Location and Pollution in a Communal Society

OWEN STANLEY New South Wales Institute of Technology,

Broadway, NS W 2007

The model presented in this paper attempts to explain the recent trend among Australian Aboriginals in remote Australia to abandon large settlements in favour of much smaller decentralizedsettlements. The model does, however, have implications for modern Western societies. Aboriginals are assumed to like money and non-money income, stability of income, nearness to a place of significance and a low degree of private property rights, and to dislike pollution when interpreted broadly. Each of these determinants of werfare is expressed as a function of location and degree of private property rights alone and a utility function is maximized with respect to these two variables. The impact on the optimal location andproperty rights decision of a number of recent changes is then considered.

I This paper develops a model that determines the

optimal location of individuals or groups in a society and the optimal degree of private property rights. It is used here to examine recent changes in Aboriginal society in remote Australia but it has much wider applications than that. It emphasizes the use of location and the degree of private property rights as alternative ways of varying per capita income, the variations in per capita income and the level of pollution. In addition, individuals are assumed to have attitudes about location and private property rights as such.

When whites colonized central and northern Australia the existing Aboriginals lived in very small groups which ranged from a family unit to one ofabout twenty people. With theestablishment of cattle and sheep stations, government settlements and missions these small groups came together voluntarily or as a result of, force. However, in recent years Aboriginals have expressed the desire and have been given the opportunity to resettle in areas away from the old settlements and in many cases the government has provided assistance in the form of educational, health and other facilities.

Many reasons exist for this desire to be resettled and they vary between cases. Amongst the most important reasons are, firstly, to provide an Aboriginal presence in some area of particular significance to the clan, and secondly, to avoid the undesirable consequences of contact with the other Aboriginals and whites at the main settlements. By 1976 there were about 3500 people living in approximately ninety-five outstations associated with the old settlements. The following are some examples of resettlement': 1. The Pintubi2 originally lived in a large area of the Western Desert in Western Australia. Over recent years they had moved east to stay at the settlements of Papunya and Docker River, while some moved to Warburton. Most of them, however, moved to Papunya which became a large settlement of over 1000 people of various language groups and clans. Life for the Pintubi at Papunya, especialry the recently arrived ones, became very stressful. A large proportion of the new arrivals

For a discussion of some of the cases mentioned in this paper and for some others see Coombs (1973), pp. 14-18.

See the Welfare Division Annuul Report 1971-72 and Coombs (1973).

244

1980 LOCATION AND POLLUTION IN COMMUNAL SOCIETY 245

between 1963 and 1966 became ill or died. They had no knowledge of basic hygiene required for a sedentary life, alcohol became an important problem, and death or ill health was often attributed to ill will or sorcery by other groups. They felt alienated and unwanted. TWO unsuccessful attempts were made to leave Papunya between 1968 and 1970. Eventually, in 1973, it was decided to move to a new bore called Yayayi, 45 kilometres west of Papunya. This was not in Pintubi country and permission had to be gained from the Kukatja who were the traditional owners. The Pintubi said that they did not wish to return to their country because there was ‘no flour, no tea, no buildings and no water out there, and too far’.3 2. A mission was established in 1899 on Sunday Island in Western Australia and this led to many mainland Bardi4 moving to the island where they intermarried with the original residents. The Bardi became culturally and numerically dominant. The mission closed in 1963 and the Sunday Island Bardi were eventually moved to the reserve at Derby. They were unhappy there. The Bardi culture was different from that of the people with which they shared the reserve and they did not mix. They often refused to work on the reserve, became known as troublemakers and were often at odds with authorities and other Aboriginals. Over the next eight years the Bardi unsuccessfully attempted to return to Sunday Island and in 1971 they established a new settlement at One Arm Point. This was a position on the mainland adjacent to Sunday Island. They were not concerned with protecting sacred sites but they wished to avoid undesirable influences of the settlement at Derby and to return to a maritime lifestyle. 3. In 1934a mission was established at YirrkalaS in the Northern Territory which attracted a number of different clans to the area. In 1974 there were about 800 people living there. The differences between theclans, and in recent years the problems caused by white influences resulting from mining in the area, had caused problems for people living at Yirrkala. Recently a number of clans have moved from Yirrkala to their traditional areas and the social problems in these new settlements seem less than they were at Yinkala. There are now a dozen

