Limits to economic growth as shown by a computable general equilibrium model

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ECOLOGICAL ECONOMICS Ecological Economics21 (1997) 141-158

ANALYSIS

Limits to economic growth as shown by a computable general equilibrium model Martin Ricker * Yale University, School of Forestry and Environmental Studies, 360 Prospect Street. New Haven. CT 06511. USA

Received I February 1996; accepted 29 August 1996

~bstract

Economic growth is distinguished from commercial growth and is defined in this article as the growth of the value a society puts in monetary terms on all commercial and non-commercial goods and values it possesses during a certain period. A computable general equilibrium model is used to show the impact of changes in the endowments, preferences and production possibilities on economic income, which in the model comprises all wealth. Besides land with its natural resources and labor, energy is the key endowment to drive an economy. The model leads in an intuitive way to the following conclusions: (1) Societies should start to use appropriate indicators for true economic growth, rather than just for commercial growth as measured by gross national product. (2) All types of economic growth are limited, no matter if based on endowment growth, production efficiency growth, or changes in preferences. (3) Economic growth should be oriented more towards increasing production efficiency and less towards using more natural resources. (4) Human population growth puts at risk the possibilities for average economic growth per person. (5) We should get better prepared to use solar energy in the future. (6) Besides economic growth, there exists pure utility growth, which is not measurable in monetary terms; it includes much of scientific progress in the long run and is of great importance even though it cannot be included in an indicator of economic growth. Keywords: Economicgrowth; Energy; General equilibriummodel; Populationgrowth

1. I n t r o d u c t i o n

The 'limits to economic growth' debate has been going on for about 30 years now (for a summary see Ekins, 1993). Despite heavy criticism from some scientists and from the environmental movement (see e.g., Commoner, 1977), today most development

Present address: lnstituto de Biologia, Departamento de Botfinica, UniversidadNacional Aut6nomade MExico, Apartado Postal 70-233, Del. Coyoacfin,MExicoD.F. 04510, Mexico. Fax: + 52-5-550-1760.

economists, macroeconomists and many politicians still consider long-term economic growth as one of the most important economic achievements (see Gillis et al., 1987; Abel and Bernanke, 1992). It is therefore of great interest for both environmentalists and developers to analyze what types of economic growth are possible and where are their limits. Gillis et al. (1987) define economic growth as a rise in national or per capita income and product. Defined in this way, an increase in the production of goods and services in a nation leads to its economic growth. This definition is problematic, because it

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M. Ricker / Ecological Economics 21 (1997) 141-158

actually refers to commercial growth. True economic growth must consider all goods and values, including non-commercial ones. Therefore, for the purposes of this paper let me define economic growth as the growth of the value a society puts in monetary terms on all commercial and non-commercial goods and values it possesses during a certain period. Thus, eliminating smog in big cities or making it possible to consume beautiful nature can contribute to economic growth in the same way as can the construction of a car factory. A pollution-poor factory will contribute stronger to economic growth than a polluting factory with the same commercial output. The problem of finding out the monetary value of supplying a non-commercial good such as clean air is a methodological one, but not one of principle. If people do not pay for a non-commercial good, they nevertheless value it, and if it is in limited supply, an income share must be paid to provide it (e.g., taxes for nature parks). A large part of the critique on economic growth is hardly at all about economic growth, but rather about not considering non-commercial values in economic development (e.g., in Commoner, 1977, or in Arrow et al., 1995; see Nordhaus and Tobin, 1977). Indeed almost everybody, including environmentalists, would agree that an economic growth, which includes not only commercial but also non-commercial goods and values, and which is not followed some day by economic collapse, is a very positive achievement. It means that societies and their environments are transformed continuously to satisfy increasingly the societies's desires and values. Unless one is opposed to any change at all and unless one's personal valuation is in disagreement with society's valuation, or the change indeed affects one negatively, such economic growth is a development to the better from the human viewpoint (since humans control all these changes, I will not consider the viewpoint of other living beings). The societies' utility, in the economic sense meaning 'satisfaction', in the process of such economic growth is continuously increasing, and one may only have to worry about equity, i.e., who benefits from the economic growth. While such true economic growth is certainly possible, growth of the gross national product is not a good indicator for it (see Ekins, 1993). Commercial growth, as measured by growth of the gross

