AUSTRALIA

A MODEL FOR I>1;J'l1E;RMININ

Bureau of Agricultural Economics

Discussion paper 86.4

A MODEL FOR DETERMINING THE SHORT TERM DEMAND FOR IRRIGATION WATER -TION AND USE IN ESTIMATING TAE SHORT TERM DEMAWD FOR IRRIGATION WATER

Project 22306

J. Briggs Clark, K. Menz, D. Collins and R. Firth

Australian Government Publishing Service Canberra 1986

@Commonwealth of Australia

ISSN 0818-4860 ISBN 0 644 05529 4

Printed in Australia by Better Printing Service, 44 Paterson Parade, Queanbeyan, N.S.W.

For seve ra l years there have been increas ing c a l l s f o r reform of i r r i g a t i o n water p r i c ing pol icy , with the aim of increas ing e f f i c i ency i n t h e use of water. Centra l t o t h i s pol icy debate a r e t h e r o l e of water p r i c ing and the impact of changing water charges on production systems and resource use. The nature of the response of t h e amount of i r r i g a t i o n water demanded t o a change i n the p r i c e of water is a key i s sue i n analys ing the p o t e n t i a l f o r demand management of water.

This paper r epor t s on the cons t ruc t ion and v a l i d a t i o n of a regional model which s imula tes water demand and a g r i c u l t u r a l production on mixed farms i n the Murrumbidgee and Coleambally I r r i g a t i o n Areas of southern New South Wales. The main f ea tu res o f the model a r e descr ibed and documented and seve ra l examples a r e given of its use i n es t imat ing the responsiveness of i r r i g a t i o n water use t o a change i n the p r i c e of water. The ana lys i s focuses on shor t run water p r i c ing policy a s a f i r s t s t e p i n a broader p r o j e c t t o examine a range of management s t r a t e g i e s .

The model was b u i l t , and t h i s paper prepared, i n t h e Bureau's Rural Production Economics Branch under the genera l supervis ion of D r Ken Menz.

ROBERT BAIN Director

Bureau of Agr icul tura l Economics Canberra ACT

October 1986

iii

The Bureau wishes t o acknowledge the a s s i s t ance which many o the r organisa t ions provided during the cons t ruc t ion of t h i s model. In p a r t i c u l a r , valuable a s s i s t ance was provided by Phi l Penman and Andrew Arch of t h e New South Wales Department of Agr icul ture , Leeton; Paul Verdich of t h e New South Wales Water Resources Commission; and Warren Muirhead of t h e Commonwealth S c i e n t i f i c and I n d u s t r i a l Research Organization's Centre f o r I r r i g a t i o n Research, Griff i t h .

CONTENTS

Summary

1. Int roduct ion

2. The Study Region

3. General Approach

4. The Regional Model and Matrix Descr ip t ion

4.1 The ob jec t ive function 4 .2 Resource c o n t r a i n t s and r e c o n c i l i a t i o n s 4.3 The matrix of t echn ica l c o e f f i c i e n t s 4 .4 Model va l ida t ion

5. Estimating Water Demand E l a s t i c i t i e s - Analyses and Resul ts 5.1 Single-price e f f e c t s 5.2 Multiple-price e f f e c t s 5.3 Spec i f i c appl ica t ion of the model

6. Discussion and Conclusions

Appendix A: Lis t ing of A c t i v i t i e s and Const ra in ts

Appendix B: Yield Response t o I r r i g a t i o n Water Functions

Appendix C: Operating the BAE's Regional Water Model

References

Figures

1 Diagrammatic layout of o v e r a l l model

2 Regional s h o r t run derived demand funct ion f o r i r r i g a t i o n water (o ther p r i c e s cons tant )

B1 Experimental r e l a t ionsh ip between crop y i e l d and water used

B2 Prac t i ca l f i e l d r e l a t ionsh ip between crop y i e ld and i r r i g a t i o n water supplied

Tables

1 Charges f o r water supplied t o i r r i g a t i o n a r e a s i n 1982-83

2 Example of land and feed supply submatrix

3 Example of cropping submatrix

4 Example of l ives tock submatrix

5 Example of water supply submatrix

6 Example of labour submatrix

7 Example of crop s e l l i n g submatrix

8 Land use: modelled and a c t u a l

9 P r i ce indexes used i n t h e p r i ce s e n s i t i v i t y experiment

10 'Base' product and water p r i c e s used i n the p r i c e s e n s i t i v i t y experiment

11 Summary regress ion f o r p r i c e parametr i sa t ion

12 I r r i g a t i o n water: s h o r t run own-price demand e l a s t i c i t i e s

13 Percentage change i n i r r i g a t i o n water demanded, given a one pe r cent change i n product p r i c e s , a t three water p r i c e s

A MODEL HIR DETEmIIPIHG TBB SHORT TgRM D B FOR IRRIGATION WATER

'Curren t w a t e r a l l o c a t i o n procedures i n A u s t r a l i a a r e g e n e r a l l y conduc ive t o economic i n e f f i c i e n c y . A l t e r n a t i v e a l l o c a t i o n s y s t e m s which cou ld reduce economic i n e f f i c i e n c e s e x i s t and shou ld be e v a l u a t e d . ' ( A u s t r a l i a n Rura l Ad jus tmen t U n i t 1982)

The BAE, i n a r e p o r t t o t h e Department o f Resources and Energy (Watson, Reyno lds , C o l l i n s and Hunter 1 9 8 3 ) , concluded t h a t , i n many r e g i o n s o f A u s t r a l i a , any changes i n water a l l o c a t i o n p o l i c i e s wwuld have a c o n s i d e r a b l e impac t on e s t a b l i s h e d p r o d u c t i o n s y s t e m s , r e s o u r c e u s e and revenue from w a t e r s a l e s . As t h e n a t u r e o f t h e s e r e g i o n a l e f f e c t s w i l l u l t i m a t e l y d e t e r m i n e t h e s u c c e s s o f wa ter a l l o c a t i o n p o l i c y i n i t i a t i v e s , the Bureau h a s under taken t o r e a s s e s s a l l o c a t i o n p o l i c i e s i n a r e g i o n a l c o n t e x t . The i n i t i a l s t e p h a s i n v o l v e d the development o f a r e g i o n a l w a t e r demand model , which i s d e s c r i b e d i n this paper. An a p p l i c a t i o n o f t h e model f o r e s t i m a t i n g t h e s h o r t r u n demand f o r i r r i g a t i o n w a t e r i s presen ted .

The model s i m u l a t e s a g r i c u l t u r a l p r o d u c t i o n on mixed farms i n t h e Murrumbidgee and Coleambally I r r i g a t i o n Areas, w i t h a n emphas i s o n i r r i g a t i o n w a t e r use . Some 36 cropp ing and e i g h t l i v e s t o c k a c t i v i t i e s a r e i n c l u d e d , t h e o b j e c t i v e f u n c t i o n o f the l i n e a r programming model b e i n g t o maximise t h e t o t a l g r o s s margin f o r the r e g i o n . C o n s t r a i n t s i n c l u d e p h y s i c a l r e s o u r c e s such a s water a v a i l a b i l i t y , channel c a p a c i t i e s and l a n d t y p e s , a s w e l l a s l a b o u r and c r o p r o t a t i o n a l requ i rements . The m a t r i x i n c o r p o r a t e s f o u r submatr ices , e a c h r e p r e s e n t i n g a s i n g l e subarea i n t e r m s o f l o c a t i o n and farm s i z e .

F l e x i b i l i t y i n t h e level (and t i m i n g ) o f i r r i g a t i o n s i s l i n k e d t o produc t o u t p u t s , and hence e a r n i n g s , b y way o f y i e l d response t o water . The u s e o f such i r r i g a t i o n produc t ion f u n c t i o n s i n l i n e a r programming models o f i r r i g a t i o n r e g i o n s i s n o t common, d e s p i t e i t s o b v i o u s impor tance .

P r e s e n t l y t h e model i s l i m i t e d t o s h o r t r u n a n a l y s e s . That i s , the t i m e per iod under r e v i e w i s n o t l o n g enough t o a l l o w i r r i g a t o r s t o v a r y a l l t h e i r f a c t o r s o f produc t ion . F o r example, r e g i o n a l c a p i t a l c o n s t r a i n t s and t h e e f f e c t s o f changing levels o f c a p i t a l i n v e s t m e n t a r e n o t c o n s i d e r e d . Fur ther development o f a l o n g r u n model would be i m p o r t a n t where s i g n i f i c a n t changes t o i r r i g a t i o n t e c h n i q u e s a r e a n t i c i p a t e d i n response t o s u b s t a n t i a l 1 y i n c r e a s e d w a t e r p r i c e s . Adopt ion o f new water a p p l i c a t i o n t e c h n i q u e s cou ld be e f f e c t i v e l y model led o n l y i f c a p i t a l were e x p l i c i t l y i n c l u d e d a s a c o n s t r a i n t . N e v e r t h e l e s s the o p p o r t u n i t y e x i s t s i n the p r e s e n t model f o r farmers t o change s u b s t a n t i a l l y t h e i r u s e o f wa ter i n t h e s h o r t t e r m , b y s h i f t i n g t o a l t e r n a t i v e cropp ing p a t t e r n s and b y v a r y i n g t h e number o f i r r i g a t i o n s p e r crop .

The e x i s t i n g model h a s been used t o e s t i m a t e the s h o r t r u n r e s p o n s i v e n e s s t o changes i n water p r i c e o f t h e demand f o r i r r i g a t i o n water . The r e s p o n s i v e n e s s o f demand t o p r i c e i s a c r i t i c a l parameter i n d e t e r m i n i n g t h e e f f e c t s t h a t p r i c e changes w i l l have on revenue t o the water s u p p l y a u t h o r i t y , wa ter c o n s e r v a t i o n i n t h e r e g i o n and r e g i o n a l farm incomes. The e s t i m a t i o n o f t h e p r i c e r e s p o n s i v e n e s s o f demand i n v o l v e d t h e

p a r a m e t r i s a t i o n o f the p r i c e o f w a t e r over a l i k e l y range o f w a t e r and produc t p r i c e s . A series o f r e s u l t s was generated b y t h e l i n e a r programming model , and t h e p r i c e - q u a n t i t y r e l a t i o n s h i p s were summarised b y means o f a r e g r e s s i o n e q u a t i o n . The e l a s t i c i t i e s presen ted h e r e , and their i n t e r p r e t a t i o n , depend on the p a r t i c u l a r model used and the l e n g t h o f t i m e a l lowed f o r ad jus tmen t t o changes.