’Coornbs (1973). p. 15. *Coombs (1973), p. 17. House of Representatives Standing Committee on

Aboriginal Affairs, Report on the Preseni Conditions of Yirrkala People. 1974.

outstations associated with the settlement. Similar decentralization had taken place at the neighbouring settlement at Maningrida, with an original population of 1200. There are now seventeen outstationsassociated with it. Thedegree of Westernization of these new settlements and amount of contact with the original settlement varies considerably but in general strong links are maintained. This pattern has been repeated elsewhere around major settlements in remote AustraIia.

One of the obvious benefits of the decentralized settlements is that traditional social mechanisms can handle the problems of externalities much more efficiently than in the larger settlements. These larger settlements are often characterized by untidiness, destruction of the countryside and unhygienic conditions. An increase in the degree of private property rights is one way of handling the pollution, both cultural and material. It would allow one group to prevent its members having undesirable contact with others, and lead to the internalization of the costs of undesirable and anti- social activity and herice to an increase in harmony on the settlement. Common property rights in some contexts, however, are essential to Aboriginal culture and cannot be easily changed. Thus adjustment through relocation has become an important way of achieving an increase in welfare.

The model developed in the rest of the paper attempts to rationalize such decisions concerning relocation and property rights.

II The analysis will be conducted in terms of a

group s f people who originally form part of a larger population living at a settlement but who contemplate moving to a new location. This group may be of any size including one family or one person. It is assumed to have a joint utility function, U:

(1) where r is an index of private property rights, I is the distance between the settlement and a new area to be occupied by the group, y is the group’s per capita income of a material and cultural form, u is the standard deviation of that per capita income received over time and P is the level of pollution experienced by the group. The group is assumed to gain utility from the cultural benefits associated with common property rights and hence to lose utility from an increase in private property rights (see below). It also gains utility from moving nearer

U = U(r , 1. Y . u, PI

246 THE ECONOMIC RECORD SEPT.

to some place of cultural and religious or aesthetic significance which is a distance, I * , from the settlement. It will be called the ‘place of significance’. Utility also increases with per capita income but decreases with increases in the variation in per capita income over time, and decreases with increases in pollution. The term ‘pollution’ is to be very broadly interpreted to mean any undesirable influence experienced by members of the group and caused by other members of the settlement. It may take the form of materials dumped, destruction of fauna and flora, contact with undesirable ideas, and feelings of alienation experienced while living a t the settlement. The marginal utilities in the utility function thus have the following properties: U, < 0, U/ Z 0 for I I,, U, > 0, U, < 0, up < 0. (2)

Two of these variables, distance and private property rights (I, r ) , are subject to the direct control of the group. The analysis of the effects of varying 1 and r is complicatled by the effects which variations in them have in turn on the other arguments of the group’s utility function (y, 0, P).

Both the group and the settlement are assumed to inhabit circular areas.of land of unit radius and thus of area R. In Figure 1 the group is located at point A and the settlement is located at point B. The line AB of length I shows the distance between the centres of the circles. Thus when I = 0 the group lives a t the settlement and when I 2 2 the areas of occupancy by the group and those remaining at the settlement d o not overlap. The group experiences no disutility from ‘pollution’ by its own members but it does from pollution by people living at the settlement. If it is assumed either that the neighbours pollute uniformly over their area or decreasingly in circles around the settlement, as the radii of the circles is increased, until it is zero at unit radius, then the pollution experienced by the group at A is a decreasing function of I for 0 I I 5 2 and P = 0 when I 2 2.

