Pricing Policies under Different Objectives: Implications for the Pricing Behaviour of AWB Ltd.

Transcription

1 AARES Conference Paper hursday, 14 th February 00 Prcng Polces under Dfferent Objectves: Implcatons for the Prcng Behavour of AWB Ltd. by Alexandra Lobb & Rob Fraser Key Words: change of objectves; prvatzaton; AWB Ltd. ABSRAC hs study s motvated by the suggeston that the objectves of the AWB Ltd have changed snce sem-prvatsaton of the Australan Wheat Board under the Wheat Marketng Act, Conceptualsng ths change of objectves as a shft from revenue maxmzaton to proft maxmzaton, ths study examnes the mpact of such a change on the prcng polces of a mult-market prce-settng frm. More specfcally, ths study nvestgates, for two hypothetcal objectve functons, a rsk averse frm s prce-settng behavour n an overseas and a domestc market, gven dfferng costs of supply, uncertan demand functons and dfferng prce elastctes of demand n each market. he am s to generate emprcally testable hypotheses relatng to the mpact of a change of objectves on prcng behavour. Fundng for ths project s provded by GRDC. PhD Student, Unversty of Western Australa Contact: aelobb@yahoo.com.au Professor of Agrcultural Economcs, Imperal College at Wye, and Adjunct Professor of Agrcultural and Resource Economcs, Unversty of Western Australa Contact: r.fraser@c.ac.uk

2 INRODUCION Hstorcally, the Australan Wheat Industry has been the benefcary of consderable government-funded support. However, commencng wth the cessaton of the Guaranteed Mnmum Prce Scheme n 1989 ths support has been n the process of beng removed, wth the am of leavng the ndustry exposed to economc realtes. Over ths perod a central player n the Industry has been the former Australan Wheat Board AWB, and ts actvtes have been partcularly targeted n relaton to the removal of governmentfunded support and the encouragement to adopt fully commercal practces. In ths context the changes mposed on the AWB have been smlar to those mposed by governments on former publc enterprses n the prvatsaton process. hs process has been the subject of a consderable economcs lterature, wth one of the nterests of ths lterature beng the mpact of prvatsaton on the objectves of the frm, and consequently on ts behavour Fraser, 1989; Vckers & Yarrow, 1989; Bshop et al., 1994; Fraser, 1991; Fraser, 1994a and Fraser, However, one key dfference s that whereas the prvatsaton of publc enterprses that retan consderable monopoly power has been assocated wth post-prvatsaton regulaton of ther behavour, typcally of the prcecap varety, the AWB Ltd, by vrtue of tradng across natonal boundares, s not subjected to any prce regulaton. hs observaton rases the queston of whether an examnaton of the AWB Ltd s stuaton usng the methods of the prvatsaton lterature mght reveal nsghts regardng how ts behavour s lkely to have been modfed by the removal of government-funded support to the Industry. he am of ths paper s to undertake such an analyss, focusng n partcular on how the government s push of the AWB towards fully commercal practces can be expected to have affected ts prcng behavour. he structure of the paper s as follows. Secton 1 develops a model of a prce-settng frm operatng n segmented markets. hese segmented markets are charactersed n such a way as to capture essental dfferences between the AWB s overseas and domestc markets. Specfcally, the overseas market s charactersed as beng more costly to

3 3 supply to, and ts demand s charactersed as beng both more elastc and more uncertan than the domestc market. Gven ths market framework, the model ncorporates a before and after commercalsaton par of objectves for the frm, where the before objectve focuses on sze, and the after on profts. Note that ths type of before and after charactersaton of objectves s common n the prvatsaton lterature for example, Fraser, 1994a and Fraser, 1994b. For each objectve functon the optmal prcng behavour of the frm s derved, wth a vew to analysng numercally the mpact of the change n objectve functons on ths behavour. hs analyss s undertaken n Secton. In partcular t s shown frst how the change n objectves affects optmal prces when the frm s markets dffer n only one of the characterstcs outlned above. Subsequently, the combned effect of the full set of dfferences s examned. he specfc am of ths secton s to generate emprcally-testable hypotheses regardng the lkely mpact of the changes mposed on the AWB by the Australan government on ts overseas and domestc prcng behavour. he paper concludes wth a bref summary.