W i t h i n t h e p r e s e n t and l i k e l y f u t u r e w a t e r p r i c e range, the s h o r t r u n p r i c e e l a s t i c i t y o f demand f o r i r r i g a t i o n w a t e r was be low u n i t y . A t p r e v a i l i n g w a t e r and produc t p r i c e levels, t h e s h o r t r u n demand f o r i r r i g a t i o n w a t e r i s more s e n s i t i v e t o p r i c e changes i n rice and o t h e r summer c r o p s t h a n it i s t o w a t e r p r i c e changes. However, e v e n these c r o s s - p r i c e demand e l a s t i c i t i e s were found t o be r e l a t i v e l y s m a l l .

For water c h a r g e i n c r e a s e s w i t h i n the r e a l i s t i c a l l y f o r e s e e a b l e w a t e r p r i c e range o f $ ~ / M L t o $ z ~ / M L , the model r e s u l t s sugges t t h a t t h e r e i s o n l y a marginal e f f ec t o n w a t e r c o n s e r v a t i o n and cropp ing a r e a s i n the s h o r t run. T h i s i s c o n s i s t e n t w i t h what i s known o f s h o r t t e r m r e a c t i o n s b y f a n n e r s t o i n c r e a s e d water charges . Because f a n n e r s have l i m i t e d o p t i o n s i n the s h o r t t e rm, t h e i r s t r a t e g i e s w i l l be aimed a t c o n t i n u i n g t o e x t r a c t the maximum n e t r e t u r n s from e x i s t i n g r e s o u r c e s and i r r i g a t i o n i n f r a s t r u c t u r e . The model i s s t r u c t u r e d t o c a p t u r e t h i s immediate r e a c t i o n b y farmers , and s o l u t i o n s r e f l e c t a r e o r i e n t a t i o n i n c r o p p i n g / l i v e s t o c k e n t e r p r i s e s , w i t h l i t t l e change i n w a t e r u s e .

However, a s the t i m e a l lowed f o r a d j u s t m e n t o f r e s o u r c e u s e i n c r e a s e s it c a n be e x p e c t e d t h a t farmers w i l l t a k e more far-reaching d e c i s i o n s o n l a n d and hence w a t e r use . I t f o l l o w s t h a t demand f o r w a t e r i s l i k e l y t o be much more r e s p o n s i v e t o p r i c e change i n t h e l o n g e r t e r m t h a n i s i n d i c a t e d i n t h i s paper u s i n g a s h o r t t e r m model. T h i s p o i n t should be borne i n mind when i n t e r p r e t i n g the r e s u l t s from the p r e s e n t mode l : the e s t i m a t e s here shou ld n o t be used a s a b a s i s f o r l o n g t e rm p o l i c i e s o n water charges . The mode l , though s i m u l a t i n g o n l y a l i m i t e d range o f o p t i o n s a v a i l a b l e t o f a n n e r s f o r r e s t r u c t u r i n g t h e i r e n t e r p r i s e s i n the s h o r t t e r m , provided q u a n t i t a t i v e measures o f t h e s h o r t t e r m impac t o n farm incomes o f changing w a t e r charges . O v e r the p r i c e range n o t e d above, a s u b s t a n t i a l n e g a t i v e e f f e c t o n r e g i o n a l g r o s s margin was i n d i c a t e d a s w a t e r p r i c e i n c r e a s e d . For example, a rise o f $ ~ O / M L ( t h a t i s , from $ ~ / M L t o $ z ~ / M L ) r e s u l t e d i n a f a l l o f approx imate ly 40 p e r c e n t i n r e g i o n a l g r o s s margin.

The reason f o r t h i s f a l l was a gradual r e d u c t i o n i n the u s e o f i r r i g a b l e a r e a a s f a n n e r s moved from i r r i g a t e d t o d r y l a n d p a s t u r e s , coup led w i t h a d e c l i n e i n c r o p y i e l d s a s t h e a p p l i c a t i o n o f wa ter t o i r r i g a t e d c r o p s was g r a d u a l l y reduced. I t would appear, however, t h a t ( i n t h e s h o r t r u n ) s i m p l y i n c r e a s i n g the p r i c e o f wa ter w i l l n o t b y i t s e l f a c h i e v e s i g n i f i c a n t a l l o c a t i v e r e f o r m s i n i r r i g a t i o n w a t e r use .

The s h o r t r u n consequences o f wa ter p r i c i n g changes a r e i m p o r t a n t , a s i s e x e m p l i f i e d b y the c u r r e n t d i s p u t e regard ing non-payment o f i r r i g a t i o n w a t e r b i l l s and b y the rice i n d u s t r y ' s r e q u e s t f o r s h o r t t e n n a s s i s t a n c e (BAE 1 9 8 6 ) . That i s , i f the s h o r t run r e s p o n s i v e n e s s o f demand t o changes i n p r i c e i s r e l a t i v e l y low, then a p r i c e i n c r e a s e w i l l have l i t t l e e f f e c t on w a t e r c o n s e r v a t i o n , b u t it can ( a s n o t e d above) have a s u b s t a n t i a l e f f e c t on incomes t o farmers .

However, t h e s h o r t r u n consequences d o n o t n e c e s s a r i l y resemble t h o s e i n t h e long run . The development o f a l o n g r u n model would permi t a more

c m p r e h e n s i ve examinat ion o f p r i c i n g p o l i c i e s and management o p t i o n s , a s hell a s e s t i m a t i o n o f the l o n g Nn p r i c e s e n s i t i v i t y o f demand f o r w a t e r - The s h o r t r u n r e s p o n s i v e n e s s o f demand t o water p r i c e de termined i n this paper i s expec ted t o set a l o w e r bound on the e s t i m a t e o f l o n g r u n response. Knowledge o f ( o r a n e s t i m a t e o f ) t h e l o n g r u n r e s p o n s e o f demand f o r i r r i g a t i o n w a t e r t o water p r i c e i s a n e s s e n t i a l component o f a sound water p r i c i n g s t r a t e g y .

1. INTRODUCTION

The management of e x i s t i n g water suppl ies , a s d i s t i n c t from the development of new schemes, is becoming an increas ingly important isSue f o r water pol icy in Aust ra l ia . Centra l t o t h i s i s sue is the r o l e of water p r i c ing and the e f f e c t of changing water p r i c e s on production systems and resource use i n many regions.

The Working Group Report t o the Minis ter f o r Primary Industry (1982) considered t h a t the Commonwealth Government should take t h e lead i n influencing S t a t e s ' dec i s ions concerning i r r i g a t i o n water a l l o c a t i o n po l i c i e s . Similar recommendations were made i n t h e 'Perspect ive on Water Resources t o the Year 2000' study (Department of Resources and Energy 1983). A Water Resources Assistance Program has been e s t ab l i shed t o implement the Commonwealth Government's po l i cy , and the f i r s t f i n a n c i a l a l l o c a t i o n s f o r t h i s program were made i n the 1984 Federal budget.

TO f a c i l i t a t e c r i t i c a l a n a l y s i s of var ious water a l l o c a t i o n p o l i c i e s , t h e Bureau has developed a regional water model. The model al lows an assessment of a wide range of pol icy and management opt ions t h a t have been the sub jec t of growing debate between economists, water resource managers and i r r i g a t o r s .

In many regions of Aust ra l ia , inland development p o l i c i e s have resul ted i n the use of water resources being publ ic ly subs id ised (Department of Resources and Energy 1983). When water was abundant r e l a t i v e t o demand, reques ts f o r i r r i g a t i o n water could genera l ly be m e t a t moderate c o s t through supply augmentation. Water has been a l loca ted by a system of adminis t ra t ive procedures, r u l e s and regula t ions , a t l o w p r i c e s which encourage excessive consumption. The s i t u a t i o n , however, has changed. me s teeply r i s i n g c o s t s of add i t iona l s torages have rendered Supply augmentation less a t t r a c t i v e (Watson and Rose 1980). A t the same t ime, funds a l loca t ed f o r water resource development have been dec l in ing i n r e a l terms (Scot t 1982), while the c o s t s of secondary t a s k s such a s s a l i n i t y treatment and r e h a b i l i t a t i o n works have r i s e n (Randall 1981). This has led water a u t h o r i t i e s t o seek a g r e a t e r l e v e l of c o s t recovery. In addi t ion , d i s s a t i s f a c t i o n is being expressed by both a g r i c u l t u r a l and non-agricultural groups of water users who cannot secure necessary water supp l i e s d e s p i t e t h e i r a b i l i t y and wi l l ingness t o pay (Aust ra l ian Rural Adjustment Unit 1982).

Concomitant with e sca l a t ing c o s t s of providing water supp l i e s and with increas ing competi t ion f o r a v a i l a b l e water resources, t he re have been c a l l s f o r reform i n water pol icy with a view t o increasing the e f f i c i ency of i r r i g a t i o n water use (Neilson Associates 1981: Working Group Report t o the Minister f o r Primary Industry 1982; Musgrave 1983: Department of Resources and Energy 1983; Watson, Reynolds, Q l l i n s and Hunter 1983). Members of the water industry a r e now reconsidering how ava i l ab le water resources a r e t o be a l loca t ed between uses , between use r s and between regions. In the i n t e r e s t s of e f f ic iency and equi ty i n the use of i r r i g a t i o n water, economic theory and fundamental market mechanisms a r e beginning t o play a g r e a t e r r o l e i n water po l i c i e s .

A c e n t r a l i s sue is t h a t of p r i c ing water t o r e f l e c t i ts f u l l economic c o s t and r e l a t i v e sca rc i ty . For many regions, t h i s change would have a cons iderable impact on e s t ab l i shed production systems, regional resource

use and the amount of revenue f o r t he water resource i n s t i t u t i o n s . A c r i t i c a l parameter influencing t h e p r i c ing decis ion i s t h e responsiveness of demand f o r water t o changes i n i ts p r i c e - t h a t is, the p r i c e e l a s t i c i t y of demand f o r water (Seagraves and Eas ter 1983). P r i ce e l a s t i c i t y of demand is defined a s the percentage change i n the quan t i ty of water demanded f o r a 1 pe r cen t change i n the p r i c e of water. It thus determines whether t o t a l revenue from the s a l e of water ( p r i c e x quan t i ty ) w i l l r i s e o r f a l l i n response t o a p r i c e change. If demand is i n e l a s t i c - t h a t is, in sens i t i ve t o p r i c e changes - p r i c e inc reases have l i t t l e e f f e c t on water conservation, but increase t o t a l revenue t o the water au tho r i ty . I f demand is e l a s t i c - responding more than propor t ionate ly t o changes i n p r i c e - a policy of increas ing p r i c e s w i l l have a s i g n i f i c a n t e f f e c t on water conservation, and t o t a l revenue t o the water au tho r i ty w i l l decrease. It should be noted t h a t the demand f o r i r r i g a t i o n water is a derived demand: water is demanded a s an input i n t o a production process and its p r i c e w i l l be dependent upon the p r o f i t a b i l i t y of c rops grown.