FIGURE 1

Being near the settlement confers two advantages on the group. Firstly, there are economies of location. Nearness reduces transport costs to the settlement and so increasesy. Secondly, the variation in the group’s income is low if it stays at the settlement because income from paid work and from the use of resources at the settlement flows independently of climatic conditions. Since the proportion of the group’s income coming from these sources will fall as I increases, the variation in the group income will increase as lincreases. Thus D

increases with 1. The intensity of private property rights is

measured by an index that lies between 0 and 1 and shows the degree of control the group has over the resources in its care and over the consequences of their use. When r = 0 the group has no power to prevent others from using ‘their’ resources. All resources, that is, are common property. When r = 1, however, the group has complete control over the impact of its resources and there is no common property. It will be assumed that a particular value of r for the group as a whole is reflected in a similar degree of private property rights for individuals within the group. Further, i t will be assumed that a low value of r for the group will prompt similar attitudes amongst some individuals in neighbouring groups. These assumptions are reasonable when it is remembered that suchagroupdoes notconstituteacountry that can impose laws on foreigners distinct from those applying to citizens but is in fact a collection of individuals living in proximity to each other, the composition of which will change over time.

The value of r will have an effect on the level of per capita income, the Variation in per capita income and the level of pollution experience by the group. Providing r > 0 members of the group and the group as a whole will be able to engage in mutually beneficial trade with others. Increases in r will bring about a n extension of the individual’s and group’s control over resources and so extend the areas in which trade can take place. Further, the incentive to trade will also be increased. Thus y will increase with r . The value of r will also affect the proportion of income redistributed from the haves to the have-nots that is compulsory and so affect the amount of income redistributed. When r = 1 charity is the only vehicle for redistribution and the level of redistribution presumably will be low. For r < I some form of ‘compulsory’ redistribution is possible and the level of income redistributed is likely to be higher than that achieved when only charity exists. This means that for a given variation

1980 LOCATION AND POLLUTION IN COMMUNAL SOCIKIY 247

in per capita income for the group before redistribution, the variation in income after redistribution will fall with decreases in r because members of neighbouring communities will assist in times of low income and expect repayment when incomes are high. Thus Q will increase with r. Finally the relationship between the degree of private property rights and the level of pollution exists through Coase’s Theorem? an increase in r allows the polluter and the polluted to engage in mutually beneficial trade in relation to unwanted residuals so that the level of pollution falls by comparison with the common property level. In the case of cultural pollution which is important here, an increase in r will allow the polluted group to prevent any unwanted contact with undesirables and to more readily punish offenders to their moral code. It is assumed here that enclosures of common property is the only effective way of increasing P. Thus P will decrease with increases in r .

From the above i t can be written that Y = f f l . r ) . f l < 0. f r o (3) a = g f l . r ) , g l > O,g, =. 0 (4) P = hfl. r) , h/ < 0, h, < 0, for I E LO, 21

and hl = h, = 0 for I > 2. (5) The analysis will be simplified by the

introduction of a ‘certainty equivalent income’ of a material and cultural form, j :

v = $cv. 4 (6) with I ( ly > 0, $ a < 0 (7)

Further, aylar = I(lu.yi + $a.gi < o (8) 2ylar = Jlv.fr + $a.gr = ? (9)

The sign of (8) follows because a n increase in the distance between the communities reduces per capita income and increases the variations in income. The sign of (9) depends on two conflicting forces. The first is the increase in per capita income that results from increased incentive and trading between the groups; the second is the increase in the variation in per capita income that follows an increase in property rights. The relative strengths of these forces depends on a complex of cultural factors and economic possibilities facing the community. If the sign of (9) is positive then it will be said that ‘income factors’ dominate, otherwise ‘sharing factors’ dominate.

The utility function now depends on the variables I, r:

from (2) above.

li = U { r , 1. WlL 4, g ( l , 41, h(I, r ) ) = Y(I. r )

irtilai + (xrjay)(ay/aO + (au/aP)(aP/ar) 5 o (1 1)

+ (8U/?P)(dP/dr) 5 0. (12)

(10) and maximization of utility requires

and d t i l d r + (?U/2,v)(ay/ar)

The inequality in (1 1 J reflects the lower bound on I and the inequalities in (12) reflect the upper and lower bounds on r .