4 4 SECION 1: he Model he model developed n ths secton s based on that outlned n Fraser 1989 of a szeorentated prce-settng frm operatng n multple markets. In that case lttle was done to specfy the frm s alternatve markets other than for them to dffer n terms of the extent to whch demand was uncertan. In ths case, n order to characterze more fully the dfferences between the AWB s domestc and overseas markets, the followng marketbased assumptons are made: a b c d e he product s a homogenous good; three markets exst: overseas, domestc and resdual producton dump market n whch revenue just covers costs; costs to supply are greater n the overseas market than the domestc; demand n the overseas market s more elastc than n the domestc market; demand n the overseas market s more uncertan than n the domestc market. Regardng the specfcaton of the frm s objectve, based on Fraser 1989, t s assumed that before commercalzaton the objectve of the frm s to maxmze the expected utlty of sales revenue EURev subject to an expected proft constrant E and a total producton constrant Q. Note that n what follows consderaton of revenue from the sale of resdual producton s omtted n order to smplfy the analyss. In ths context t can be shown that because the frm s prcng behavour s always constraned, ths resdual revenue source has a neglgble effect on behavour, even f the frm s very rsk averse. In ths case the frm s objectve s gven by: Max EU Rev 1 By choce of overseas po and domestc pd prces. Subject to: Q E q E q q o d x

5 5 and, E z 3 E p E q c E q p E q c E q 4 o o o o d d d d where: Eqo = expected sales n the overseas market; Eqd = expected sales n the domestc market; qx = sales of resdual producton; co = costs of supply per unt to the overseas market; cd = costs of supply per unt to the domestc market; z = mnmum feasble expected proft level. Demand n both the overseas and domestc markets s assumed to be charactersed by constant elastcty b demand functons subject to addtve uncertanty u, where s ether o or d. b q a p u and where prce s chosen as an optmal mark-up on per unt costs of supply: p 1 c where: a = scalng factor n each market Eu and demand s assumed to be uncorrelated n the two markets. As a consequence: b E q a p 7 and expected revenue ERev s gven by: ERev p E q p E q 8 o o d d

6 6 Whle the varance of revenue VarRev s gven by: VarRe v p o Varu o p d Varu d 9 where: Varu = varance of demand n each market. On ths bass, usng the mean-varance specfcaton of expected utlty, the frm s objectve s to maxmze 1 : Subject to: 1 EU Rev U ERev U '' ERev VarRe v 10 Q E q E q q 11 o d x and, E z E p o Eq o c o Eq o p d Eq d c d Eq d 1 he frst order condtons for the optmal prces, subject to the expected proft and total producton constrants are as follows: 1 1 foc U ERev * ERe v =0 U ERev * Var Re v * ERe v U ERev * Var Re v 13 where, 1 See Hanson & Ladd, 1991 for emprcal support for ths assumpton.

7 7 ERe v VarRe v c E q 1 b c p Var u he after commercalzaton stuaton s assumed to be represented by a focus on proft rather than revenue, n whch case the frm s objectve s to maxmze the expected utlty of proft, subject only to the total producton constrant Fraser, 1994a. Max EU E U p E q c E q 16 Subject to: Q E q E q q 17 o d x Usng the same specfcaton of the demand functons, expected proft s gven by: E p o Eq o p d Eq d c o Eq o c d Eq d 18 and the varance of proft s gven by: Var p o c o Varu o p d c d Varu d 19 Once agan usng the mean-varance formulaton gves: Subject to: 1 Max EU U E U E Var 1 Q E q E q q o d x

8 8 On ths bass, the frst order condtons for the optmal prces subject to the total producton constrant are gven by: r Va E U E Var E U E E U foc * 1 * * 1 * = 0 3 where, 1 1 b c a b c q E c E 4 u Var c r Va 5 hs completes the specfcaton of the model on whch the numercal analyss of the next secton s based.