This paper documents t he regional water model developed, and its underlying assumptions. In sec t ion 2 t he study region chosen is ou t l ined . This is followed by desc r ip t ions of t he approach taken i n modelling and of the l i n e a r programming s t r u c t u r e adopted ( sec t ions 3 and 4 ) . The f i n a l s ec t ion of the paper ( sec t ion 5) provides an examination of the s h o r t run p r i ce e l a s t i c i t y of demand f o r i r r i g a t i o n water, demonstrating both the usefulness of the model and the complexity of the water p r i c ing issue. The d a t a employed a r e f o r t h e year 1982-83.

The development of a long run model would permit the es t imat ion of the long run p r i ce e l a s t i c i t y of demand f o r water, a s well a s a f u r t h e r examination of pr ic ing p o l i c i e s and management options. A s a genera l ru l e , t he p r i ce e l a s t i c i t y of demand f o r water increases a s more t i m e is allowed f o r farmers t o ad jus t t o p r i c e changes. Thus, the sho r t run e l a s t i c i t y determined i n t h i s paper can be expected to form a lower bound on t h e es t imate of long run demand e l a s t i c i t y .

2. TAE STUDY REGION

The Murrumbidgee Valley, which was chosen f o r i nves t iga t ion i n t h i s study, c o n s i s t s of two i r r i g a t i o n a reas - Murrumbidgee and Qleambally. I r r i g a t i o n water i s heavily subsidised i n these areas , t he charges following a decreasing block schedule ( see t a b l e 1). Randall (1981) be l ieves t h a t revenue from i r r i g a t i o n water s a l e s covers only about one-third of the f u l l resource c o s t of t he water provided. To t h e i r r i g a t o r , water r ep resen t s a low c o s t input (usually l e s s than 10 pe r cen t of t o t a l farm production c o s t s ) , and its apparent abundance, combined with s u i t a b l e s o i l s , has f a c i l i t a t e d the expansion of r i c e and fodder production i n the region. Currently, over half t he i r r i g a t e d lands a r e producing r i c e and fodder (30 per c e n t and 25 per cen t , respect ive ly) . Rice is by f a r t he g r e a t e s t income earner f o r t he region, and it i s t h e most p r o f i t a b l e crop i n terms o f r e tu rn per hectare , but it is a l s o the most i n t ens ive user of water (15-18 ML/ha). In terms of g ross margin per megal i t re of water used, however, r i c e is s imi l a r t o o the r crops. I r r i g a t e d pas ture , i n con t r a s t , is r e l a t i v e l y una t t r ac t ive from an economic viewpoint, having a low g ross margin both per hectare and per megal i t re of water used.

In the pas t , water pol icy i n the Murrumbidgee Valley has been charac ter i sed by:

- a philosophy of the S t a t e serving i d e n t i f i a b l e needs, associa ted with regional decen t r a l i s a t ion p o l i c i e s , so t h a t the supply system has been expanded t o meet reques ts f o r water;

- subsidised water charges, which have not r e f l ec t ed the f u l l economic c o s t of de l ivered water, but have been set t o recover only opera t ing and maintenance c o s t s (Scot t 1982), representing about one-third of t o t a l c o s t s ;

- the attachment of water l i cences t o the land, l i cens ing bas i c consumption by i r r i g a b l e a rea (volumetric a l l o c a t i o n s having been introduced only recent ly) ; and

- a decl in ing water charge schedule, the average u n i t p r i c e of water decreasing a s consumption increases . (The number of p r i c e l e v e l s was reduced from th ree t o two only i n 1982.)

As i r r i g a t o r s do not pay the f u l l economic c o s t of de l ivered water, the quant i ty of water used and its a l l o c a t i o n between users and uses do not r e f l e c t t h e t r u e sca rc i ty of t he resource. That is, producers may be presumed t o use higher app l i ca t ion r a t e s o r grow lower value crops than they would i f t h e f u l l economic c o s t of supplying the water were charged.

Also a t t r i b u t a b l e t o the heavily subsidised water charges i n t h e Murrumbidgee Valley is the s i t u a t i o n of excess demand f o r water. To br ing demand i n t o l i n e with t h e ( f u l l y committed) supply, some form of demand management is necessary. This could be achieved through regula t ion by t h e c e n t r a l author i ty , through water pr ic ing pol icy o r by a combination of both. The success of 'demand management' v i a p r i c ing pol icy depends c r i t i c a l l y on the p r i c e e l a s t i c i t y of demand f o r water - the focus of t h i s paper .

Table 1: CHARGES FOR WATER SUPPLIED TO IRRIGATION AREAS I N 1982-83(a)

Area and supply block Charge

Murrunbidgee Irr igat ion Area

(i) an amount in megalitres equal t o three times the number of hectares assessed by the Commission a s i r r igable ( t o an allowable maximum of 220 ha for t h i s purpose)

(ii) a l l further water supplied

Colearnbally Irr igat ion Area

(i) the f i r s t 600 ML supplied (ii) a l l further water supplied

(a) For non-horticultural holdings.

Source: New South Wales Water Resources Commission.

3. GENERAL APPROACH

A r e g i o n a l l i n e a r programming model was s e l e c t e d i n o r d e r t o s i m u l a t e t h e main consequences o f v a r i o u s wate r p o l i c i e s , g i v e n r e s o u r c e a v a i l a b i l i t y , c o s t s and p r i c e s i n t h e Murrumbidgee I r r i g a t i o n Area and Coleambally I r r i g a t i o n Area.

Water p r i c e s and q u a n t i t i e s have been s o h e a v i l y r e g u l a t e d t h a t econometr ic e s t i m a t e s d e r i v e d from h i s t o r i c a l d a t a a r e o f l i t t l e u s e i n e v a l u a t i n g t h e consequences o f changing t h e s e paramete rs i n t h e absence o f r e g u l a t i o n . The u s e f u l n e s s o f l i n e a r programming f o r a n a l y s i n g t h i s t y p e o f problem h a s been demonstrated i n p r e v i o u s r e s e a r c h and f o r t h e same g e n e r a l s tudy a r e a by Ryan (1969) and F l i n n (1976) , who bo th used a r e p r e s e n t a t i v e farm approach. T h i s s t u d y , i n c o n t r a s t , f o c u s e s on r e g i o n a l consequences. There have i n any c a s e been major changes i n r e l a t i v e p r i c e s and a g r i c u l t u r a l t e c h n o l o g i e s s i n c e t h o s e s t u d i e s were done.

I n de te rmin ing which e n t e r p r i s e s a r e most p r o f i t a b l e from a r e g i o n a l v iewpoin t , l i n e a r programming is a n i d e a l t o o l , s i n c e it a l l o w s r e t u r n s t o t h e 'most l i m i t i n g ' r e s o u r c e t o be maximised. Furthermore, t h i s approach p r o v i d e s t h e most p r a c t i c a l method f o r s imul taneous ly de te rmin ing t h o s e e n t e r p r i s e s and t e c h n o l o g i e s which a r e b o t h t e c h n i c a l l y and economical ly most e f f i c i e n t (Longworth and Menz 1980) . Pomerada (1978) p r e s e n t s a good mathematical e x p o s i t i o n o f t h e g e n e r a l problem, i n c l u d i n g s p e c i f i c r e f e r e n c e t o t h e concep t o f i r r i g a t i o n p r o d u c t i o n f u n c t i o n s .

Flood i r r i g a t i o n i s t h e on ly wate r a p p l i c a t i o n method c o n s i d e r e d . I t is t h e technology c u r r e n t l y used w i t h i n t h e s tudy region. New wate r a p p l i c a t i o n t e c h n o l o g i e s a r e being developed t o improve e f f i c i e n c y of wa te r use , b u t it w i l l be some y e a r s b e f o r e they c a n be widely a p p l i e d commercial ly . As t h e s e p o s s i b i l i t i e s and t h e a b i l i t y to change o t h e r f i x e d ( c a p i t a l ) f a c t o r s o f p r o d u c t i o n a r e n o t inc luded , t h i s model is s h o r t run i n n a t u r e . S i m i l a r l y , f o r purposes o f t h i s s h o r t run model t h e h o r t i c u l t u r a l s e c t o r h a s been excluded. H o r t i c u l t u r a l f a rms - which i n 1982-83 comprised on ly 5 p e r c e n t o f t o t a l i r r i g a t e d l a n d i n t h e s tudy r e g i o n - a r e d i s t i n c t i v e i n t e rms o f t h e i r s i z e and t h e i r wa te r a p p l i c a t i o n r u l e s and r e g u l a t i o n s . Due t o t h e f i x i t y o f t r e e s and v i n e s , an examina t ion o f t h e consequences o f v a r i o u s w a t e r p o l i c i e s f o r h o r t i c u l t u r a l c r o p s would be meaningful o n l y i n t h e l o n g e r term.

I n t h e model, t h e Murrumbidgee Val ley is d i v i d e d i n t o f o u r s u b a r e a s , each o f which is r e p r e s e n t e d i n c o n s i d e r a b l e d e t a i l i n terms of t h e number o f a c t i v i t i e s and r e s o u r c e s inc luded . The s u b a r e a s a r e d i s a g g r e g a t i o n s o f each o f t h e two i r r i g a t i o n a r e a s i n terms of farm s i z e s o a s t o make each subarea r e l a t i v e l y homogeneous. As r e g i o n a l consequences a r e being c o n s i d e r e d , f u r t h e r d i s a g g r e g a t i o n was n o t c o n s i d e r e d a worthwhile a d d i t i o n t o model complexi ty and r e s e a r c h t i m e . In format ion on farm s i z e s p rov ided by t h e New South Wales Water Resources Commission i n d i c a t e d t h a t , i n t h e Murrumbidgee I r r i g a t i o n Area, 50 p e r c e n t o f fa rms were w i t h i n t h e 20-200 ha range and t h e remaining 50 p e r c e n t were i n t h e 200-640 ha range , whi le i n t h e Coleambally I r r i g a t i o n Area 50 p e r c e n t o f fa rms were between 200 ha and 220 ha and t h e remaining 50 p e r c e n t ranged from 220 ha t o 370 ha. A g r i c u l t u r a l p r o d u c t i o n w i t h i n t h e model was aggrega ted to t h i s subarea l e v e l .

