A systems analysis of the guyanese livestock industry

A SYSTEMS ANALYSIS OF THE G U Y A N E S E LIVESTOCK I N D U S T R Y

T. KELLEY WHITE & B. A. MCCARL

Department of Agricultural Economics, Purdue University, West Lafayette, htdiana, USA R. D. MAY

Department of Agricultural Economics, Univetwity of Arkansas, Fayettet'ille, Arkansas, USA & T, H. SPREEN

Food attd Resource Economics Department, Unit;ersity of Florida, Gahts~,ille, Florida, USA

SUMMAR Y

This paper attempts to contribute to the capability for livestock sub-sector analysis. A model structure which offers potential for evaluation of changes of policy, available production technology, or factor and product market conditions is described. The structure integrates a multi-year biological cattle simulator with a price endogenous model of the cattle sub-sector to yield a model designed to shnulate aggregate behaviour of profit maximising cattle producers interacthlg through competitiee factor and product markets. The general model structure is specified to reflect conditions in Guyana, South America. The model, specified for Guyanese conditions, is used to evaluate the probable impact of a number of technical and economic changes in the system.

INTRODUCTION

Many of the less developed countries located in the tropics have relatively large unpopulated land areas which are best adapted to forage production and grazing of ruminant livestock. Actual livestock production in these areas is lower than apparent potential. This lower performance is often attributed to factors such as animal diseases, seasonal feed availability, inadequate transportation, market conditions, genetic characteristics of the herd and production practices. Technical efficiency, as indicated by beef production relative to herd size, is low. 47 Agricultural Systems (3) (1978)--© Applied Science Publishers Ltd, England, 1978 Printed in Great Britain

48

T. KEI.I,EY W H I F E , B. A. M C C A R I . , R. 1). MAY, I . 'II. SPREI'N

The divergence between potential and actual livestock production is of concern to policy makers who desire to implement policies and programmes which will stimulate production and increase the economic contribution of the livestock sub-sector. Choosing a set of policies and programmes which will be consistent with development goals and resources is a complex problem. Production is influenced by many environmental, social and economic factors. Thus any policy or programme affecting the livestock industry is likely to have multiple impacts within the livestock sector and the economy as a whole. Experimentation with, and the implementation of, policies is a very expensive, time-consuming process. Thus there is need for means by which experimentation can be carried out without the necessity for actual implementation. Sub-sector modelling is the approach employed in this paper to provide a framework for evaluation of alternative interventions on the cattle sub-sector. Byerlee & Halter (1974) discuss sector analysis and give an overview of the objectives of such an analysis. This study presents a model which uses the methodology of Duloy & Norton (1973) and White et al. (1975), extending the work of May (1975). The remainder of this paper is devoted to the description of a systems model designed to analyse the multiple impacts of alternative programmes and policies, technical innovations and changes in market conditions on the cattle sub-sector. This model is also intended to be useful in identifying constraints on growth of the sub-sector. The model is specified largely to reflect conditions in Guyana, but the general structure is applicable to many less developed countries. Following a description of the model, details of a Guyanese application are presented.

MODEL OVERVIEW

The cattle industry model (hereafter referred to as the 'model', see Appendix for formal description) is designed to simulate the behaviour of producers and consumers of beef and milk as they interact in the market place over time. The market for beef is assumed to be competitive (i.e. individual producers and consumers are price takers). The price and quantity of beef produced and consumed are determined by the model through the interaction of endogenously determined supply with an exogenously determined demand schedule. Both supply and demand may be modified by changing model parameters. The national cattle herd is divided into regional herds on the basis of geographic location. Each regional herd is disaggregated into sub-herds on the basis of: (1) performance capacity of animals due to either genetic characteristics or prior treatment and (2) ownership patterns which imply differential response to production and marketing opportunities. Animals in different sub-herds would be expected to react differently when confronted with similar treatments. Time, in the model, is considered to consist of a number of one-year production-

SYSTEMS ANALYSIS OF T H E G U Y A N E S E L I V E S T O C K I N D U S T R Y

49

marketing-consumption periods and a terminal inventory transfer period. Within a year, all model parameters are fixed. Between years, parameters may change due either to endogenously determined levels of decision variables or to exogenously specified shifts in parameters over time. Thus, the model has the capacity to reflect the process of adjustment within the sub-sector over time. However, the smallest unit of time within which change can be simulated is one year. Thus, seasonal variations in production, price or consumption are not treated. The model is solved for a planning horizon consisting of a variable number of one-year periods (a practical limit imposed by model size is four or five years) and successive solutions can be used to reflect a sequence of planning horizons. Production decisions are assumed to be made at the beginning of the planning horizon and remain unchanged throughout the planning horizon. Decisions are made with the knowledge of product demand, factor supply and technical production relationships in each year of the specified horizon. Even more distant repercussions of decisions are reflected by a set of exogenously specified inventory values at which assets are transferred to future planning periods. Thus production systems are chosen on the basis of both current results and future expectations. Biological constraints, reflecting possible changes in herd size and composition over time, are recognised utilising a herd simulator in the construction of production activities and for herd accounting. Data requirements are specified by a detailed input form which serves to organise data in a format acceptable for computer manipulation. Major types of data required are initial herd inventory, inputoutput coefficients, product demand and input supply parameters, inventory values for animals at the end of the explicit planning horizon and resource availabilities. Input data are processed through a matrix generator to formulate a linear programming problem. The structure of the linear programming model is presented below.

