestry or long cycle crops. The model is an aggregate of regional submodels, which are linked through a national market structure (domestic and foreign) and by some common resource constraints. CHAC is a static equilibrium model and provides the perfect competition solution to all mar- kets for both prices and quantities through use of the kind of maximand de- tailed in equation (11). To keep this study within manageable limits, a smaller version of CHAC was used which included only selected areas of irrigated land. These selected areas represent eight of the more than 100 administrative districts of the Mexican Ministry of Water Resources. They are not contiguous districts, but are scattered throughout the arid agricultural areas of Mexico. The districts and their locations are as follows: Area District Pacific Northwest Culiacdn, Cmisifn del Fuerte, Guasave, Rio Mayo, Santo Domingo North Central Ciudad Delicias, La Laguna Northeast Bajo RiO San Juan 7C*lAC, wshidh names after tihe Mavan rain gtx, was constructed by the World Bank in collaboration xth the Secretiri, de la Presidencia in Mexico. A complete description of the model can be found in Duloy and Norton (1973) and Bassoco and RendOn 11973). Table 19.1 Average district cropping patterns, 1967/68 to 1969/70 (Harvested hectares*) Crops Fl Fåerie Culiacan Rio Mayo Guasave Delicias San Juan St. Domingo Laguna Aggregate N %o u NationalPr<uin Dr% alfalfa 1.988 - 2.144 - 6.510 - 285 5.498 16.425 34 Coiuon 46.364 - 15.535 - 7.903 1,190 17.585 67.964 156.541 25 Green alfalfa - 543 - - - - - 5.224 5.767 2 Rice 11,335 23.568 - 3.480 - - - - 38.383 25 Sugar cane 12.706 24.172 - - - - - - 36.878 12 Safflowe, 4.790 13.374 10.435 3.737 - - 1.098 - 33.434 29 Barle 112 - - - - - 112 C hihes 386 1.570 - 48 - . - - 2.004 Bejns 16,224 11.024 - 202 - - - - 27.450 3 Chickpeas 561 938 - 271 - - - - 1.770 Tomatoe, 3.049 9.563 - 381 - - - - 13.193 37 Sesame 3.010 2.815 8.390 144 - - - - 14.250 - s 10.792 4.302 4.071 2.420 10.053 '54.269 1.038 6.213 93.158 2 Caia loupC 231 397 - 722 - - - - -1.340 4 P>otawes 1.320 - ---- - 1.320 5 Cucunbers - - 8 - - - - 8 0 Waterrelons, 757 325 - 41 - 74 - - 1,197 5 Sorghum 24.238 22.795 10,616 1,238 7.719 19.876 - 5.592 92,074 I l Smrbeans 16.264 4.392 11.886 - - - - - 32.543 20 Sheat 23.561 3.057 29,969 5.742 29.668 1.048 11,738 16.150 120.933 16 TOTAL 177.576 122.825 93.158 18.634 61.853 76.457 31.744 106.641 688.8,8 Numbr of farrns 16.484 6.224 9.185 2.984 10,710 4.480 647 48.341 99.055 4 Ava;~~l ectarage ~. A ral h 10 12 8 6 4 16 47 2 5.8 *Seeded hectares melude signiltcant amiunts ofdouble croppng in most di-triet. 374 P. B. R?. H-azell atid P. L. Scandizzo Taken together, thie 8 districts account for significant shares of the national production of cotton, tomatoes, dry alfalfa, rice, soybeans and safflower (Table 19.1). They also produce a wide range of cereal crops and vegetables, together with sorte sugar cane. Some double cropping is practiced in all the districts, but particularly in the vegetable growinig areas. The average district cropping patterns for the years 1967/68 to 1969/70 ile given in Table 19. 1, but excluding a small percentage of land devoted to crops which are not included in the models. Crop production is almost entirely dependent on irrigation in all 8 districts, and small areas of rainfed land have been excluded. In total, the 8 district models cover 99,000 farms of an average size of 5.8 hectares - a district breakdown is included in Table 19. 1. For modeling purposes, each district is treated as a single large farm. The farms are thought to be sufficiently homogenous, that this procedure is unlikely to lead to any serious aggregation bias problems. The model activities provide for thle production, in each district, of the crops grown by that district in Table 19. 1, each with a choice of 3 mechanization levels and 2 planting dates. A set of labor activities provide flexibility in selecting seasonal combinations of family and hired day labor. Family labor is charged a reservation wage of one-half of the hired day labor rate. Purchasing activities provide for the supplies of mules, machinery and irrigation wvater. Seasonal constraints are imposed on land and labor, and an annual constraint is imposed on water supplies. Technical coefficients and costs are taken at average levels from 1967/68 to 1969/70. The model constraints are also based on this period. Average yields are based on the 6-year period from 1966/67 to 1971/72, and risk parameters were estimated from time se ries da ta spa n ning the period 1961/62 to 1970/7 1. The district models are linked in block diagonal form and integrated into an aggregate market structure, similar to that in CHAC. That is, the market comprises linear domestic demand functions of the form P =A - BWX, and has import and export possibilities at fixed