F igure 1 shows t h e block d i a g o n a l s t r u c t u r e o f t h e o v e r a l l mat r ix . Each of t h e s u b a r e a m a t r i c e s is i d e n t i c a l i n t e r m s o f t h e range o f

Figure 1: DIAGRAMMATIC LAYOUT OF OVERALL MODEL BAE chart

a c t i v i t i e s and cons t r a in t s . A more d e t a i l e d desc r ip t ion of these subarea matr ices is given i n sec t ion 4.

OB3ECPIVE

The subarea matr ices a re l inked by a s e r i e s of regional c rop commodity s a l e and labour h i r e a c t i v i t i e s . In addi t ion , the so lu t ion of t he matrix is const ra ined by the ' r i g h t hand s ide ' block which con ta ins the resource l e v e l s of the subareas and region ( see f i g u r e 1).

Small farms - MIA

1 Subarea

4 submatr ices

Large farms - MIA

2

Small farms - CIA

3

Regional reconciliation and constraints

----- Resource levels

Regional

v h r g e farms - CIA

4

activities

-------

- - - - - - .

-- - -- -

4. THE REGIONAL MODEL AND MATRIX DESCRIPTION

The l i n e a r programming model is annual i n nature and con ta ins the bas i c d a t a from which a regional plan is determined. The c u r r e n t version uses a f ixed matrix of 291 columns and 103 rows t o accommodate a l l a c t i v i t i e s and cons t r a in t s .

The key components of t he model are:

- t he ob jec t ive function; - the resource c o n s t r a i n t s and r econc i l i a t ions ; and - the matrix of t echn ica l coe f f i c i en t s .

4.1 The Objective Function

The ob jec t ive funct ion i n the model is the maximisation of the t o t a l g ros s margin fo r the whole region, f o r a given year and subjec t t o t h e given r e s t r i c t i o n s . The funct ion incorpora tes t he va r i ab le cos t s , n e t of labour and water charges, f o r a l l c rop a c t i v i t i e s . Crop product s e l l i n g a c t i v i t i e s a r e included t o account f o r g ross i n c m e i n the ob jec t ive funct ion , and a r e l inked t o the crop a c t i v i t i e s wi th in the matrix. This f a c i l i t a t e s s e n s i t i v i t y ana lys i s with respect t o crop prices. For l ives tock en te rp r i se s , t he g ross margin is included d i r e c t l y i n the ob jec t ive funct ion , ne t of labour cos t s . 'Buy water' and ' h i r e labour ' a c t i v i t i e s have t h e i r own negative ob jec t ive funct ion c o e f f i c i e n t s and a r e l inked wi th in the matrix t o a c t i v i t i e s requiring water and labour. Data sources f o r the ob jec t ive funct ion c o e f f i c i e n t s a r e d e t a i l e d i n the following d iscuss ions of submatrices.

4.2 Resource Const ra in ts and Reconci l ia t ions

The ' cons t r a in t ' c o e f f i c i e n t s l i m i t t he l e v e l a t which a c t i v i t i e s can e n t e r the optimal so lu t ion e i t h e r d i r e c t l y , a s through the t o t a l a r ea cons t r a in t , o r i n d i r e c t l y , a s through feed r econc i l i a t ion pools. D e t a i l s of da t a sources f o r t he non-zero c o n s t r a i n t c o e f f i c i e n t s a r e presented i n the following d iscuss ions of submatrices.

Const ra in ts on the model include a v a i l a b i l i t y of water, land types , labour, and i r r i g a t i o n channel capaci ty . Rota t ional c o n s t r a i n t s a r e a l s o included t o ensure t h a t s o i l f e r t i l i t y is maintained. The remaining c o n s t r a i n t s c o n s i s t of r econc i l i a t ion poo l s f o r feed, water and crop produce. Two measures of t he a v a i l a b i l i t y of land (maximum i r r i g a b l e and t o t a l a r ea ) were used i n q u a n t i t i e s cons i s t en t with average holdings observed i n each of the four subareas. The area of r i c e grown is l imi t ed i n accordance with t h a t s e t by the New South Wales Water Resources Commission. As lucerne is a perennia l c rop, its area was r e s t r i c t e d i n the sho r t run model t o r e f l e c t cu r ren t l e v e l s of production (approximately 1000 ha) .

4.3 The Matrix of Technical Coef f i c i en t s

A s mentioned e a r l i e r t h e model is s p l i t i n t o four subarea matr ices with l inking regional a c t i v i t i e s and cons t r a in t s . Each of the subarea

matrices is i d e n t i c a l i n terms of the range of a c t i v i t i e s and c o n s t r a i n t s . A c t i v i t i e s represented include crop and pas tu re ( i r r i g a t e d and dryland) and l ives tock e n t e r p r i s e s cu r ren t ly a f e a t u r e of t he area . The only producing sec to r omitted from the model - f o r reasons given above - is hor t i cu l tu re ; t he r e s u l t s of the model t hus apply only t o t h e non- h o r t i c u l t u r a l s ec to r of the region.

The model incorpora tes a c t i v i t i e s such a s ' h i r e labour ' and 'buy water ' and al lows f o r t r a n s f e r s between qua r t e r ly feed pools. To inc rease the management opt ions f u r t h e r , a d d i t i o n a l p o t e n t i a l cropping e n t e r p r i s e s were included - crops l e s s commonly grown i n the a rea which a r e considered t o have p o t e n t i a l f o r fu r the r app l i ca t ion . Hence, a wide range of summer and winter grown crops a r e considered.

The main body of each subarea matr ix is, therefore , d iv ided i n t o a s e r i e s of submatrices r e f l e c t i n g these d i f f e r e n t a c t i v i t i e s . These a r e described more f u l l y below. Appendix A con ta ins d e f i n i t i o n s of code names used i n the matrix.

(a ) Land and feed supply submatrix (see t a b l e 2)

l ko measures f o r t h e a v a i l a b i l i t y of land a r e used - t o t a l a r ea and maximum i r r i g a b l e area (data supplied by P. Verdich, New South Wales Water Resources Commission, personal communication, September 1983). Feed supply is expressed i n l ives tock months on a qua r t e r ly b a s i s (December-February; March-May; June-August; September-November). The t r a n s f e r of feed between per iods is permitted, based on assumed r a t e s of pas ture de t e r io ra t ion .

With regard t o i r r i g a t e d pas tu re s the re a r e four winter and t h r e e sununer pas ture a c t i v i t i e s . W t a l annual i r r i g a t e d pas ture production was taken from Penman (1983), but the seasonal p a t t e r n of production and the pas tu re y i e ld response t o i r r i g a t i o n were obtained from Fl inn (1976). For i r r i g a t e d summer pas ture , three i r r i g a t i o n l e v e l s were examined - 10 ML/ha, 7 ML/ha and 5 ML/ha. For i r r i g a t e d winter pas ture , only one l e v e l was considered - 4 ML/ha; however, var ious t imings of t he i r r i g a t i o n s were allowed. This was t o account f o r winter pas tu re being a user of res idual water, the timing of i r r i g a t i o n s being f a i r l y f l e x i b l e . The i r r i g a t i o n s t r a t e g i e s allowed f o r winter pas tu re were:

Water s t r a t egy (1) : 1 ML/ha i n spr ing; 1 ML/ha in summer, 2 ML/ha i n autumn

Water s t r a t egy (2) : 2 ML/ha i n autumn; 2 ML/ha i n spr ing Water s t r a t egy (3 ) : 4 ML/ha i n autumn Water s t r a t egy (4) : 4 ML/ha i n spring.

Feed quant i ty and qua l i ty d i f f e rences a r e r e f l e c t e d i n d i f f e r e n t feed production l e v e l s between pas tu re types. For example, t o t a l feed production from dryland winter pas ture is 54 l i ves tock months per hectare , compared with 140 l ives tock months per hectare from i r r i g a t e d winter pas ture adopting water s t r a t egy 1.

(b) Cropping submatrix ( see t a b l e 3)

Up t o 36 cropping a c t i v i t i e s (29 i r r i g a t e d and 7 dryland) a r e included i n the model. These a c t i v i t i e s represent those p re sen t ly conducted i n t h e region a s well a s some which a r e l e s s commonly grown i n the a r e a but a r e considered t o have f u r t h e r po ten t i a l .

C o n s t r a i n t

O b j e c t i v e f u n c t i o n T o t a l a r e a l a n d Max i r r i g a b l e l a n d R ice q u o t a R o t a t i o n summer c r o p R o t a t i o n w i n t e r c r o p I r r i g a t e - Dee.-Feb. - Mar.-May - Sept.-Nov. T o t a l a r e a l u c e r n e Labour r e c o n c i l i a t i o n - autumn - w i n t e r - s p r i n g - summer C a l r o s e r i c e p o o l Maize p o o l Wheat p o o l T r i t i c a l e p o o l Lucerne p o o l

( a ) N, O b j e c t i v e row; L,

Un i t

$ h a h a h a h a ha

ML ML ML h a

h h h h t t t t t

L e s s

ha ha ha ha ha ha h a h a h a h a h a h a

-345.9 -345.9 -409.3 -409.3 -174.2 -174.2 -168.0 -168.0 -175.9 -175.9 -644.2 -55.7 N

1.0 1 .0 1 .0 1 .0 1.0 1.0 1 .0 1.0 1 .0 1 .0 1 .0 1.0 L 37 090 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 1 .0 L 30 377 1.0 1 .0 L 17 302 1 .0 1 .0 1 .0 1 .0 L 0

1 .0 1.0 1.0 1.0 1.0 1.0 1.0 L 0

9.5 7.6 6.0 5.0 1 .6 1 .6 1.6 1 .6 3.3 L 0 0.5 0.4 1.0 1.0 3.2 L 0 5.3 4.2 1.0 3.9 2.9 4.0 3.0 3.9 2.9 3.3 L 0

1 .0 L 1 000

0.2 0.2 3.9 3.5 1 .6 1 .6 1 .7 1 .7 1.6 1.6 3.3 0.9 L 0 2.3 2.3 0.2 0.2 0.2 0.2 0 .1 L 0 2.9 2.5 2.0 2.0 1 .6 1 .3 1 .4 1.1 1.6 1 .3 2.4 L 0 3.4 2.7 2.5 2.1 3.4 3.4 1 .3 1 .3 3.4 3.4 2.9 0.9 L 0

-7.5 -5.4 L 0 -6.0 -4.0 L 0

-5.0 -4.7 -4.0 -3.5 -1.7 L 0 -5.5 -5.2 L 0

-8.5 L 0

t h a n or e q u a l t o row.