LINEAR P R O G R A M M I N G MODEL

The model of the cattle sub-sector is formulated as a linear programming problem incorporating stepped price-quantity schedules to reflect product demand and factor supply relationships. The general structure is to minimise the negative (maximise) of a function which represents the area under the demand curve less the area under the industry marginal cost curve. This function is (1) - P . : ~ - : ' f i X -~FD

!- S Z

~

Wfl

- R y " B T + N Y,

The area under the demand curve is represented by P~ and M X . P gives areas under the annual demand curve at given steps of the demand curve and ~ identifies the step. M gives inventory values for live animals by class at the end ofthe planning period and X is the number of animals in inventory. The area under the industry marginal cost curve is given by the miscellaneous costs of production (F) times

50

T. KELLEY \VHITE, B. A. MCCARL, R. D. MAY, T. H. SPREEN

the production level (D), plus the costs of fixed price purchased inputs (S) times their quantity (Z), plus the area under the labour supply function (W) by step (//), plus the area under the land supply function (R) by step ('/), plus the transportation cost (B) times quantity of goods transported (T), plus a theft disincentive (N) times the quantity of theft (Y). The objective is maximised as a multi-year problem with the variables X, Z, /3, ~, 7, T and Y dependent upon time. Maximisation is subject to a series of constraints. The first constraint (2) Qct - A D < 0 ensures that meat and milk sold (Q~) is less than, or equal to, meat and milk produced ( A D ) in each year. (3) X - J D <_ 0 ensures that in the terminal year inventory transfer by animal class (X) is less than, or equal to, the inventory held by the production activities (JD). (4) C D -- I Z _<_ 0 ensures that annual use of purchased inputs by input class ( C D ) is less than, or equal to, the inputs purchased (IZ). (5) E D -- Lfl < 0 ensures that yearly labour use ( E D ) does not exceed labour

supplied (L/3). (6) S D -- Ky < 0 ensures for each year that land used in production ( S D ) is less than, or equal to, land supplied (KT). (7) G D -- T < 0 ensures that each year the use of transport by production (GD) is less than, or equal to, the transportation supplied. (8) U D -- Y <_ 0 ensures that the annual quantity of theft is less than, or equal to, the theft paid for. (9) H D < b ensures that fixed factor use ( H D ) (mainly the sub-herds) is less than, or equal to, fixed factor supply (b). Constraints (10), (11) and (12) require that the sum of the step variables for each curve is less than. or equal to, one: (10) V ~ _< 1 (] l) V2fJ ~ I (12) V37 < 1 where V~, V2 and V3 are matrices containing row vectors whose elements are all equal to one. This ensures that each demand and supply curve is approximated as a convex combination of its step variables during each year. (This specification of the supply and demand functions is due to Duloy & Norton (1975), The variables ~, fl and "/ are vectors of positive weights which represent the areas under the curves as a convex combination.) The model as summarised above (for details on Guyana see May (1975)and Ford et al. (1976)) has the basic structure of a spatial and intertemporal equilibrium activity analysis model (Takayama & Judge, 1971) formulated using separable programming (Miller, 1963 and Duloy & Norton, 1975). A two-year two-region tableau of this model is presented in Table 1. Selected portions of the model are described below. Objective function and model behaeiour

The objective function maximised is the area beneath the product demand curve

SYSTEMS ANAI.YSIS OF THE GUYANESE LIVESTOCK INDUSTRY

51

minus the area under the product supply curve. This area is commonly referred to in the economics literature as consumers" plus producers' surplus and is often used in welfare analysis. However, in this analysis no welfare implications are drawn from the value of the objective function. Instead, maximisation of this objective function is employed as a means of imposing competitive market behaviour on the model (Takayama & Judge, 1971; Duloy & Norton, 1975). Product demand and factor supply curves are explicit while product supply is a function of factor supplies, fixed factor constraints and technical production alternatives. Factor demand is a function of product demand and production possibilities. Thus, coefficients entering the objective function are areas under explicit product demand and factor supply curves. The nature of these demand and supply curves is discussed below. The advantage of this formulation of the linear programming model of the cattle sub-sector is that it provides a means of simulating the aggregate behaviour of an industry composed of many firms, each of which faces perfectly elastic product demand and factor supply curves. Solution of the model yields a set of competitive equilibrium prices and quantities for products and factors, subject to the constraints imposed in specifying factor supply and product demand relationships. Market distortions such as quotas, taxes, subsidies and price controls can be imposed on the model without violating the basic assumption that each firm is a price taker. Thus a powerful tool is provided for planners and policy makers who are primarily interested in the aggregate impacts of modifications in the system.

The production sub-matrix Animals are disaggregated by region and sub-herd. Animals within different sub-herds are expected to perform differently when affected by change. Cattle production activities are thus specified by region, sub-herd and management system. A particular sub-herd may be treated by several management systems which may differ with respect to (1) kind and quantity of inputs required per unit of output and (2) marketing practice (rate of culling, replacement policy and age of animals sold). Generally, production activities are defined for the number of periods for which the model is solved. Thus both resource requirements and output coefficients reflect changes in herd size and composition over time induced by the particular management system. This is accomplished by a herd dynamics simulator which applies the set of performance rates characterising the management system to the sub-herd and calculates herd structure, input requirements and output for each year of the planning horizon. These values are used to specify an activity for the linear programming model. Once allocated to a production activity, mature cows are assumed to remain in that activity throughout the planning horizon. However, live animals may be transferred as yearlings or three-year olds. This makes possible the inclusion of

+

+

+

+ + +

+

+

+ +

+ + ........