prices. To approximate cross- elasticity relationships in demand, the crops are classified into demand independent groups, and linear substitution is allowed between products within each group as rates fixed by base year relative prices.8 The definition and characteristics of these demand groups are summarized in Table 19.2. The demand curves for each group have the same price elasticities as in CH-AC, but are located at mean output levels appropriate for the 8 district aggregates. Export and import constraints are also pro-rated according to the ratio of output from the 8 districts to national output for each product. The resultant model was solved for eqluilibrium values of expected prices and quantities using the type of maximand detailed in equation (13). That is, assuming farmers maximize M - OPS utility. The model was also solved for optimal price distortions using the welfare function defined in equation (1 5) as 8For a more detailed description, see Duloy and Norton ( 1973, 1975). Risk and price stabilization 375 Table 19.2 Characteristics of demand groups Base period price Demand Commodity Commodity Group indexa Own price group elasticity (Pesos/ton) 1 Sugar cane 70 70 -0.25 2 Tomatoes 1150 1150 -0.4 3 Chillies 1500 1500 -0.2 4 Cotton fiber 5770 5770 -0.5 5 . Dry alfalfa 400 Green alfalfa 100 Barley 930 Chickpeas 990 446 -0.3 Maize 860 Sorghum 630 6 Rice 1220 Beans 1830 Chickpeas 990 1285 -0.3 Potatoes 930 J 7 Maize 860 817 -0.1 Wheat 800 8 Cantaloupe 680 741 -2.0 Watermelons 780 9 Safflower 1550 Sesanie 2410 1164 -1.2 Cotton oil 830 Soybeans 1600 10 Cucumbers 590 590 -0.6 a Group price indices arW CoMputed using base year quantity weights (Duloy and Norton, 1973, 1975). 376 P. B. R. Hazell and P. L. Scandizzo the model maxinand. In both cases, the aggregate risk aversion parameter 4) was varied in order to evaluate the effects of different levels of risk averse behavior on the model solutions. Solutions for 4)=0 correspond, of course, to the risk neutral case in which farmers simply maximize expected profits. 3.2. The Results In Table 19.3, the values of social welfare, as measured by equation (15), are reported for both the equilibrium and optimally distorted solutions for different values of 4). These welfare gains are much larger than suggested by the earlier theoretical analysis for the single product case. For(D=0, for example, optimal market distortion policies could increase social welfare by as much as 6.4 per cent or an equivalent of 270 million pesos. Since it can be shown that the welfare gain accrues entirely to producers (Hazell and Scandizzo, 1975), this would be equivalent to an average gain of 2,727 pesos per farm. The'welfare gain obtainable from optimal distortion policies diminishes as 4) increases. This suggests that private risk costs are positively correlated with the social risk term responsible for the distortions, the former tending to substitute for the latter as 1b increases. Indeed, when )= 2.0, the gains from optimal distortion policies are quite trivial at 20 million pesos. Private risk aversion might therefore be considered desirable because it tends to restore competitive market efficiency. The optimal price distortions are summarized in Table 19.4 for different values of 4). Since the relative prices of commodities within demand groups are fixed at base year values, only the group price indices are reported. Table 19.4 reports the value of these price indices at market equilibrium for each value of 4,as well as the percentage distortion required to maximize social welfare. As expected, most of the distortions involve price increases and, hence, reductions in domestic market supplies. A few negative price distortions do occur, particularly for larger values of 4), and which have their origin in negative yield covariances both between crops and between irrigation districts. Many of the price distortions are quite large despite opportunities for world trade at fixed prices. In fact, only the price of cotton fiber (group 4) is consistently pegged at its export value. The price distortions are largest for low volume specialist crops - chillies (group 3), cantaloupes and watermelons (group 5) and cucumbers (group 10) - and smallest for the important food and wage good crops - wheat and maize (group 7). The magnitude of the distortions tends to diminish as 4) increases, but they do not disappear when 4) = 2.0, even though the welfare gain becomes very small. The international trade results are summarized in Table 19.5. The op- timally distorted solutions call for greater levels of exports and imports, and a larger trade surplus, for all values of 4). This result arises in part because export and import prices are fixed and nonrisky in the model. More realistic Risk and price stabilization 377 Table 19.3 Welfare gains with various + values Values of 4i Item 0.0 0.5 1.0 1.5 2.0 Social welfare Equilibrium model 4.21 4.04 3.97. 