The model a l s o al lows f l e x i b i l i t y i n the l e v e l of i r r i g a t i o n . I t has been r e l a t ive ly uncommon f o r such ' i r r i g a t i o n production funct ions ' t o be included i n l i n e a r programming models of i r r i g a t i o n regions (but see Pomerada 1978). The most economically e f f i c i e n t of t h e poss ib le l e v e l s is se l ec t ed v i a t h e l i n e a r programming algori thm a s p a r t of the genera l so lu t ion procedure. This l e v e l changes i n response t o p r i c e changes. However, due t o the nature of t he production systems, only two poss ib le i r r i g a t i o n l e v e l s were permitted ( a s well a s t he dryland opt ion , i n some ins tances) . This r e f l ec t ed the stepped nature of y i e ld response functions, a s well a s the d i s c r e t e nature of f lood i r r i g a t i o n , which generally does not al low f i n e tuning of the amount of water applied per i r r i g a t i o n . Appendix B provides f u r t h e r information on the de r iva t ion of t h e function fo r y i e ld response t o i r r i g a t i o n water.

For each of twelve i r r i g a t e d crops, i r r i g a t i o n a t t he average l e v e l (from Penman 1983) and one a t l e s s than the average l e v e l were permitted. (For fu r the r d e t a i l s on which crops t h i s provision applied t o , s ee appendix B.)

A s mentioned e a r l i e r , r o t a t i o n a l c o n s t r a i n t s a r e included t o ensure t h a t s o i l f e r t i l i t y is maintained. These c o n s t r a i n t s i n d i r e c t l y l i m i t t he area of crops grown. Crop produce e n t e r s a regional r econc i l i a t ion pool and is subsequently so ld through regional s e l l i n g a c t i v i t i e s .

(c) Livestock submatrix (see t a b l e 4)

A range of l ives tock a c t i v i t i e s (both sheep and c a t t l e ) a r e included i n the model. Sheep a c t i v i t i e s range from merino breeding t o second-cross lamb production. C a t t l e a c t i v i t i e s include vea le r production and s t e e r f a t t en ing . Livestock production c o e f f i c i e n t s were est imated from d a t a supplied by the New South Wales Department of Agriculture (P.F. Penman, personal communication, November 1983).

(d) Water supply submatrix (see t a b l e 5)

Water a v a i l a b i l i t y is based on the assumption t h a t t he region w i l l normally receive a 120 pe r cent a l l o c a t i o n ( i n accordance with the New South Wales Water Resources Commission gu ide l ines on volumetric a l l o c a t i o n ) and may, i n addi t ion , use 'above a l l o c a t i o n ' water o r ' su rp lus flow' i n spr ing and summer. Surplus flows represent water ava i l ab le t o i r r i g a t o r s on an ad hoe b a s i s when dam s to rage capacity is exceeded. In order t o l i m i t t he amount of water t h a t could be used i n any season, channel capaci ty c o n s t r a i n t s were a l s o imposed (data supplied by P. Verdich, New South Wales Water Resources Commission, personal communication, September 1983).

Water was pr iced on the b a s i s of the two-tiered dec l in ing charging schedule i n opera t ion i n 1982-83. To descr ibe t h i s system simply: an amount of water is ava i l ab le t o farmers a t $x/ML; a d d i t i o n a l water above t h i s amount is ava i l ab le a t $y/ML, where y < x. The f a c t t h a t the average u n i t p r i c e of water decreases a s consumption increases presented a problem i n modelling. Under normal circumstances, i f a l i n e a r programming model with a maximising objec t ive funct ion con ta ins two s e t s of inputs with d i f f e r e n t p r i c e s , it w i l l s e l e c t , up t o the maximum ava i l ab le , the set with the lower p r i c e before drawing on t h e set with the higher pr ice . It was necessary t o introduce seve ra l dummy a c t i v i t i e s and c o n s t r a i n t s ( D l , D2, D3, D4 and D5) t o overcome t h i s problem.

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Merino breeding

First cross lamb production (BL x M)

First cross lamb production (DH x M)

second cross lamb production

Merino wethers

Vealer production

Summer fattened steers

Winter fattened steers

Sign (b)

RHS constraint

To determine the water use s t r a t egy t h a t maximises g ross margin it is necessary t o conduct two runs of t he model. The f i r s t run enables the model t o use any amount up t o the maximum of the f i r s t t i e r of water. This run must incorpora te the c o n s t r a i n t s D2 and D3 (with D4 and D5 excluded). The second run r equ i r e s t h e model t o use a l l t h e a v a i l a b l e water of the f i r s t t i e r and any amount up t o the maximum of the second (lower p r i c e ) t i e r . This run must incorporate the c o n s t r a i n t s D4 and D5 (with D2 and D3 excluded). After t he two runs have been conducted t h e r e remains a simple Process of comparing t h e i r ob jec t ive funct ion r e s u l t s and se l ec t ing t h a t water use s t ra tegy which achieves the higher r e s u l t .

(e ) Labour submatrix (see t a b l e 6)

Labour requirements f o r t h e farm a c t i v i t i e s a r e provided by two groups of labour (operator and casua l labour) and a re measured i n work-hours. Each of the labour groups is f u r t h e r ca tegor ised by seasonal a c t i v i t i e s .

The labour use da t a associa ted with the var ious production a c t i v i t i e s were taken from Penman (1983). The one p i ece of labour d a t a not ava i l ab le i n Penman was the labour required d i r e c t l y f o r i r r i g a t i o n water appl ica t ion . The f igu re used f o r t h i s was 0.36 work-hours per hectare , an es t imate obtained from B.G. Johnston (BAE, personal comunicat ion , May 1984) and the e a r l i e r s t u d i e s of the a rea by Ryan (1969) and Fl inn (1976). The labour a v a i l a b i l i t y d a t a were taken from Ryan (1969). The assumption underlying these a v a i l a b i l i t y d a t a is t h a t t he re is one opera tor per farm with a c e r t a i n period of time a l loca ted t o 'maintenance-type' a c t i v i t i e s . This opera tor labour then e n t e r s t he model a s a ' c o n s t r a i n t ' ( r i g h t hand s i d e ) , and t h a t amount of labour is regarded a s being ava i l ab le without changing the o v e r a l l f a n incme. Addit ional labour beyond t h a t amount can be hi red without any upper l i m i t , a t a spec i f i ed c o s t per hour.

(£1 Crop s e l l i n g submatrix (see t a b l e 7)

Regional c rop s e l l i n g a c t i v i t i e s a r e included t o account f o r g ross income i n the ob jec t ive funct ion and a r e l inked t o the subarea c rop a c t i v i t i e s within the matrix. This f a c i l i t a t e s s e n s i t i v i t y ana lys i s with respect t o crop p r i ces . The on-farm crop r e tu rns per tonne were taken from Penman (1983).

4.4 Model Validation

Resul ts of such l i n e a r programming a r e ind ica t ive of what should happen i n production given the underlying assumptions concerning average production funct ions and commodity and input p r i ces . Val ida t ion of models is d i f f i c u l t , because outcomes i n p r a c t i c e may d i f f e r from those modelled given the presence of uncertainty o r v a r i a b i l i t y in commodity p r i c e s and production re la t ionships . Nevertheless, a reasonable assessment may be made by gauging, i n an h i s t o r i c a l context , t h e e f f e c t i v e n e s s of the model i n determining regional c rop areas . As the model was cons t ruc ted using 1982-83 p r i ces , c o s t s and resource a v a i l a b i l i t y , v a l i d a t i o n necess i ta ted only incorporating information on water charges (two t i e r s appl icable) and water a v a i l a b i l i t y ( including su rp lus flows) f o r t h a t year. The model r e s u l t s compared favourably with the a c t u a l a r e a s of var ious c rops grown i n t h a t year ( t a b l e 8 ) , giving some confidence t h a t t he model is a reasonable representa t ion of r e a l i t y .

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T a b l e 7: EXAMPLE OF CROP SELLING SUBMATRIX

( a ) N, O b j e c t i v e row; L, L e s s t h a n o r e q u a l t o row.

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Table 8: LAND USE: MODELLED AND ACTUAL

Act iv i ty Modelled Actual 1982-83

ha ha

Rice 49 064 45 245

Other c e r e a l s 50 127 50 288

Lucerne 1 000 1 009

Irrigated pastures 22 259 27 730

5. ESTIMATIE WATER D m KLASTICITIES - ANALYSES AND RESULTS 'Rro types of sho r t run ana lys i s were conducted. The f i r s t involved t h e parametr i sa t ion of t he p r i c e of water only, and is described i n s e c t i o n 5.1. The re levant price-quanti ty r e l a t i o n s h i p s were p l o t t e d t o produce a derived demand funct ion (marginal value product funct ion) f o r water. The second ana lys i s ( s ec t ion 5.2) examined how demand f o r i r r i g a t i o n water was jo in t ly a f f ec t ed by independent v a r i a t i o n s i n water and product p r i ces .

A s mentioned e a r l i e r , the ana lys i s reported i n t h i s paper was undertaken t o examine the sho r t run e l a s t i c i t y of demand f o r i r r i g a t i o n water r a the r than t o evaluate d i f f e r e n t p r i c ing pol icy op t ions such a s increasing o r decreasing t h e marginal c o s t . Consequently, t h e two-tiered water p r i c ing system which was used i n the model f o r va l ida t ion was replaced by a s ing le water buying a c t i v i t y . Such an a n a l y s i s is considered more re levant , given t h e moves toward the a b o l i t i o n of the decreasing block p r i c e s t r u c t u r e (see Musgrave 1983). The channel capaci ty c o n s t r a i n t s on water de l ivery obviously remained, but no independent 'volumetric a l l o c a t i o n l i m i t ' applied, s i n c e the analyses were examining the amount of water which would be used a t each l e v e l of p r i ce .

In sec t ion 5.3, the ana lys i s is applied t o an assessment of t h e e f f e c t s of proposed increases i n water charges i n t h e study region - a proposal which has coincided with f a l l i n g r i c e p r i ces . In a l l analyses of shor t run e l a s t i c i t i e s , subarea d i f f e rences were found t o be not g r e a t and consequently have not been reported i n t h i s paper. A desc r ip t ion of t h e impact of r i s i n g water p r i c e s on a subarea b a s i s is given i n an e a r l i e r paper (Clark, Col l ins , Menz and Johnston 1984).