The interpretation of the first optimal condition when it holds with equality is that the loss of utility from the decline in the certainty equivalent income caused by an increase in the distance between the group and the settlement should be just equal to the gain in utility from a reduction in pollution and from the gain or loss from moving near or away from the place of significance. The second optimal condition when it holds with equality has the following interpretation. An increase in property rights has three effects: it reduces utility directly from its cultural effect, it varies the certainty equivalent income and reduces the level of pollution. In the optimal state the marginal variations in these must offset each other. If the community is able to determine its location and the degree of private property rights then (1 1) and (12) must hold simultaneously.

Aboriginal attitudes to property rights are often considered to be fundamental to Aboriginal culture and either worthy of support and preservation or at the very least not easily changed over a short period of time. Thus the short-run equilibrium to the situation involves holding r constant and optimizing in relation to equation (1 1) alone. Figures 2(b) and 2(c) show various optimal values of I = I * .

The terms in equation (1 1) have the following properties. Firstly, it assumed that the marginal utility of being near the place of significance declines as that place is approached. Thus

( a 2 v ) / ( a l ) 2 < 0. (13)

Secondly, from (8) above

and has a slope of ( w a y 3 w a r ) < 0 (14)

a { (aui ay) ( e j / at ) j 1 d I = ( a y j a r ) ( w / 8 y a o + (au/ay)[a’y/,lar)2] < 0. (15)

Since j is the certainty equivalent of the material and cultural income received, the marginal utility of j should be independent of I so that the first term of R. Coase (1960).

248 THE ECONOMIC RECORD SEPT.

( 1 5 ) is zero. The marginal utility of? is positive and since

[a2y/(ao21 = ( a y i a m m a r ) + (ajlaa)(aa/ar) < o (16)

the right-hand term of (1 5 ) is less than zero. Thus a line representing (14) falls to the right.

Thirdly, the slope for I 5 2 of (au IaP) (aP/ar ) > o (17)

can be likewise determined. Differentiating (17) with respect to 1 yields

a { ( a u i a P ) ( a P / a r ) l ia r = (aP/ar)(z* uiaPar)

+ ( a u l a ~ ) [ a ~ ~ / ( a o ~ l < 0. (18) The variation in marginal utility of pollution with respect to distance between settlements can be assumed to be zero. The marginal utility of pollution is negative and it is assumed that pollution falls at a decreasing rate in terms of 1. Thus (17) has a negative s!ope in terms of I for I I 2. Both (17) and (18) are zero for I > 2.

A number of situations are possible. One division of possibilities is on the basis of the relationship between 1, and 2. Consider the case where I , > 2. In Figure 2(a) the line A2 shows the term

and the difference between A2 and the line Bl, is aU/aI. For I > 2 the value of BI, is the marginal utility of being near the piace of significance alone. That marginal utility becomes negative for I > I,. The line BI, is the sum of those marginal utilities and will be called the marginal benefit of moving away from the settlement ( M E ) . The marginal cost of moving away from the settlement (MC) is the loss in utility as a result of the decline in certainty equivalent income

that takes place. Until the present it has been assumed that this term is always non-zero. However, there may be communities that are sufficiently independent for

and so (20) is zero. If this is true for all 1 then the optimal position for the group's outstation is at I , in Figure 2(a).

Figure 2(b) shows optimal locations for various marginal cost curves. In the case of MC, the loss of certainty equivalent income from leaving the settlement more than offsets the benefits from leaving in the form of a reduction in pollution and getting closer to the place of significance. Thus it is

(auw) ( a p i do (19)

(aulaj) (ayldl) 120)

ayiar = o (21)

optimal for the group to remain at the settlement. In the case of MC, it is optimal to move to I,*. At this new site the group will experience some pollution, will have a lower certainty equivalent income because of the move but will live closer to the place of significance. If the marginal cost curve is MC, then the marginal benefits of moving away from the settlement are greater than the marginal cost until I = I,. Thus in this case the group moves to the place of significance, beyond the pollution from the original settlement and beyond a distance where certainty equivalent income is affected by nearness to the original settlement.