+ + +

. . . . . . . . . . + + h+ + + + + +

+ +

+ +

+ + . . . . . . . . . + + + + + + + +

Beef Dem. Year 1

Milk Dem. Year 1

Signing convention: ( + ) indicates use of a resource. ( ) indicates yield or supply of a resource. Note: SH -- Sub-herd.

Nat. Beef Acct. Year 2 Nat. Milk Acct. Year 2 Nat. Pur. Input Acct. Year 2 Land Year 2, Reg. 1 I.abour Year 2, Reg. I Land Year 2, Reg. 2 Labour Year 2, Reg. 2 Transport 1-2 Cap. Year 2, 2-1 Product Trans. Year I, I- 2 Input Trans. Year 2, 2-1 Reg. 10 Meat Dem. Year 2 Theft Acct., Year 2 Ending Inventory

Obj. Function Nat. Beef Acct. Year 1 Nat. Milk Acct. Year 1 Nat. Put. Input Acct. Year 1 Cow Use Reg. 1, SH I Cow Use Reg. 1, SH 2 Land Year 1, Reg. 1 Labour Year I, Reg. I Cow Use Reg. 2, SH 1 Land Year 1, Reg. 2 Labour Year 1, Reg. 2 Transport 1-2 Capacity, Year I, 2- I Product Trans. Year I, I - 2 Inputs Trans. Year 1, Reg. 10 Meat Dem. Year 1 Theft Acct., Year 1

Prod. Prod. Prod. Reg. 1 Reg. I Reg. 2 SH 1 SH 2 SH 1 +

Pure. Input Supply Year 1 +

+

Land Labour Supply Supply Year 1 Year 1 Reg. 1 Reg. 1 +

+

Land Labour Supply Supply Year 1 Year I Reg. 2 Reg. 2

TABLE 1 A SCHEMATIC REPRESENTAI"ION OF THE CA'VFLEINDUSTRY MODEl.

.4_

+

I-2

+

+

2-1

Transport Year 1

_.

+

Reg. 1 Meat Dem. Year I

[-.,

),

,-r

,<

m t-~ t"

,--I

b~

--

+

-4-t+

+

+

-t-

+

Beef Milk Pure. Land Labour Land Dem. Dem. Input Supply Supply Supply Year2 Year2 Supply Year2 Year2 Year2 Year2 Reg. I Reg. I Reg. 2 +

+

+

+

+

Labour Transport Supply Year 2 Year2 I-2 2 I Reg. 2

+

+

Reg. I Meat Dem. Year2 +

+

--

+ 0" 0 + 0 0 + + 0 0

< :< _< < < r< < < < < <

N _< _< < _<_ _< _< _< _<

_< _< < _<

_<

0 0

0

0

~

+ +

"~ .<

~

~_ ~

0

e~

~-

m

~

",m O. ..<

..< "" ~',

;>

z

'~

~

0

0

0

0 0

0

+

o <

_<

o 0

_<

<

(rain)

Theft hn,entory Year 2 tramfer R H S

Signing convention: ( + ) indicates use of a resource. ( ) indicates yield or supply of" a resource. Note: SH ~ Sub-herd. * RIIS on land accounting rows m a y be greater than zero to allow for an e n d o w m e n t of land to a region at zero cost.

Nat. Beef Acct. Year 2 Nat. Milk Acct. Year 2 Nat. Pur. Input Acct. Year 2 Land Year 2, Reg. 1 L a b o u r Year 2, Reg. 1 Land Year 2, Reg. 2 I.abour Year 2, Reg. 2 Transport 1-2 Cap. Year 2, 2-1 Product Trans. Year I, 1 2 Input Trans. Year 2, 2-1 Reg. 1, Meat Dem. Year 2 Theft Acct., Year 2 Ending Inventory

Obj. Function Nat. Beef Acct. Year I Nat. Milk Acct. Year I Nat. Put. I n p u t Acct. Year 1 Cow Use Reg. 1, SH I Cow Use Reg. 1, SH 2 l.and Year 1, Reg. I L a b o u r Year 10 Reg. I Cow Use Reg. 2, SH 1 Land Year I, Reg. 2 l.abour Year 1, Reg. 2 Transport I --2 Capacity, Year 1, 2-1 Product Trans. Year 1, 1-2 Inputs Trans. Year 1 Reg. I, Meat Dem. Year I Theft Acct., Year 1

Year I

T A B L E I--contd.

54

t . KELLEY W H I T E , B. A. MCCARL, R. D. MAY, T. It. SPREEN

specialised production systems for production of feeders and for finishing of purchased feeders. The model also provides for animals of these two ages to be transferred among regions and sub-herds. Cattle production is constrained by the initial breeding herd, land, labour, purchased inputs, machinery, feedlot capacity, transportation availability, slaughter capacity and veterinary services. Purchased input constraints are national while all other constraints are regional. Theft is an important factor in beef production in many countries and was modelled explicitly. Each production activity has a specified theft rate for each category of animal. Stolen animals of slaughter weight are converted into stolen meat and transferred into the meat supply row (i.e. theft is treated as an alternative market channel). The stolen meat transfer activity has a price (cost) which should reflect the disincentive to the producer of theft loss. The structure of the production component of the model is illustrated in Table 1. This schematic of the production tableau is restricted to two regions and two time periods. To conserve space, constraint types are indicated rather than individual constraints. For example, the land constraint includes multiple soil types and land development status (uncleared, cleared or improved pasture). Four types of labour are specified--permanent labour, temporary labour, farm managers and slaughter labour. Purchased input constraints include eleven different feeds or feed supplements and three types of fertiliser.