5.1 Single-Price Ef fec t s

In order t o de r ive the demand funct ion f o r i r r i g a t i o n water f o r t h e region, t he p r i c e of water was parametrised over t he range $4/ML t o $64 /M~, with a l l o ther p r i c e s remaining f ixed a t 1982-83 l eve l s . The price-quanti ty r e l a t ionsh ip was then p l o t t e d t o produce t h e derived demand function.

The derived demand f o r water is shown i n f i g u r e 2. A s is t y p i c a l of supply and demand schedules derived from l i n e a r programming formulations, t he demand schedule f o r water is a stepped function. The a r c e l a s t i c i t y of demand f o r i r r i g a t i o n water was ca l cu la t ed between each s tep . The main change i n cropping mix a t each s t e p is a l s o shown. The most dramatic e f f e c t i n i r r i g a t i o n water use occurs when water p r i c e s reach such a l e v e l t h a t t he r i c e area is reduced.

The model showed t h a t a t cu r ren t p r i c ing l e v e l s (around $8/ML) a s i t u a t i o n of excess demand exis ted . F u l l a l l o c a t i o n is i n the region of 1.1 mi l l ion ML, y e t i n t h e absence of a water c o n s t r a i n t some 1.36 m i l l i o n ML was demanded.

The shor t run p r i c e e l a s t i c i t y of demand (measured by the a r c e l a s t i c i t y ) i n the water p r i c e range $4/ML t o $21/ML is only 0.13. A t p r i c e s between $21/ML and $42/ML it is higher, a t 0.65, but s t i l l wel l below unity. Between $42/ML and $51/ML, demand f o r water becomes q u i t e e l a s t i c (3.8) and within the range $52/ML t o $58/ML extremely e l a s t i c (14.1).

Figure 2: REGIONAL SHORT RUN DERIVED DEMAND FUNCTION FOR IRRIGATED WATER (OTHER PRICES CONSTANT)

-

6 0 Irrigated cropping ceases

All rice replaced by irrigated winter cereals and dryland pastures

50

Some rice replaced by irrigated winter cereals and dryland pastures

4 0 \ 1 W w e r levels of irrigation on winter cereals

3 0

2 0

10 -

$ f i L

million

BAE chart - I I I 1 I I I 0 . 2 0 .4 0 .6 0 .8 1.0 1 . 2 1 . 4

ML

Thus, for a pr ice increase from $8/hL t o $28/ML, the demand for i r r igat ion water was found t o be ine las t ic in the short run. Oonsequently, price increases within t h i s range do not dramatically lower the amount of water used, and would not be expected t o resul t i n major short term s h i f t s in cropping patterns. Such s t ab i l i t y of cropping patterns was confirmed by the model resul ts , which indicate t ha t producers' i n i t i a l response t o the raising of water charges would be t o s h i f t from i r r iga ted t o dryland pastures. Total regional gross margin would f a l l , over t h i s water p r ice range, by approximately 40 per cent.

5.2 Multiple-Price Effects

There are some limitations in the measures of short run pr ice e l a s t i c i t y of demand presented i n figure 2. The arc e l a s t i c i t i e s imply constant e l a s t i c i t i e s over fa i r ly wide pr ice ranges, where in pract ice a gradual change in water demand (and thus in e l a s t i c i t i e s ) would be expected. Also, a l l product prices were assumed constant. I t is of in te res t t o apply the model further t o assess the e f fec t s of changes i n product prices on the short run demand for i r r iga t ion water. Finally, information is lacking on how demand for i r r iga t ion water is joint ly affected by various canbinations of high and low prices for water and irrigated crop products. If these ' interact ion effects ' are important, they may af fec t the short term e l a s t i c i t y of demand for i r r iga t ion water with respect t o water price. These interact ions can be examined by the following procedure :

- parametrise prices of selected products over a relevant range, in a systematic way designed t o capture price interact ion e f fec t s ;

- run the programming model for each price combination; and - f i t a summary regression equation t o the s e t of resu l t s thus generated.

This procedure allows short term price e l a s t i c i t i e s of demand t o be derived a t specif ic water price levels , rather than over a range, a s i n figure 2. Furthermore, the f i na l regression equation provides a convenient summary of the price parametrisation and the price interaction e f f ec t s on water demand. An example of the procedure is given i n Wicks and Dillon (1978) in relation t o broadacre supply e l a s t i c i t i e s . The authors a re not aware of similar methodology being applied in relat ion t o the demand for water.

In order t o reduce the number of price change combinations, products were combined in to categories - winter cereals, summer crops, livestock and rice. The prices for these groups were parametrised, along with water price, making f ive price variables in a l l . Five levels were chosen for each variable. A f u l l fac tor ia l combination of f ive treatment leve ls of f ive factors would require over 3000 treatments; however, a cen t ra l composite experimental design (Cochrane and Cox 1957) was chosen which allows a condensation t o 43 treatments. The price index levels used for the experiment encompass the range thought t o be feasible in the foreseeable future, representing 20 per cent and 40 per cent decreases and increases on the 'base' product price, and 50 per cent and 75 per cent decreases and increases, respectively, on the 'base' water pr ice (table 9) . The 'base' price ( level 3) generally approximates the 1982-83 price except for water, where $16/ML was used rather than the 1982-83

price of around $8/ML. This allowed a range of $4/ML t o $28/ML t o be included, reflecting a more likely range of water price. Table 10 shows the 'base' product and water prices used in the experiment.

Table 9: PRICE INDEXES USED I N THE PRICE SENSITIVITY EXPERIMENT

Index level

Winter S unnne r Rice cereals crops Livestock Water

Table 10: 'BASE' PRODUCT AND WATER PRICES USED I N THE PRICE SENSITIVITY EXPERIMENT

Category Unit Price

Rice - calrose - inga Winter cereals - wheat - t r i t i c a l e - barley - oats Summer crops - sunflower - sorghum - maize - soybean - rapeseed - lupin - safflower - linseed Livestock (a) - Merino - Border Leicester x Merino - Dorset Horn x Merino - prime lamb - Merino wethers - vealer production - summer fattened s teers - winter fattened s teers Water $/ML 16.00

(a) Gross margin, rather than price.

A s t he f i n a l s t e p i n the a n a l y s i s an equation of t he following form was f i t t e d :

where

Q = quant i ty of water demanded; I = p r i c e index f o r r i c e ; C = pr i ce index f o r winter c e r e a l s ; L = gross margin index f o r l i ves tock : W = p r i c e index f o r water; and S = p r i c e index f o r summer crops.

The Qs a r e generated by the programming model f o r each of the 43 p r i c e combination treatments. In these circumstances the f i t t e d quadra t i c equation, equation (1) (shown i n t a b l e 111, provides only a d e s c r i p t i o n of these de t e rmin i s t i c data. Standard e r r o r s a r e not shown, a s they a r e not re levant i n t h i s de t e rmin i s t i c con tex t (Candler and Cartwright 1969). Thus, t he re a r e no c r i t e r i a f o r accepting o r r e j e c t i n g explanatory v a r i a b l e s on t h e b a s i s of t h e i r s t a t i s t i c a l s igni f icance .

The shor t term e l a s t i c i t y of demand f o r i r r i g a t i o n water with r e spec t t o i t s own p r i ce , tw, can be ca l cu la t ed using equation (1) ( t a b l e 11) with the 1982-83 values of the p r i c e l eve l s . (An example of such ca l cu la t ions is shown i n sec t ion 5.3.)

The shor t run own-price e l a s t i c i t i e s corresponding t o a range of water p r i c e s , with product p r i c e s a t 1982-83 l e v e l s , a r e shown i n t a b l e 12. A comparison of the e l a s t i c i t i e s i n t a b l e 12 and f igu re 2 i n d i c a t e s t h a t they a r e s imi l a r . Apparently, t he p r i c e i n t e r a c t i o n e f f e c t s (IW, CW, LW, WS i n t a b l e 11) have not g rea t ly influenced the sho r t run own-price e l a s t i c i t y es t imates , a t l e a s t wi th in the water p r i c e range $8/ML t o $28/ML.

These r e l a t i v e l y low es t imates of own-price demand e l a s t i c i t y r e f l e c t t he sho r t run nature of the a n a l y s i s and i n p a r t i c u l a r the assumptions made about l imi ted cropping a l t e r n a t i v e s and f i x i t y of c a p i t a l . Despite these r e l a t ive ly low e l a s t i c i t y measures, increased water charges do have a major e f f e c t on g ross margin f o r t h e region, and by inference on t h e p r o f i t a b i l i t y of indiv idual farms. For example, increas ing charges from $8/ML t o $28/ML reduces the regional g ross margin by approximately 40 per cen t .

The procedure which has r e su l t ed i n the equation shown i n t a b l e 11 a l s o enables the e f f e c t s of product p r i c e changes on the s h o r t run demand f o r i r r i g a t i o n water t o be determined. These cross-pr ice e l a s t i c i t i e s ( t a b l e 13) show the percentage change i n i r r i g a t i o n water demand f o r a 1 per cen t change i n any p a r t i c u l a r product pr ice . For example, the sho r t run cross-price e l a s t i c i t y f o r water a s soc ia t ed with changes i n the p r i c e of r i c e , ~ j , is:

Table 11: SUMMARY REGRESSION MR PRICE PARAMETRISATION: Equation (1)

Term Coefficient

I C I L IW IS CL cw CS LW LS ws Constant ~2

I = price index for r ice: C = price index for winter cereals; L = gross margin index for livestock; W = price index for water; and S = price index for summer crops.

Table 12: IRRIGATION WATER: SHORT RUN OWN-PRICE DEMAND ELASTICITIES (a)

Water pr ice Elast ic i ty

(a) A l l prices, other than of water, held a t 1982-83 levels.

Elast ic i ty of water demand with respect t o r ice price is positive, as would be expected: a s the price of r ice increases, the r ice area increases and hence the quantity of water demanded r ises , r i ce being a heavy user of water. Conversely, the short run cross-price e l a s t i c i t i e s of water demand with respect t o changes in other summer crop prices are negative (see

Table 13: PERCENTAGE CHANGE I N IRRIGATION WATER DEMANDED, GIVEN A ONE PER CENT CHANGE I N PRODUCT PRICES (FROM BASE), AT THREE WATER PRICES

Water p r i c e

Product $8/ML $16/ML $24/ML

Rice Winter c rops Summer crops -0.352

(o ther than r i c e ) Livestock +O. 017

Water demand e l a s t i c i t y

t a b l e 13) because a s t h e i r p r i c e s increase , the a r e a p lanted t o them increases a t t he expense of r i c e a rea , and these summer crops use l e s s water than r i ce .