3.83 3.83 (billions of pesos) Distorted model 4.48 4.27 4.10 3.96 3.85 (billions of tesos) Gain from distortion (%) 6.4 5.7 3.3 3.3 0.5 Gain to average farm (pesos) 2727.0 2323.0 1313.0 1313.0 202.0 Table 19.4 Optimal distortions in domestic prices for various P values Demand 4). 0.0 011 0.5 # 1.0 4) 1.5 D 2.0 group p P T P T P TP T 1 68 10.3 68 7.3 70 5.7 68 7.3 69 7.2 2 330 29.7 705 7.2 1071 7.3 1319 5.2 1636 5.7 3 700 318.1 741 302.2 748 310.6 828 290.5 965 250.3 4 5770 0.0 5770 0.0 5770 0.0 5770 0.0 5770 0.0 5 410 18.5 415 6.3 432 -1.0 445 -3.8 456 -2.2 6 1279 28.4 1200 36.9 1158 36.5 1167 29.4 1194 28.9 7 991 -1.6 931 0.0 938 0.2 983 -3.7 1006 -3.5 8 309 101.9 368 62.2 434 13.8 547 4.6 533 6.8 9 1052 7.8 1037 7.6 1089 4.1 1263 -1.9 1368 -2.2 10 569 1.8 6$ 3.1 838 -65.3 790 -86.4 317 -98.1 aThe demand groups are in Table 19.2. bP denotes the equilibrium price index for a commodity group in pesos/ton, cT denotes the optimal market price distoruon for a group from s equilibrium value PcxpIessed in per cent. 378 Risk and price stabilization Table 19.5 International trade results (million of pesos) Item Values of D 0.0 0.5 1.0 1.5 2.0 Equilibrium model Value exports 196.96 143.05 133.93 59.54 17.70 Value imports 0.07 0.07 0.07 0.07 6.45 Trade surplus 196.89 142.98 133.86 59.47 11.25 Optimally distorted model Value exports 213.66 213.67 201.36 84.57 84.57 Value imports 8.46 2.79 0.64 7.94 8.58 Trade surplus 205.20 210.88 200.72 76.63 75.49 assumptions might have reduced the levels of trade in the optimally distorted solutions, but only if world prices are at lea,- as risky as domestic prices. 4. CONCLUSIONS in this chapter, we have attempted to demonstrate, within the bounds of an agricultural subsector model, that competitive market equilibria may be far from efficient in terms of social welfare when production is risky. The poten- tial welfare gains to be had from optimal intervention policies are surprisingly large, in fact, far greater than might be anticipated from simple algebraic models. We have not considered the distributional aspects of the welfare gain in this chapter, suffice to say that the main benefits lie with the farmers, while consumers tend to lose. Implementation of an optimal distortion scheme might need to be supplemented with some kind of taxation scheme to obtain appropriate redistribution of the gains. 'P. B. R. Haze/i and P. L. Scandizzo 379 The results in this chapt'or do, of course, hinge on the welfare measured used. The measure of producers' surplus presents few problems (it is simply average realized profits), but the expected consumers' surplus is more objec- tionable. Basically, it ignores the income effects incurred by consumers from increasing food prices, and which, in a country like Mexico, must be expected to be quite large, especially for the magnitude of price changes envisaged here. We are encouraged, however, by the fact that the price of the basic wage goods - maize and wheat - are hardly changed in the optimally distorted results. Consequently, the major price effects would impinge upon the in- comes of the more prosperous nonagricultural households, effecting an in- teresting transfer of income to the rural areas. So far,'we have avoided the question of how optimal market distortions could be implemented. An obvious and simple procedure in autocratic societies would be to introduce production quotas at the regional level. However, more sophisticated intervention policies can be devised for free market situations through the design of optimal buffer stock and price stabilization schemes. This, however, is a topic which cannot be embarked upon here. 5. POSTSCRIPT Newbery, in his comments on this chapter, argues that the distortion results obtain only because it is assumed that farmers plan each period on the basis of indepei?dent forecasts about prices and yields. He shows that more ra- tional eqpectations which take account of negative correlations between prices and yields would lead to market equilibria which are efficient. The authors have subsequently shown (Hazell and Scandizzo, 1977) that there exists an even simpler class of behavioral models which ensure competitive market efficiency, namely those models in which farmers are assumed to act on the basis of a linear lagged function of past (per unit) revenues. The posi- tion is now such that results about competitive market efficiency and the need for government intervention policies depend very much on the way farmers actually do forecast enterprise profitability each year when planning their in- put decisions. Given the magnitudes of the welfare losses demonstrated in this chapter for reasonable but less than optimal behavior, there is a clear need for empirical research to determine how farmers do behave.