Product demand and factor supply sub-matrix Beef demand and land and labour supplies are incorporated in the linear programming model as step functions, as in Duloy & Norton (1975). Each demand and supply activity contains coefficients (1) in the objective function equalling the area under the curve to the appropriate quantity, (2) in a beef or input row to give the number of units demanded or supplied and (3) in a row which forces a convex combination of activities (steps) from each curve. A single set of beef demand activities is defined for each year representing a single national demand for beef. The product demanded is carcass beef at the slaughterhouse door. This national demand draws from a beef supply row fed by all beef production activities in all regions. Thus, demand is assumed to be national while supply is regional. Demand curves can be shifted between years to reflect changes in population, income or prices of competing products. Demand curves may also be modilied to simulate the imposition of policies such as minimum or m a x i m u m prices, taxes or subsidies. Export demand and import supply functions for beef may be specified for the model. These functions may be perfectly elastic, reflecting the small country situation, or may be sloped if the country is ' i m p o r t a n t ' in the foreign beef market. Tariffs, quotas and subsidies may be imposed and export demand may be allowed to compete directly with domestic demand for all beef produced, or separate production activities may be specified which provide beef for export. The latter is

SYSTEMS ANALYSIS OF THE GUYANESE LIVESTOCK INDUSTRY

55

more appropriate when only certain regions are allowed to export because of disease problems or when export demand is for a different quality of beef. While the principal emphasis of the model is on beef, large portions of the cattle herds in developing countries arc dual purpose and milk constitutes an important source of income. The demand for milk is treated as being perfectly elastic. (The case country, Guyana, is a net importer of milk and is not sufficiently important to affect the import price. Thus the demand for domestic milk as a substitute for imported milk is very elastic over a rather large quantity range.) This provides a means for evaluating the consequences of alternative levels of milk price without unduly complicating the model. Sets of annual supply activities are included for each region for each of three types of labour (in the current formulation farm managers are acquired through a fixed-price, bounded purchase activity rather than a sloped supply function because of the small number of professional managers in Guyana) and four classes of land. Land and labour supplies are modelled as positively sloping functions to reflect competition between cattle and other agricultural production for these important inputs. Thus, supply prices may be thought of as opportunity costs of employing these resources in cattle production. This provides an important linkage between the cattle industry and the rest of the agricultural sector without explicit modelling of the entire sector. Supply curves can be shifted between years to reflect changing population, trends in inter-regional migration, changing returns to resources employed in other agricultural production or increasing reservation wages. Policy instruments such as minimum wage, employment taxes and land use restrictions can be incorporated by modifying supply curves. All other inputs are acquired through single price purchase activities. The assumption of perfectly elastic supplies of purchased inputs is not unrealistic for many developing countries. A number of by-product feeds are available but the cattle industry is a relatively unimportant consumer and its purchases would not affect price unless very large increases occurred.

Transportation sub-matrix Transportation activities are included for routes linking each other region with a central region. (This formulation is specitic to Guyana and would need to be modified to reflect actual transportation structure for application of the model to another country.) Separate activities provide transportation from each mode of transport relevant for the route (truck, boat, air). Shipment between any two non-central regions requires trans-shipment through the central region. In general, inputs are shipped from the central region and beef is shipped to the central region. The demand for transportation services is generated by coefficients in production and live animal transfer activities. Transportation is provided by transport activities at a price equal to the net sub-sector cost. That is, when rates are sub-

56

T. KELLEY \ V H I r E , B. A. M C C A R I . , R. D. MAY, T. 14. SPREEN

sidised, the subsidised rate enters the objective function. Alternative modes of transportation compete for the tonnage over a given route. Each transport activity is bounded to reflect capacity constraints. The transportation activities introduce a minimum price differential between the goods in the central region and the outlying regions. The price differential will be the transport cost or greater, depending on goods flows and capacity.

Land deL,elopment Land is supplied to the livestock sub-sector through supply activities discussed above as either cleared or uncleared land. The production activities require cleared land which is assumed to be natural or improved pasture, depending upon management system. The available supply of cleared land and improved pasture can be augmented by activating a set of land development activities. Three types of land development activity are included. They are land clearing, pasture establishment and pasture maintenance. All three types of activity use labour, purchased inputs, machinery, etc. Land clearing uses uncleared land and produces cleared land in the second year. It is assumed that once land is cleared, it remains cleared. Pasture improvement uses cleared land and produces improved pasture which is assumed to be available for half of the current year and for the following year. Hereafter, improved pasture must be maintained or it will revert to cleared land. Subsidisation of land development can be modelled by entering the subsidy as a return in the objective function row. This will offset a portion of the input costs which enter through purchase activities.

Ending inventor)' retention The inventory retention sub-matrix consists of activities and constraints for each of the sub-herds of cattle by class and for developed land. These activities and constraints are included for the last year of the planning horizon only. Their purpose is to provide a current weighting, in the objective function, for the future return to investments. As presently formulated a single retention price is specified for each investment item. Given the endogenous pricing of beef for current consumption, this formulation presents problems in maintaining a reasonable relationship between the current and future value of cattle. A demand curve for carry-out inventory appears to be a more appropriate formulation and is being incorporated.