A t 1982-83 water p r i c e s ($8/?4L), winter c e r e a l and l i ves tock p r i c e changes have l i t t l e influence on i r r i g a t i o n water demand. Rice and o t h e r summer crop p r i c e s have a g r e a t e r influence, a s would be expected given t h a t these crops a r e r e l a t i v e l y heavy water users . A t higher water p r i c e s , however, l i ves tock p r i c e changes have a g r e a t e r influence. It would appear t h a t a s water p r i c e increases the g r o s s margin f o r l i ves tock becomes r e l a t i v e l y higher than t h a t f o r crops.

Within t h e complex programming matrix of input/output c o e f f i c i e n t s , an increase i n the p r i c e of r i c e o r l i ves tock , coupled with an increase i n the p r i c e of water, has the e f f e c t of increasing the g ross margin o n t h a t product r e l a t i v e t o the g ross margins on o the r products. The r e s u l t of t h i s i n t e r a c t i o n is re f l ec t ed i n t a b l e 1 3 where, f o r r i c e and l i ves tock , t he responsiveness of water use t o an increase i n the p r i c e of t h a t product is g r e a t e r a t higher water pr ices . This r e s u l t does not, however, imply an upward sloping demand curve f o r water.

5.3 Spec i f i c Application of the Model

Equation (1) ( t a b l e 11) can be used t o es t imate the a c t u a l quant i ty of water demanded and the s h o r t run e l a s t i c i t y of demand f o r water f o r any p r i c e combination wi th in the range of p r i c e s out l ined . Without making assumptions concerning the water p r i c ing s t r u c t u r e i n use, t h e s e e l a s t i c i t i e s g ive an ind ica t ion of the magnitude of l i k e l y changes t o t h e production system a t various water and product p r i c e l eve l s . For ins tance , water charges i n the i r r i g a t i o n a r e a s increased by 22 per c e n t i n t h e 1984-85 season. Coupled with a 7 pe r c e n t increase i n 1983-84, t h i s implies t h a t t h e c o s t of water had increased s ince 1982-83 approximately from $8/ML t o $10/ML. Over the same period, r i c e p r i c e s t o growers had been f a l l i n g . Assuming a r i c e p r i c e f a l l of 11.5 per c e n t from 1982-83 l e v e l s then, i f o the r product p r i c e s were assumed t o remain cons tant , t he p r i c e indexes would be: I = 88.5; C = 100; L = 100; W = 62.5; S = 100.

(Note tha t the 'base' price level used for W is $16/ML, so an increase from $8/ML t o $10/ML is represented by the price index for water increasing from 50 t o 62.5).

After substituting for S , C and L, equation (1) becomes:

This regional demand function for i r r iga t ion water w i l l indicate the impact of water and r ice price movements on regional water use. The short run price e l a s t i c i t i e s of demand for i r r iga t ion water with respect t o water charges and r ice prices are derived by different iat ing equation (2) with respect t o W and I:

and

Substituting the above values for I and W into equations ( 3 ) and (4 ) , respectively:

The short run own-price e l a s t i c i t y of demand for water becomes:

This means tha t a 1 per cent increase in the pr ice of water should lead t o a 0.041 per cent decrease i n the quantity of i r r igat ion water demanded, a t the assumed prices.

The short run cross-price e l a s t i c i t y of demand for water with respect t o the price of r ice i s :

This means tha t a 1 per cent decrease in the pr ice of r ice should lead t o a 0.573 per cent decrease i n the quantity of i r r igat ion water demanded, a t the assumed prices.

A s seen from equation (5 ) , the increase in the water charge t o $lO/ML remains well within the price-inelastic range of the demand function. Consequently, while the price increase w i l l serve t o increase considerably the t o t a l revenue t o the water authority (since demand for water f a l l s proportionately fa r l e s s than the price increase), there is no major effect on water conservation i n the short term. Also, while there would be l i t t l e e f fec t on r ice area, the t o t a l regional gross margin would f a l l a s producers' costs r i se a s a resul t of the increased water charges.

The short run cross-price e l a s t i c i t y of demand fo r water with respect t o the price of r ice - equation (6) - indicates a greater , though s t i l l inelast ic , effect. The ccnnbined e f fec t on the demand fo r i r r iga t ion water of a $2/ML increase i n the water charge and an 11.5 per cent f a l l i n the price of r ice may be derived by substituting the new indexes for I and W in to equation (2) . This would resul t i n the quantity of i r r igat ion water demanded fal l ing from 1 . 4 million ML t o 1.3 million ML, a f a l l of 6.5 per cent.

Water charge increases of t h i s magnitude and expectations of similar future r ises , in combination with depressed commodity pr ices , may induce greater adjustment in water use and commodity production in the longer term.

6. DISCUSSION AND CONCLUSIONS

A regional l i nea r programming model has been cons t ruc ted f o r i r r i g a t e d ag r i cu l tu re i n the Murrumbidgee I r r i g a t i o n Area and Coleambally I r r i g a t i o n Area i n order t o simulate the major consequences of var ious water p o l i c i e s , given known resource a v a i l a b i l i t i e s , c o s t s and pr ices .

Presently the model is l imi ted t o sho r t run analyses. A long run model would need t o take account of regional c a p i t a l c o n s t r a i n t s , a l t e r n a t i v e water app l i ca t ion technologies, and the h o r t i c u l t u r a l sec tor . Such a model could be used t o examine the e f f e c t on regional production, income and resource use of water pr ic ing p o l i c i e s such as volumetric a l l o c a t i o n of water, increas ing block p r i ce s t r u c t u r e s and water r i g h t s t r a n s f e r a b i l i t y .

In t h i s paper t he model has been applied i n its present form t o es t imate the s h o r t run e l a s t i c i t y of demand fo r i r r i g a t i o n water. Subarea d i f f e rences i n e l a s t i c i t i e s and r e s u l t a n t cropping p a t t e r n s have not been reported, s ince they were found t o be small within the range of Current p r i ces . They a r e l i k e l y t o be more important i n r e l a t i o n t o p o l i c i e s d i r e c t l y r e l a t ed t o farm s i z e , and thus subareas, which were not examined i n t h i s paper.

A t the 1982-83 l e v e l of water and product p r i ces , s h o r t run demand f o r water was highly p r i ce - ine l a s t i c . The ' s ingle-pr ice ef f e c t ' ana lys i s i nd ica t e s t h a t a s water p r i c e r i s e s , demand e l a s t i c i t y increases but remains below unity wi th in the r e a l i s t i c a l l y foreseeable range of $8/ML t o $28/ML. I t is only when the water p r i c e r i s e s t o l e v e l s which lower the r i c e area t h a t the s h o r t run e l a s t i c i t y of demand r i s e s above uni ty . These increases i n the e l a s t i c i t y of demand a t higher water p r i c e s a r e t o be expected, s ince a 1 per cen t change i n the water p r i c e is then a g r e a t e r absolute amount and the incent ive t o move t o crops which use l e s s water is g r e a t e r than a t low water p r i c e s (Seagraves and Eas ter 1983). The s h o r t run p r i c e e l a s t i c i t i e s of demand a r e broadly i n l i n e with the es t imates of Fl inn (1976) and Arch and Penman (1983) f o r the same region, a t l e a s t around the present p r i c e l eve l . In f a c t , highly i n e l a s t i c demand fo r i r r i g a t i o n water a t prevai l ing p r i c e s has been a common f e a t u r e of many previous s t u d i e s of water demand ( f o r example, Ayer and Hoyt 1981), though not a l l ( f o r example, Shumway 1973). A t p revai l ing water and product p r i c e l eve l s , s h o r t run i r r i g a t i o n water demand is more sens i t i ve t o p r i c e changes f o r r i c e and summer c rops than it is t o water p r i c e changes, but even these s e n s i t i v i t i e s a r e not g rea t .

These r e s u l t s a r e l i k e l y t o be condit ioned by the f a c t t h a t t he model is shor t run i n na ture and hence c a p i t a l expansion is not modelled. Although an increase i n water p r i c e wi th in t h e range mentioned has l i t t l e e f f e c t on water conservation o r cropping pa t t e rns , it does have s u b s t a n t i a l negative e f f e c t s on regional g ross margin. For example, a p r i c e increase from $8/ML t o $28/ML resul ted i n regional g ross margin f a l l i n g by approximately 40 per cent . The e f f e c t of such an increase i n water p r i ce , although not s u b s t a n t i a l i n changing s h o r t run land use pa t t e rns , w i l l have a major e f f e c t on shor t run f a n p r o f i t a b i l i t y and i n the longer term w i l l have adjustment impl ica t ions f o r t he region.

The p r i c e s e n s i t i v i t y ana lys i s ( 'mult iple-price e f f e c t s 1 ) d id not g ive very d i f f e r e n t s h o r t run own-price water demand e l a s t i c i t i e s from the above s ingle-pr ice e f f e c t analysis . However, it d i d enable a set of sho r t

run cross-price demand e l a s t i c i t i e s t o be calculated. Furthermore, the resulting equation was used t o estimate the short run demand for water (and own-price and cross-price e l a s t i c i t i e s of demand) for a number of combinations of water and product prices within the relevant range; t ha t is, interpolation within the experimental price combinations is possible.

I t is worth restating that t h i s analysis is short run in scope, and t h i s should be kept in mind when interpreting the resul ts . The estimated e l a s t i c i t i e s should not be used a s a basis for long term pol icies on water charges.

The estimate of the short run demand e l a s t i c i t y for i r r iga t ion water can be regarded a s providing a lower bound on the long run e l a s t i c i t y . Some of the longer run responses t o water pr ice changes may require additional cap i ta l , which can be effectively modelled only i f c ap i t a l is expl ici t ly included as a constraint.

A complete assessment of the impact of water pr ice r i s e s on a region requires incorporation of both off-farm and on-farm effects . In t h i s paper, only the on-farm sector i s addressed. The two sectors could, however, be linked through a regional input-output model.

The planning and management systems required t o permit the e f f ic ien t and equitable allocation of present water supplies and related dis t r ibut ional consequences have been stressed a s being the major issues facing the Australian water industries. In the short run it would appear that moderate increases in the price of water w i l l not, alone, have a great impact on water use patterns. In t h i s respect it is likely tha t a systems approach which incorporates both supply and demand concepts w i l l prove more successful. This work can be seen a s a f i r s t s tep in tha t direction. Concepts in demand management such a s al ternat ive pricing pol icies coupled with t ransferabi l i ty of water r ights , i n conjunction with supply augmentation where t h i s is economically desirable, are likely t o be important i n t h i s regard.