FIGURE 2(a)

t

.

FIGURE 2(b)

A

FIGURE 2(c) Effects of Varying 1 on Group Utility

1980 LOCATION AND POLLUTION IN COMMUNAL SOCIETY 249

Influence

A. Assistance in establishing out- stations

B. Increase in income

C. Reduction in variability of income

Figure 2(a) also shows the marginal benefit curve for the case where the distance between the settlement and the place of significance is less than 2. This distance will be called 11, and the marginal benefit curve corresponding to this case is CD. Again various cases can be examined and some are represented in Figure 2(c). Depending on the position of the marginal cost curve the optimal distance from the settlement may be zero (as in the case of MC,) or 12* (as for MC,). It may be optimal to move further away from the settlement than is the place of significance (as for MC, and MC.,). It will never be optimal to move beyond I = 2 if the place of significance is less than or equal to 2 because the marginal benefit curve cannot cut the horizontal axis beyond I = 2 in this case. Thus if the place of significance lies in such a position that a separate settlement there would experience pollution, then the optimal location of the new settlement is always in a position when pollution is experienced. When Ill = 2, then the optimal settlement is at 2 in the case of MC,. Cases involving multiple equilibria have been Ignored, although they are possible.

We are now in a po>ition to examine the impacts of modern European influences on Aboriginal communities in terms of their desires for resettlement. To summarize these effects we will examine the impact on P for cases involving non- comer solutions. What happens in the cases where the initial optimal values of P are zero or I , or 2 can be inferred from the discussion to be presented.

The various European influences to be considered are the following:

A. The Australian government has assisted groups to leave the original settlements by offering to provide, or by actually providing, bores, schooling and health facilities in areas where the people wish to resettle. This policy makes @/dl less negative and with sufficient public investment and sufficient cultural independence between the groups, ay/al may rise to zero. The impact of this policy, thus, is to lower the M C curve and so to increase I*. If 1, > 2 and if there is sufficient public investment and cultural independence the group will move to 1,. If ajvai becomes zero and lI < 2 then the group may move to point 0 in Figure 2(c).

B. The Australian government has increased the material income of Aboriginals through the social security system. These payments are made regardless of whether the person is at a settlement or not so that any increase in such payments leaves a j l a l unaffected but lowers au/ay by the law of

AP

'

+ +

+

diminishing marginal utility. This means that the M C line is lowered and hence the policy increases I*. C. The social security system has also reduced the variability of the material part ofy and so increased y. By the analysis for the case B above, P is increased because of a reduction in MC. D. The introduction of motor vehicles has made contact between distant settlements much easier than before. This improvement in transport has meant that the cultural and material losses from moving away from the original settlement are lessened and so ay/ai' becomes less negative. This lowers the MC curve and increases I*. E. The introduction of consumer durables has increased material pollution around settlements and so has increased a U / a P and aP/al. This change increases the marginal benefit curve and so leads to an increase in P if the initial equilibrium I is I < 2. If, however, the initial optimal level of I is 1 > 2 then pollution is zero so that this change has no effect. F. European education and indoctrination has in some places led to an increase in private property rights and a reduction in desires to be near places of significance. This change will have decreased aP/al and aUldl but has an unknown effect on ay/dl since it will have increased ,y but also will have increased c. If income factors dominate then 1 will have increased for a given 1. This lowers a U / a j for a given I and so the change becomes indeterminate. However, education and indoctrination are likely to change the utility function so dramatically that

F. European education ~

?

D. Increase in availability of motor vehicles

E. Increase in consumer durables I +,o

250 THE ECONOMIC RECORD SEPT.

without further information of its nature it is not possible to determine the change in I*.