GUYANESE APPLICATION

Guyana possesses a large land base, most of which is sparsely settled, and a narrow coastal strip which is densely populated. Interior land is largely unexploited and presents potential for the expansion of beef production. Market conditions are

SYSTEMS ANALYSISOF THE GUYANESELIVESTOCKINDUSTRY

57

such that the supply of beef is lagging behind domestic demand. Guyana is located in close proximity to the beef deficit countries of the Carribean. Expansion of cattle production into new areas is seen by the Government as a means of frontier development, employment expansion, income generation and increasing foreign exchange. Guyana's cattle production has historically been limited to two regions--the Coastal Belt and the Rupununi Savannas bordering Brazil. Production in frontier regions (Matthews Ridge in the Northwest and Ebini in the Intermediate Savannas) currently consists of small experimental herds owned by the Government. During the last five years, the coastal herd has declined by 30-50%. The price of beef has been steadily rising. No beef is exported. Data for specification of the Guyanese model were obtained through a combination of surveys, interviews and government rccords. Specific data are prcsented in Ford et al. (1976). Data sources and collection procedures are discussed in May (1975). The model as specified for the Guyana case generally rellects production and demand conditions existing during 1973-74. A brief summary of initial herd structure and,technical production and marketing alternatives will be presented as an aid to interpreting model results. A national herd of approximately 150,000 head, including 66,000 adult females, is distributed among four producing regions. The regional breeding herds in the two traditionally important production regions were allocated among sub-herds on the basis of differences in ownership, animal treatment and products sold. A single sub-herd is specified for the other two regions where a single government owned experimental herd exists. Table 2 shows the initial distribution of cows among regions and sub-herds. It is assumed that live animals are immobile among sub-herds and regions for TABI.E 2 N U M B E R OI- C O W S BY R E ( H O N A N D S U B - H E R D .--BASE D A T A

Region

Rupununi

Northwest Intermediate Savannas Coast

Sub-herd

1. 2. 3. 4.

LargeCommercial Small Commercial Amcrindian World Bank

Total 1. Matthews Ridge I.

I. 2. 3. 4.

Number

10000 10030 4000 1000 25000 480

Ebini Extensive Commercial Small Non-Commercial Commercial Dairy Intensive Commcrcial

900 12300 19203 1818 6100

Total

39421

58

T. KELLEYWHITE, B. A. MCCARL, R. D. MAY, T. H. SPREEN

the base run of the model. Technical coefficients applied to each sub-herd reflect the predominant production system observed for that sub-set of producers. Four off-take alternatives are provided for each technical production alternative. These are combinations of retaining all heifers versus selling all heifers for slaughter and selling steers at the traditional age versus selling one year younger. Selling all heifers provides a method of herd eradication while retaining all heifers provides for maximum herd build-up. Intermediate rates of herd growth or reduction may be achieved by choosing a linear combination of the two extreme heifer retention activities. Labour supplies are represented by price-quantity schedules for all four regions. For the coastal region this reflects agricultural and non-agricultural employment opportunities (including benefits paid to the unemployed) within the region. The other three regions have few employment alternatives available internally but labour migrates between the coast and other regions. Land supplies are represented by price-quantity schedules for the coastal region reflecting competition between livestock and crop production. In the other regions there are few alternative uses for land and it is assumed to be available at a constant lease price fixed by the Government. In the two frontier regions, Matthews Ridge and Ebini, additional grazing land must be developed through land clearing and pasture establishment activities. Model results--Base situation

Selected output from a four-year solution of the model for the base situation is presented in Table 3. Beef prices increased slightly between years one and two, held essentially stable in year three and increased in the last year. The quantity of beef marketed declined slightly between years one and two, increased by approximately 5% in year three and exhibited a small increase in year four. Two characteristics of model specification are important in explaining these endogeneous price-quantity results. First, beef demand is assumed to increase by 2~, per year to reflect increasing population and stable per capita real income. Secondly, all production-marketing activities are specified to sell all animals of TABLE

3

St'LECTED MODEL OUTPUT--BASE

SITUATION

Item

Year 1

Price beef (G $/lb) Quantity beef (million Ib) Ending inventory (head) Rupununi Northwest Intermediate Savanna Coast Nat ion