Appendix A

LISTING OF ACTIVITIES AM) CONSTRAINTS

Region 1: Murrumbidgee Irr igat ion Area - small farms Region 2: Murrumbidgee I r r iga t ion Area - large farms Region 3: Coleambally I r r iga t ion Area - small farms Region 4: Coleambally I r r iga t ion Area - large farms (a) Brief description of ac t i v i t i e s

Variable name Variable description

SMCRSS*l or 2 Region 1 Calrose r ice (sod-sown) - water level 1 or 2 SMCALR*l or 2 Region 1 Calrose r ice - water leve l 1 or 2 SMINGA*l or 2 Region 1 Inga r ice - water level 1 or 2 SMSUNF*l or 2 Region 1 Sunflower - water leve l 1 or 2 SMSORG*l or 2 Region 1 Grain sorghum - water level 1 or 2 SMCORN*l or 2 Region 1 Maize - water level 1 or 2 SMSOYB*l or 2 Region 1 Soybean - water level 1 o r 2 SMWTCM*l or 2 Region 1 Wheat (combine) - water leve l 1 or 2 SMwTSS*l or 2 Region 1 Wheat (sod-sown) - water level 1 or 2 SMTRIT*l or 2 Region 1 Tr i t ica le - water leve l 1 or 2 SMBRLY*l or 2 Region 1 Barley - water level 1 or 2 SMOATS*l or 2 Region 1 Oats - water level 1 or 2 SMLCRN* 1 Region 1 Lucerne - water level 1 SMWINP*l or 2,3,4 Region 1 Winter pasture - water strategy 1,2,3 or 4 SMSUMP*l or 2,3 Region 1 Summer pasture - water level 1 , 2 or 3 SMRAPE*l Region 1 Rapeseed - water leve l 1 SMLUPN* 1 Region 1 Lupin - water level 1 SMSAFF*l Region 1 Safflower - water level 1 SMLINS*l Region 1 Linseed - water level 1 SMDUM Region 1 Dummy water act ivi ty SMwTR1 Region 1 Buy water t i e r 1 SMWTR2 Region 1 Buy water t i e r 1+2 SMTDUM Region 1 Transfer dummy water ac t iv i ty SMSWDJF Region 1 Surplus water - summer SMSWSON Region 1 Surplus water - spring SMDWHEAT Region 1 Dryland wheat SMDBARLY ~ e a i o n 1 Dryland barley SMDOATGN Region 1 Dryland oa ts (grain) SMDOATGZ Region 1 Dryland oa ts (grazing) SMDLUP IN Region 1 Dryland lupins SMDRAPES Region 1 Dryland rapeseed SMDTRITC Region 1 Dryland t r i t i c a l e SMDIMPAL Region 1 Dryland winter pasture (&year l i f e ) SMDIPNAL Region 1 Dryland winter pasture (10-year l i f e ) SMNTVPST Region 1 Native pasture SMMERINO Region 1 Merino breeding SMBLXM Region 1 First-cross lamb production (BLxM) SMDHXM Region 1 First-cross lamb production (DHxM) SMPLAMB Region 1 Second-cross lamb production SMWETHER Region 1 Merino wethers SMVPRODN Region 1 Vealer production SMSFATEN Region 1 Summer fattened s teers SMWFATEN Region 1 Winter fattened s teers

Variable name

SMTRFDSA SMTRFDAW SMTRFDWS SMTRFDSS SMWTRD JF

Variable description

Region 1 Transfer feed summer t o autumn Region 1 Transfer feed autumn t o winter Region 1 Transfer feed winter t o spring Region 1 Transfer feed spring t o summer Region 1 I r r iga te December-February Region 1 I r r iga te March-May Region 1 I r r iga te September-November

LMCRSS*l - LMWTRSON Region 2 a c t i v i t i e s SCCRSS*l - SCWTRSON Region 3 a c t i v i t i e s LCCRSS*l - LCWTRSON Region 4 a c t i v i t i e s SELCRICE SELIRICE SELSUNFL SELSORGM SELLCORN SELSOYBN SELWHEAT SELLTRIT SELBARLY SELLOATS SELLUCRN SELLRAPE SELLUPIN SELSAFLW SELLINSD OPAUTLBR OPWINLBR OPSPRLBR OPSUMLBR HRAUTLBR HRWINLBR HRSPRLBR HRSUMLBR

Sel l calrose r ice Se l l inga r ice Se l l sunflower Se l l grain sorghum Sel l maize Se l l soybean Se l l wheat Se l l t r i t i c a l e Se l l barley Se l l oa t s Se l l lucerne Se l l rapeseed Se l l lupins Se l l safflower Se l l linseed Hire operator labour - autumn Hire operator labour - winter Hire operator labour - spring Hire operator labour - summer Hire additional labour - autumn Hire additional labour - winter Hire additional labour - spring Hire additional labour - summer

(b) Brief description of right hand side

RHS name RHS description

Objective function Total area - Region 1,2,3 o r 4 Maximum irr igable land - Region 1,2,3 or 4 Rice quota - Region 1,2,3 or 4 Rotation summer crop - Region 1.2.3 or 4 Rotation winter crop - Region 1,2,3 or 4 Total water - Region 1,2,3 or 4 Water dummy row 1 - Region 1,2,3 o r 4 Water dummy row 2 - Region 1,2,3 or 4 Water dummy row 3 - Region 1,2,3 or 4 Water dummy row 4 - Region 1,2,3 or 4 Water dummy row 5 - Region 1,2,3 o r 4 Water reconciliation - Region 1,2,3 or 4 Feed pool December-February - Region 1,2,3 or 4 Feed pool March-May - Region 1,2,3 or 4

FDJJA*l or FDSON*l or IRDJF*l or IRMAM*l or IRSON*l or LCRNRN INGRICE CALRICE SUNFLWR SORGHUM MAIZE SOYBEAN WHEAT TRITICL BARLEY OATS LUCERNE RAPESED LUPINS SAFFLWR LINSEED AUTLAB WINLAB SPRLAB SUMLAB OLABAU OLABWI OLABSP OLABSU CCMIASU CCMIAAU CCMIASP SFMIASU SFMIASP CCCIASU CCCIAAU CCCIASP SFCIASU SFCIASP

2,3,4 Feed pool June-August - Region 1,2,3 or 4 2,3,4 Feed pool September-November - Region 1,2,3 or 4 2,3,4 Irrigate December-February - Region 1,2,3 or 4 2,3,4 Irrigate March-May - Region 1,2,3 or 4 2,3,4 Irrigate September-November - Region 1,2,3 or 4

Total lucerne area Inga rice reconciliation pool Calrose rice reconciliation pool Sunflower reconciliation pool Grain sorghum reconciliation pool Maize reconciliation pool Soy bean reconciliation pool Wheat reconciliation pool Triticale reconciliation pool Barley reconciliation pool Oats reconciliation pool Lucerne reconciliation pool Rapeseed reconciliation pool Lupin reconciliation pool Safflower reconciliation pool Linseed reconciliation pool Autumn labour reconciliation pool Winter labour reconciliation pool Spring labour reconciliation pool Summer labour reconciliation pool Operator labour pool - autumn Operator labour pool - winter Operator labour pool - spring Operator labour pool - summer Channel capacity MIA - summer Channel capacity MIA - autumn Channel capacity MIA - spring Surplus flows MIA - summer Surplus flows MIA - spring Channel capacity CIA - summer Channel capacity CIA - autumn Channel capacity CIA - spring Surplus flows CIA - summer Surplus flows CIA - spring

Appendix B

YIELD RESPONSE TO IRRIGATION WATER FUNCTIONS

There is ve ry l i t t l e q u a n t i t a t i v e d a t a o n t h e y i e l d r e s p o n s e to i r r i g a t i o n w a t e r i n A u s t r a l i a . Under e x p e r i m e n t a l c o n d i t i o n s , t h e r e l a t i o n s h i p between y i e l d and w a t e r u sed by c r o p s is o f t h e form shown i n f i g u r e B1.

However, i n a p r a c t i c a l f i e l d s i t u a t i o n , t h e r e is n o t a l i n e a r r e l a t i o n between i r r i g a t i o n w a t e r a p p l i e d and w a t e r u sed by c r o p s . Thus t h e r e l a t i o n s h i p between y i e l d and i r r i g a t i o n w a t e r a p p l i e d is o f t h e fo rm shown i n f i g u r e B2. (For a more d e t a i l e d e x p l a n a t i o n , see W a r r i c k and Gardlier 1983.) I n t h e f i g u r e s , p o i n t s A and C a r e i d e n t i c a l b u t d i f f e r e n c e s o c c u r i n t h e r e g i o n of p o i n t B.

i

F i g u r e B1: EXPERIMENTAL RELATIONSHIP BETWEEN CROP YIELD AND WATER USED

B C

Yield

Evapotranspiration

F i g u r e B2: PRACTICAL FIELD RELATIONSHIP BETWEEN CROP YIELD AND IRRIGATION WATER SUPPLIED

Yield

C

A

Irrigation water applied

BAE chart

A summary of the Austral ian published and unpublished experimental da ta was provided i n the format of f i g u r e B l by W. Muirhead (CSIRO, personal communication, December 1983). This information gave p o i n t s A and C i n f i g u r e B2. To ob ta in the shape of t h e curve i n the in termedia te range, o ther d a t a had t o be used: s p e c i f i c a l l y , the dryland commercial c rop y i e l d s i n the region (given normal r a i n f a l l ) and the i r r i g a t e d commercial c rop y i e l d s i n the region (given normal i r r i g a t i o n p r a c t i c e s ) . This procedure gave four po in t s i n a l l on the response curve f o r each c r o p type, with the exception of r i ce . The water de l ivery system used i n t h e a rea (flood i r r i g a t i o n ) is capable of supplying water only i n 'lumps' of approximately 1 ML/ha. Thus it is not necessary t o consider a l a r g e number of a l t e r n a t i v e s water appl ica t ion l e v e l s , but only those t h a t a r e physica l ly f eas ib l e . Also, because of the hot c l imate and low r a i n f a l l , low l e v e l s of i r r i g a t i o n simply do not g ive a harves table y i e l d f o r summer crops and can be disregarded.

( a ) Winter c e r e a l s

For the winter c e r e a l s , it was noted t h a t the s c a t t e r of po in t s (y i e lds versus water use) f o r t he indiv idual c rops (wheat, o a t s , e t c . ) tended t o c l u s t e r about the same t rend l i n e , s o it was judged t h a t , given the spa r s i ty of d a t a , more accura te es t imate of t he response could be obtained by f i t t i n g a simple curve through a l l observat ions than by at tempting separa te curves f o r each crop type. The curve was f i t t e d using ordinary l e a s t squares, and the r e s u l t s