Table 1 summarizes the effects of various influences discussed above For the case where the initial optimal location is less than the distance f, from the place of significance viz., I is 0 < P < I,.

III Long-run changes in Aboriginal communities in

the south-east of Australia have often involved very substantial changes in attitudes towards private property and in some cases there exists a degree of private property rights that is the same as that for the community as a whole. Many pressures have existed which have produced this change over the past 200 years. These include general pressure to conform to the values of a dominant European community, indoctrination by educational and religious institutions, the practice of fostering Aboriginal children, official administration of the income and assets of Aboriginals, European supervision of activities on reserves, and are likely to have included those influences that are emphasized in this paper. Whether those Aboriginals currently living in remote Australia will experience similar changes in attitudes to property is open to speculation. However, we will proceed in this section by assuming the institutional and cultural rigidities that prevent changes in attitudes to property rights are not great in the long run. If these rigidities in fact prove to be overwhelming then this section should be regarded as being concerned with principle only.

Since the long-run situation for the Community involves optimization in relation to location and attitudes to private property rights equations (1 1) and (12) must hold simultaneously. The general solution to the problem is provided in the

1

!

FIGURE 3

Effects of Varying r on Group Utility

t I

-01 r* 1 r

Appendix and involves comparisons of cross- partial derivatives whose values are unknown. Thus a solution will be obtained here via the simplifying assumption that the terms in (1 1) are independent of r and the terms in (12) are independent of 1. An additive utility function in 7 and P is sufficient for this.

An indifference map in r and I will be used. Since along any indifference curve dU = 0, the slope of an indifference curve is given by dr dl _ - -

= - a / j . ( 2 2 ) It has already been established that for noncorner solutions in terms of I, the numerator of (22) behaves as follows

< a $ 0 for every 15 I, (or i t*) . (23)

The behaviour of the denominator of (22) is given by differentiating f l with respect to r . The first term in this process is

that is, it is assumed that increases in private property rights cause disutility at an increasing rate. The second term is

[?U/(ar)21 < 0 (24)

( a u/ ay) [ ? z j / (?r)z] + (2yIar)(d2 U/?$r) < 0. ( 2 5 )

This inequality will hold under the following assumptions: that the cross-partial derivative is zero, that income factors dominate and that the law of diminishing marginal productivity applies to r . The third term is

This inequality will hold if it is again assumed that the cross-partial derivative is zero and the law of diminishing marginal productivity applies to the way r reduces P.

The optimal value of r for a given I can now be analyzed in Figure 3. The marginal benefit of r curve, AB, shows the increase in utility that arises from an increase in j (since income factors are assumed to dominate) and a reduction in pollution. The marginal cost of r curve, CB, shows the loss in utility that arises from an increase in r itself. The optimal value of r for an interior solution holds when

(aviap)[az ~ / ( d r ) ~ ] + (aP/ar)(aZu/aPar) < 0 . ~ ~ 1

(au/aj)(aj j /ar) + (au/aP)(aP/ar) = au iar . (27)

1980 LOCATION AND WLLUTlON IN COMMUNAL SOCIETY 25 1

A B C D E

Corner solutions and multiple solutions may exist and can be easily shown.

The behaviour of the denominator of (22) for 0 < r* c 1 is thus given by

B ZOforeveryr $ r * . (28) This means that (22) describes ‘circular’ indifference curves as shown in Figure 4. Satiation takes place at point A.

The way in which point A moves as a result of the influence considered earlier can now be observed. To do this it must be known how r* is affected by these influences for a given 1. Any change which increases the certainty equivalent income regardless of r (influences A. B, C and D below) reduces dU/dy . This lowers the marginal benefit of r curve and thus reduces r* .