2

3

4

1-53 6.376

1-56 6.341

1.55 6-602

1-57 6-619

63215 1440 2283 87154 154092

64016 1586 2111 88170 155883

64902 1776 1897 88075 156650

65930 1996 1631 87862 157420

SYSTEMS ANALYSIS OF T H E G U Y A N E S E L I V E S I ' O C K I N D U S T R Y

59

marketable age and older. Thus, when the model chooses to sell animals at younger ages than had produced the initial herd structure (e.g. five- rather than six-yearolds), two or more age classes of animals are marketed in the first year. Results presented in Table 3 suggest that few sub-herds were allocated to production activities with reduced sales age. Some year-to-year variation in beef sales results from the uneven age distribution of initial sub-herds. This explains the large increase in beef quantity between years two and three, followed by a very small increase in year four. The national herd increased slowly but consistently over the four year time horizon. Regional herds increased in size except in the Intermediate Savannas. While the coastal herd showed a small increase over the four years, it actually decreased in the last two years. The model results indicate varying degrees of economic viability, under existing conditions, among regions and sub-herds. In the Rupununi region all brood cows of all four sub-herds were allocated to management systems that retain all heifers for breeding herd replacements and additions. That is, the optimal solution for that region had all sub-herds growing as rapidly as possible, given existing technology as reflected by herd performance rates. Results for the two regions in which the Government has established pilot cattle production units were different. The technology employed by the Government and used to specify activities in the model for both regions employs relatively large quantities of modern inputs which must be imported. The Northwest District has more evenly distributed rainfall and more fertile soil than do the Intermediate Savannas and thus yields higher output per unit of cash outlay. The entire breeding herd in the Intermediate Savannas was allocated to the management system which sells all heifers for slaughter and markets steers at the youngest age allowed. Choice of this management system depletes the herd at the most rapid rate allowed in the model and implies that the capital intensive production technology currently being used is not economically viable. Thus, if cattle production is to play an important role in the development of this region, either a less capital intensive technology will have to be introduced or production will have to be subsidised. In contrast, the Northwest District herd was allocated to a management system which retains all heifers, implying that production under current conditions is economically viable. In the Coastal Region all sub-herds except one are allocated to management systems that retain heifers. The extensive commercial sub-herd is allocated to a system that sells all heifers. This system uses almost no modern inputs but has very low technical efficiency as measured by calving, mortality, theft and weight gain rates. Technical coeiiicients are so low that, even if all heifers were retained, the breeding herd could not be sustained. However, since most resources used by this sub-herd have very limited alternatives, the herd depletion alternative was chosen by the model only after a relatively high cost was imposed for stolen animals.

60

T. KELLEY WHITE, B. A. MCCARL, R. D. MAY, T. H. SPREEN

Model results--Intensive system .for extensive commercial sub-herd To evaluate the impact of improved management of the extensive commercial sub-herd, a new set of production activities was introduced into the model to provide an intensive management alternative. The intensive management alternative introduced is essentially the same as that specified for the intensive commercial sub-herd in the base model. It involves closer supervision of animals, keeping them out of flooded areas during the rainy season, providing more veterinary care and better pasture management. This results in higher calving rates, lower death and theft losses and faster rates of gain. It also requires more management input, more labour, more fencing, but less land per animal due to better pasture management. Approximately 15% of the brood cows of the extensive commercial sub-herd are allocated to the intensive management system. Adoption of the intensive system is limited by the availability of qualified managers. The shadow price for managers on the Coast was over SI00,000 in year three, the year in which managers are most limiting. These results suggest that an extension training programme to develop traine~t managers would have a high potential payoff. The model selects the intensive management system which sells heifers rather than building the breeding herd. This results from the interaction of the increasing management requirement of a growing herd and a supply of managers that is assumed, in the model, to be constant. The intensive management system was economically superior to the extensive system and the portion of the breeding herd that could be transferred to the more efficient technology was limited by availability of managers. Also, brood cows can be transferred only in the initial year. Therefore, the optimal decision for the model was to transfer the maximum proportion of the breeding herd to the intensive system even though this required adopting a sales strategy of selling all heifers. Modification of the mode[ to permit the availability of managers to increase each year would allow the adoption of a management system which retains females. Simply increasing the number of managers in all four years resulted in a larger number of cows being transferred into the intensive management system but heifers are still sold. When the management constraint was completely removed, permanent labour became an effective constraint again, preventing heifer retention. This set of results, by identifying successive constraints, illustrates a benefit of the model for evaluating policy and programme alternatives. The national effect of introducing the intensive system was small because of the small number of animals affected. Results presented in Table 4 show a decrease in price in years one and four with no price effect in the other two years. These price changes were too small to induce changes in other sub-herds and regions. Thus, the impact on national herd inventory was small. Given an adequate and increasing supply of managers, the intensive system is clearly preferable (economically) to the extensive system. Moreover, it offers a means for stimulating, at a low cost, beef supply from the coastal herd.

61

SYSTI'MS ANAI.YSIS OF TIlE GUYANESE LIVI-STOCK INDUSTRY

TABLE 4 SELECTED MODEl, OUTPUT- .IN]ENSIVE TECHNOLOGY FOR LARGE EXTENSIVE SUB-IIF.RD ON COAST

Item

Year

Price beef (G $'lb) Quantity beef (million IbJ Ending inventory (head) Coast Nation

1

2

3

4

1.50 6-616

1.56 6-305

1.55 6.572

1.55 6-769

86852 153791

88263 155976

88474 157050

87962 157519

Model results--Short.feeding o f skinny coastal steers M a n y coastal cattle, especially those o f small n o n - c o m m e r c i a l producers, are m a r k e t e d in p o o r c o n d i t i o n . T h e G u y a n e s e are c o n s i d e r i n g placing these animals on i m p r o v e d p a s t u r e and p r o v i d i n g s u p p l e m e n t a l feed to t a k e a d v a n t a g e o f c o m p e n s a t o r y gains as a means o f increasing the coastal beef supply. A m a n a g e m e n t system was d e v e l o p e d to feed t h r e e - y e a r old steers from the small n o n - c o m m e r c i a l s u b - h e r d on the coast for a period o f 100 d a y s on i m p r o v e d pasture. Steers are fed molasses, free choice, with bone meal as a mineral supplement. A s t o c k i n g rate o f three a n i m a l s per acre o f i m p r o v e d pasture is assumed. T h r e e batches per y e a r can be put t h r o u g h the process. T h e effects o f i n t r o d u c i n g the s h o r t - f e e d i n g o f steers from the small nonc o m m e r c i a l s u b - h e r d can be seen by c o m p a r i n g the results presented in Table 5 with those o f the base situation presented in T a b l e 3. Beef price is reduced and q u a n t i t y m a r k e t e d is increased in all four periods. However, price and q u a n t i t y effects are larger in years one and four. T h e e x c e p t i o n a l l y large increase in beef m a r k e t e d in y e a r one results from a r e d u c t i o n in age at m a r k e t i n g m o r e than from feeding o f thin steers. In effect, two years" off-take is m a r k e t e d in y e a r one. One g r o u p o f 1945 steers t h a t would, u n d e r the base situation, have been sold in year two, are fed and sold in y e a r one. In a d d i t i o n , those steers are sold, without being finished, t h a t would n o r m a l l y have been m a r k e t e d in y e a r one. Since steers are sold at a y o u n g e r age, inventories are reduced in all years. A m o r e meaningful i n d i c a t i o n o f the m a r k e t effect o f i n t r o d u c i n g steer finishing is p r o v i d e d by the results o f years two t h r o u g h f o u r when 2798, 2732 and 3588 TABLE 5 SELECTED MODEL OUTPUT-- SHORT-FEED COASTAl, STEERS