9 9 SECION : Numercal Analyss In order to undertake a numercal analyss of the model developed n the prevous secton s t necessary to specfy a functonal form for the frm s utlty functon, and a set of base case parameter values. In what follows, use s made of the constant relatve rsk averson utlty functon see Fraser 1994a and b. On ths bass, total utlty for the before commercalzaton case URev s gven by: U Rev Rev 1R 1 R 6 And n the after commercalzaton case, the frm s utlty s gven by: U 1R 1 R 7 he parameter values used for the base case n the numercal analyss are as follows: Overseas Market Domestc Market Resdual Market ao = ad = p x = cx = 1 bo = 1.5 bd = 1.3 Q = 40 co = 10 cd = 10 uo = 5 ud = 5 Note that the only dfference n the characterzaton of the two markets n the base case s n the elastcty of demand, wth demand beng more elastc n the overseas market. In addton, the relatve rsk averson coeffcent s set at R = 0.5 and the expected proft constrant z for the expected utlty of revenue maxmser s set at 95% of that acheved by the expected utlty of proft maxmser. hs s an arbtrary assumpton, whch s made for smplcty, and n order to keep the two types of prcng behavour close to each other.

10 10 On ths bass, able 1 shows the before and after scenaros for the frm. able 1: Dfferences n elastctes b Before After bo=1.5 bd=1.3 bo=1.5 bd=1.3 po $4.00 $30.00 pd $6.30 $43.30 Q Eotal $ $ hs table shows that the shft to a proft-orentated objectve results n an ncrease n prce n both markets, wth an assocated decrease n sales overall. Note that the ncrease n prce s greater n the less elastc market. able, shows the mpact of allowng for dfferences n the costs of supply on prcng behavour. Elastctes and varances are held at the same levels as n the frst case. Note also that the expected utlty of revenue maxmser wll choose to lower prces untl t s constraned by the expected proft constrant. Because of ths the frst order condtons are not equal to zero for the expected utlty of revenue maxmser. However, they must be equal to each other n order for the best contrbuton to be made to ncreasng the expect utlty of the revenue maxmser.

11 11 able : Dfferences n costs c and elastctes b Before After co=15 cd=10 co=15 cd=10 po $3.70 $44.85 pd $7.60 $43.30 Q Eotal $ $ he results for case dffer to those n the frst case wth po>pd for both objectves. However, there are also smlar movements n prces and sales between the before and after scenaros. able 3, ndcates the mpacts that occur where elastctes and costs dffer between the two markets as wth the prevous scenaro bo=1.5, bd=1.3 and co=15, cd=10 but wth the ncluson of the fnal market dfference: a dfference n the varances on the demand functons, wth ths varance beng greater for the overseas market Varuo=500, Varud=5. able 3: Dfferences n varances u, costs c and elastctes b Before After Varuo=500 Varud=5 Varuo=500 Varud=5 po $33.00 $41.10 pd $7.40 $43.30 Q Eotal $ $ Wth ths ncrease n the varance of the overseas market s demand there s a mnmal mpact on the prcng behavour of the expected utlty of revenue maxmser compared wth the results for the prces n case. hs s due to the fact that ths frm s choce of prces s constraned by the expected proft constrant. Whereas, n the after scenaro, the frm s free to adjust ts prces to reflect the ncreased demand uncertanty n the overseas market. Gven the frm s rsk averson, ths results n the overseas market beng

12 1 perceved as less attractve, and the prce set for that market s lowered n order to reduce the varablty of profts. Note that ths decrease s suffcent to reverse the relatve level of domestc and overseas prces for the expected utlty of proft maxmser from that n case. In order to examne these ssues further a senstvty analyss of the mpacts of dfferent levels of rsk averson was undertaken. he results of such an analyss are recorded below n able 4. able 4: Senstvty to changes n the relatve rsk averson coeffcent. R=0.1 Before After po $3.70 $43.90 pd $7.60 $43.30 Q R=0.9 po $33.0 $39.10 pd $7.10 $43.30 Q he results n able 4 show once agan the nsenstvty of the prcng behavour of the expected utlty of revenue maxmser, although there s a slght nclnaton for the more rsk averse frm to concentrate on ncreasng sales by lowerng prce, n the less rsky domestc market he effects for the expected utlty of proft maxmser ndcate that varyng rsk averson reverses the rankngs of po and pd whch s consstent wth the senstvty of ths rato to the varance of demand dentfed n able 3. Nevertheless, the prevous fndngs that the shft from a sze-orentated objectve to a proft-orentated objectve results n ncreases n prces n both markets, and an assocated decrease n total sales, remans robust.