+ - R,BR,B + - R,BR,B + - R,BR,B + - R,BR,B

+.o + T,TR,R

‘ t

I I a :

01 I* L

FIGURE 4

The introduction of consumer durables increases P for a given land it is likely that the institutions that can be developed when r > 0 will be more sensitive to pollution. If this is so then dP/dr becomes more negative and a U / d P will increase as Pis increased. Thus the marginal benefit curve shifts upward and r* is increased.

Now, influences A , B, C and D cause an increase in jj or a reduction in @ / d l and may lead to an increase in I in the first instance. If 1 is increased theng will be no less than before the introduction of the influence. Thus the optimal value of r will fall or remain the same (it will remain the same where j j is unchanged as a result of the adjustment in 0. Influence E increases (aU/aP)(8P/ar> and will lead to an increase in 1 in the first instance. After the adjustment P will be no less than before and so r* is increased. If there is no change in as a result of an influence then all of the adjustment will take place in r* in accordance with the discussion in the previous paragraph.

Table 2 summarizes the effects of the various influences on P and r* taken separately, and on the

direction which point A will move in Figure 4. In that figure ‘T’ refers to top, ‘B’ refers to bottom, ‘R’ to right, ‘L’ to left, ‘TR to top-right, etc.

‘TABLE 2

The implications of these results for Aboriginal society are as follows. If it is assumed that living at the settlement was optimal a t some time and influences A to D dominate influence E then the change over time will involve an increase in I or a decrease in r or both. Certainly these influences d o not threaten those aspects of Aboriginal culture which require a low .value of r . If pollution influences dominate then the change over time should involve an increase in I or r or both. This does, then, represent a threat to aspects of Aboriginal culture. The long run may, however, involve great changes in the nature of the utility function and the model is not equipped to analyze these circumstances.

These results may also be used to predict trends in modern Western societies. If incomescontinue to grow and become more stable and if pollution problems do not dominate then Westerners are likely to demand more space and become more communal in their attitudes. The latter may take various forms. It may for instance, involve a growth in charity, or a growth in parks and open areas, or an increase in controls over private property for the purpose of redistribution. If pollution problems ‘dominate in the future then Westerners are likely to demand more space and are likely to increase the degree of private property rights. In a Western context this may be achieved by the enclosure of common property or by the imposition of rules or taxes and subsidies for the purpose of internalizing externalities. Controls for the purpose of redistribution, however, create externalities and so decrease private property rights as defined above. Finally, the model throws some light on ‘alternative lifestyle’ movements which, apart from the selected application of pollution controls, advocate a low degree of private property rights. They have, firstly, been associated with

SEPT. 252 THE ECONOMIC RECORD

growing incomes in Western societies and, secondly, have often involved the establishment of decentralized rural communities. Both of these are predicted by the model.

APPENDIX

The necessary conditions for the maximization of the utility function are z, = a q a r + (au/av3(aj/ar) + (au/ap)(d~/ar) = o ( I ) z, = au/ar + ( a u / a f i a j / a r ) + (au/amdP/dr) = 0. (2) Toconsider theeffectsofvariationsinjand PonI*andr* for the general case it is necessary to totally differentiate (1) and (2) with respect to j . .P, I and r and fo solve simultaneously for dl and dr. Thus ( a z , i a r ) d r + (az, /ar)dr* = - (az,/ajwj - ( a z , / a p ) d P (az , iar )dr + (dZ,/ar)dr* = - ( a z , / a j ) d j j - ( a z , / a m P . By Cramer’s rule

1 - ( a z , / a j ) d j - ( a z , / a P ) d P , a z , / d r

1.1

Coase, R. (1960). ’The Problem of Social Cost’, The Journal of Lruv und Economics. Vol. 3, October, 1-44.

Coombs, H. C. (1973), ‘Decentralisation Trends Among Aboriginal Communities’, Aboriginul News, Vol. I , No. 3, October, 14-18.

House of Representatives Standing Committee on Aboriginal Affairs, Report on the Present Conditions of Yirrkala People, 1974. AGPS, Canberra.

Northern Territory Administration, Welfare Division Annual Report 1971. Commonwealth Government Printing Ofice, Canberra.