Item Price beef (G S/lb) Quantity beef (million Ib) Ending inventory (head) Coast Nation

Year 1

2

3

4

1-43 7.046

1.51 6-713

1.53 6-693

1-51 7-025

85209 152147

85372 153085

85342 153918

84275 153832

62

T. KEI.LEY W I l l ] E . B. A. MCCARI.. R. D. MAY. T. 17. SPREEN

steers were fed. The number of steers fed is a function of the age distribution of the herd. Thus, the increase in beef marketing results from both increasing animal weights and numbers. While the price effect of introducing this new production alternative in the coast was relatively l a r g e - thirteen cents in year one and five, two and six cents in other years--it was insufficient to cause changes in any other sub-herd or regional production pattern. This indicates a production system that is relatively insensitive to price changes due to asset tixity.

C O N C L U D I N G COMMENTS

In this paper, a model structure has been described which integrates the multi-year biological cattle production process into a model which represents the cattle sub-sector. The model is designed to simulate the aggregate behaviour of profit maximising cattle producers interacting through the competitive factor and product markets. Product demand and factor supply schedules are exogenously specified while product supply and factor demand are internally generated. Factor supply schedules reflect the opportunity cost of using resources in cattle production and thus competition between cattle and other agricultural production. Initial cow herd is allocated among production technologies on the basis of multi-year factor supply, product demand and technical production relationships. A model solution yields a set of equilibrium prices and quantities of factors and products. The model is solved simultaneously for a number of one-year productionmarketing periods and an inventory retention period. Exogenously specified retention prices are used to value assets in inventory at the end of the planning horizon. These retention prices represent the expected value of terminal assets held for future production and are intended to serve as a proxy for producer expectations of the future. The level of exogenously specified retention prices was an important variable in determining model solutions. The authors recognise the need for an endogenous retention price determination process in the model. Work is under way to introduce such a feature. Results from the Guyanese application of the model demonstrate benefits from model use in analysing the cattle sub-sector reaction to technical and economic interventions. Within the time frame of the model, herd size and biological performance rates were the most important constraints to increasing beef production. The adoption of a more intensive management system for the extensive commercial sub-herd of the Coast was limited by availability of farm managers. When this constraint was relaxed permanent labour became a limiting factor. Short feeding of steers normally marketed in poor condition was shown to be a viable means of increasing beef output in the Coastal Region. While the price effect of this increased output was more than 5%0, the optimal behaviour of

63

SYSTI'-MS ANALYSIS OF T H E G U Y A N E S E LIVES-I'OCK I N D U S T R Y

producers in other regions and sub-herds was unaffected. The inelasticity of beef supply in the model was consistent with the high degree of asset fixity in the cattle sub-sector due to very limited alternative uses for resources. Model results suggest that production systems which use traditional techniques and rely largely on resources with low opportunity cost are more profitable than systems requiring the purchase of modern inputs. This finding has important implications for pilot livestock projects initiated to stimulate the economic development of frontier regions. The model structure, integrating biological and economic behaviour, seems to provide a realistic tool for the evaluation of interventions into the livestock subsector. Such a tool can be useful in devising development policies and programmes in many tropical countries where cattle are actually or potentially an important source of food, employment and economic growth.

ACKNOWLEDGEMENT

This paper is Journal Paper No. 6826 of the Purdue Agricultural Experimcnt Station. The research described was supported under the USAID 211d grant entitled 'Expansion of Competence in the Design and Execution of Ruminant Livestock Development Programs for the Tropics: With Emphasis on the Analysis of Systems of Production and Marketing'. The authors wish to thank Lee Schrader, Bob Thompson, Carlos Pomerada and the journal referees for comments. The help of the Guyanese agricultural ministry, USAID and the other members of the 21 ld consortium is also gratefully acknowledged.