13 13 It follows from the numercal analyss that the followng three hypotheses can be developed: H1: p p Rev o o H: p p Rev d d H3: Q Q Rev Based on the numercal analyss, there are also several ambgutes regardng relatve prce levels, whereby relatve prces were shown to be dependent on dfferences n elastcty and n costs, and n the varance of demand or the rsk averson of the frm. In partcular: p o Rev or p d Rev In the numercal analyss, ths rato was shown to be dependent on market-based dfferences elastctes and costs of supply. In addton: p o or p d he above rato was also shown to be ambguous and dependent on market-based dfferences between elastctes, costs and on both the varance of demand n each market and the rsk averson of the frm.

14 14 CONCLUSION In ths paper a model has been developed to nvestgate the mpact on mult-market prcng behavour as the objectve of a frm s shfted from a revenue-orentated publc enterprse to a sem-regulated proft maxmser. he motvaton for the paper has been the Australan government s push of the former AWB towards fully commercal practces and the queston of how ths can be expected to have affected ts prcng behavour n domestc and overseas markets. Emprcally testable hypotheses have been developed through the algebrac and numercal analyss of a rsk averse frm s prce-settng behavour for two dfferent objectve functons and gven dfferng costs of supply, uncertanty of demand and dfferng prce elastctes of demand for the frm s markets. Adaptaton of Fraser s 1989 modellng framework was outlned n Secton 1. he model s of a sze-orentated prce-settng frm operatng n multple and segmented markets. hese markets are specfed to capture the dfferences between the AWB Ltd s overseas and domestc markets. he overseas market s charactersed as beng a hgher cost market, wth more elastc and more uncertan demand than the domestc market. Wth ths structure, the model ncorporates a before and after commercalsaton par of objectves for the monopolst, where revenue and profts are the two objectves respectvely. Results of the numercal analyss were presented n Secton. hree emprcally-testable hypotheses were generated dentfyng the lkely mpact on the AWB Ltd s overseas and domestc prcng behavour of the changes mposed on t by the Australan government. In partcular, t was suggested that the mpact of commercalsaton would have been to ncrease prces n both domestc and overseas markets, wth an assocated decrease n total sales. hs secton also showed how the change n objectve affects optmal prces when the frm s markets dffer n each respect as well as the combned effect of all dfferences. hs and a further senstvty analyss of the effect of the frm s level of rsk averson was conducted whch confrmed the robustness of the three hypotheses, but also

15 15 ndcated a set of nconclusve results that wll requre further attenton n an emprcal context. In concluson, ths study has developed a modellng framework that has been adapted from prevous prvatsaton lterature and has been appled to an aspect of the prvatsaton process not yet fully nvestgated. he AWB Ltd represents a useful case study for further emprcal work on ths applcaton due to the lkely shft n ts objectves followng changes n Australan federal government polcy.

16 16 REFERENCES Bshop, M., Kay, J. & Mayer, C. eds. 1994, Prvatsaton and Economc Performance, Oxford Unversty Press, Oxford, UK Fraser, R.W. 1989, Uncertanty and the Postve heory of Publc Enterprse, Bulletn of Economc Research, 41, pp Fraser, R. 1991, Prvatsaton n the Unted Kngdom: Lessons for Australa?, Economc Papers, September 1991, 103, pp30-37 Fraser, R. 1994a, Prvatsaton: Prce-cappng and Relablty, Utltes Polcy, Aprl 1994, 4, pp11-17 Fraser, R. 1994b, Prce, Qualty and Regulaton: An Analyss of Prce-Cappng and the Relablty of Electrcty Supply, Energy Economcs, July 1994, 163, pp Fraser, R. 1996, Prvatsaton n the Unted Kngdom: Lessons for Australa, Economc Papers, December 1996, 154, pp14-19 Hanson, S.D. and Ladd, G.W., 1991, Robustness of the Mean-Varance Model wth runcated Probablty Dstrbuton, Amercan Journal of Agrcultural Economcs, May 1991, 73, pp Vckers, J. & Yarrow, G., 1989, Prvatzaton An Economc Analyss, he MI Press, Cambrdge, MA, USA

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