APPENDIX

Formally, the model is as follows: (13) Minimise

t

i

u

n

j

t

r

j

i

o

j

k

t

L

i

j

m

t

p

q

i ~ NtYt l

subject to : (14)

~ Qit,,~i,u-~. £ ~ Ajk~.t,,Dikt.<0 i

j

k

L

foralltandu

t

64

T. KELLEY W l t l T E ,

(15)

B. A. M C C A R I . , R. D. MAY, r .

X,

for all r j

y

(16)

/.

for all j, m and t

L

~EnjkLtDjkL--~Lnktiflnkti'(O L i

for all j, n and t

k

~ Sojkl.tOjkL-- ~ Kojri,ojti ~ O 1. i

for all o,j and t

k

~

for all j, p, q and t

(18) (19)

(20) J

GpqjkLtDjk L -- T~.o, <_ 0

L,

k

(21)

k

C,~kLtDjkL .... Z,.t _< 0

k

(~7)

H. SPREEN

~~'kLtOjkL k L

-

~ H~jkLtDjgt. < b,jk t L

(22)

Yt
for all t for all s,j, k and t for all t and u

i

~

(23)

B,j,i < 1

for all n, j and t

7oj, < 1

for all o, j and t

i

(24)

~ i

(25)

~i,.,, X,, DikE, Z,,,, fl,j,i, "2oJ,, Tjpu,, Y, >- 0

where" i J k L m n o

p q r s

Pit.

stands for stands for stands for stands for stands for stands for stands for stands for stands for stands for stands for stands for is the area U.

step n u m b e r on a curve. region. sub-herd. m a n a g e m e n t system. a particular fixed price input. a particular labour type. a particular land type. the g o o d being transported. the mode of transport. animal type being retained. fixed factor type. p r o d u c t (1 for meat, 2 for milk). under the d e m a n d curve at step i during year t for product

SYSTEMS A N A L Y S I S OF T I l E GUYANESI" L I V E S T O C K I N D U S T R Y

O~i tu

M, X, Fjk L DjkL

Zm t Wnjti flnjti RoJti

~]ojti /~jpqt Tjpqt

N, Y,

Q itu Ajk I.tu Jjk Lr Cmjk L t ~Lnjk Lt l~njt i ~oJkLt Kojti G pqjk L t UjkLt b xjk f

65

is a variable which gives the a m o u n t o f step i used in year t for p r o d u c t u. is the retention price for animal type r. is the quantity of animal type r retained, is the miscellaneous cost o f production for region j, sub-herd /,', m a n a g e m e n t system L per cow unit. is the n u m b e r o f cow units in solution in region j, sub-herd k, m a n a g e m e n t system L. is the cost o f fixed price input m during year t. is the quantity used o f tixed price input m during year t. is the area under the supply curve for labour type n in region/', year t at step i. is the a m o u n t of step i of r e g i o n j ' s labour type n supply curve used in year t. is the area under the supply curve for land type o in r e g i o n j , year t, step i. is the a m o u n t o f step i o f r e g i o n j ' s land type o supply curve used in year t. is the cost o f transporting one unit o f good p between region j and the coast by transport mode q, year t. is the quantity o f item p transported by mode q in year t from r e g i o n j to the coast. is the cost per unit o f beef stolen during year t. is the quantity of beef stolen during year t. is the quantity of product u at step i of the d e m a n d curve in year t. is the a m o u n t o f product u produced by management system L, sub-herd k, region j in year t. is the quantity of retained animal class r produced by management system 1,. sub-herd k, region j. is the quantity o f purchased input m used by l)jkt, in year t. is the quantity of r c g i o n j ' s labour o f type n used by l)jk~, in year t. is the quantity of labour type n supplied at step i of the supply curve for region.,," in the period t. is the quantity of land type o used by D~kL in year t. is the quantity of land type o supplied at step i of r e g i o n j ' s supply curve in year t. is the quantity of good p required to be transported by mode q by l)jkz, in year t. is the a m o u n t o f theft from D~k~. in year t, is the use o f the sth fixed factor by Dike. in year t. is the e n d o w m e n t o f the sth fixed factor in year t to sub-herd k in region j.

66

r . KELLEY WHITE, B. A. MCCARL, R. D. MAY, T. 1t. SPREEN REFERENCES

BYERLEE, D. • HALTER, A. N. (1974). A macro-economic model for agricultural sector analysis, American Journal o f Agricultural Economics, 56, 520--33. DULOY, J. H. & NORTON, R. J. (1973). C H A C : A programming model of Mexican agriculture. In: Multi-let:el planning: Case studies in Mexico (Goreaux, L. & Manne, A. eds). 291-337. Amsterdam, North Holland Publishing Co. DULOY, J. H. & NORTON, R. D. (1975). Prices and incomcs in linear programming models, American Journal o f Agricultural Economics, 57, 591-600. FORD, J. R., MAY, R. D., McCARL, B., MORRIS, W. H. M., PETRITZ, D. C., SCHRADER, L., SPREEN, T. & WroTE, T. K. (1976). 21 ld Livestock Consortium Report to the Government of Guyana. Unpublished report, Department of Agricultural Economics, Purdue University, February 1976.

MAY, R. D. (1975). A systems model of the cattle economy--A Guyana application. Ph,D. Thesis, Purdue University. MILLER, C. (1963). The Simplex method for local separable programming. In: Recent adcances in mathematical programming (Graves, R. L. & Wolfe, P., eds), 88-100. New York, John Wiley & Sons. SPREEN, T. H., MCCARL, B. A., MAY, R. D., SANTINI, J, & KELLEY WHITE, T. (1977). Users Guide to the Purdue Cattle Industry Model Computer Program, Purdue Agricultural Station Bulletin 170. TAKAYAMA,T. ~. JUDGE, G. G. ( 1971 ). Spatial attd temporalprice and allocation models. Amsterdam, North-Holland Publishing Co. WHITE, T. KELLEY, MCCARL, B. C., MAR]ELLA, D. R. & OBERMILLER, F. W. (1975). The Purdue Development Model: A Systems Approach to Modeling Demographic -Economic Interaction in Agricultural Development, Research Bulletin No. 925.