national product, is frequently accompanied by negative growth of non-commercial growth (e.g., more pollution or habitat destruction). An indicator of true economic growth must reflect the outcome of this trade-off. In the following model, non-commercial goods receive a price and income share payment in the same way as commercial goods (unless they are in excess supply). In the real world, these payments would be made via taxes, voluntary donations, or by means of forgone income (e.g., when legislation forbids to cut a forest). In the following model, non-commercial goods cause no problem, as their supply translates directly into income and their demand in spending. The argumentation about the limits to economic growth is generally divided into four subthemes: First, how should non-renewable resources be used such that their depletion is efficient (see Hotelling, 1931; Dasgupta and Heal, 1974; Stiglitz, 1974a; Stiglitz, 1974b; Weinstein and Zeckhauser, 1974; Devarajan and Fisher, 1982). Second, how should non-renewable resources be used that their use is equitable between generations (see Solow, 1974; Howarth and Norgaard, 1990; Howarth, 1991; Daly, 1991; Victor, 1991, also discuss long-term availability of natural resources). Third, how can renewable resources be used such that their use is efficient and/or sustainable (see e.g., Repetto, 1988, for a discussion about forests). Fourth, which variables make an economy grow and what factors influence those variables (see Solow, 1956; Solow, 1994; Mankiw et al., 1992; Romer, 1994). In this paper I like to focus on the fourth subtheme, taking the view of a scientist who analyzes a closed system with the exception of solar energy influx. In the model, economic wealth is defined as weekly income from the endowments ( = inputs into production, from which goods result). In the case of non-commercial endowments, the income represents a hypothetical value flow in monetary terms. Savings are not treated explicitly and would have to be expressed in non-used endowments. I am interested to see how weekly income can be increased and in which ranges that is possible. Economists have developed a computable model which is ideal for such purposes: the general equilibrium model. The computable general equilibrium model looks at an economic system as a whole and determines all

M. Ricker / Ecological Economics 21 (1997) 141-158

prices and quantities of all endowments and goods simultaneously. The term 'good' refers to goods in the widest sense, including services and non-commercial ones. Such a model is especially attractive and useful for analyzing economic growth because it models the economic system as a whole, demonstrating the interrelationship between resource use, preferences and production possibilities in their effect on product distribution, prices and income. As a mathematical/economic problem, the general equilibrium model accompanied economists conceptually for about two centuries before it could be solved. L6on Walras (1874) Walras, 1874 is generally credited for having introduced the formal model in his book Elgments d'Economie Politique Pure, but he was unable to either solve it mathematically nor to prove rigorously that an equilibrium always exists. This was possible only after Brouwer's fixed-point theorem had been introduced (Brouwer, 1912). In the 1960s/70s, generally applicable, computational algorithms were developed to solve mathematically any general equilibrium model (for a description of the complex algorithm see Scarf, 1969; Scarf, 1983; Scarf, 1984). For the development of my paper, I will take a different route than would most economists, in order to keep a readership with me, which is not keen on general mathematical derivations. After only a brief mathematical presentation of the model, I don't use general mathematical equations, but rather turn quickly to present a computable example with numerical results, subsequently considering how general these results are. This approach is intuitive and should be accessible also to readers who are not economists. In this way, not only is the topic as such one of ecological economics, but also the methodological approach attempts to be appropriate for an interdisciplinary readership, typical in the field of ecological economics. After introducing the basic market equilibrium model, changes in the underlying determinants of the market equilibrium are carried out to demonstrate and examine the effects.

143

for a given scenario its input and output fluxes remain constant and make the system appear static. Changes over time, for example from depletion of non-renewable resources, are modeled as abrupt events, i.e., changing a system variable causes the system to 'jump' to the new market equilibrium. This is in so far no problem, as one can make infinitesimally small changes in the model, resulting in continuous movements of the market equilibrium. In that case, the model result represents only a snapshot situation in a changing economic system. In the general model, one wants always to produce the maximum quantity possible of demanded goods (commercial and non-commercial goods). The relative prices of all goods and endowments add up to 1 (choosing 1 is arbitrary). There are endowments (such as land), which enter the production process to supply demanded goods; the quantity of supplied goods is linearly dependent on the quantity of available endowments. The demand on the endowments cannot be higher than the supply; however, there can be excess quantity of an endowment. All produced goods are sold in the market, so that there is no excess production. Spending of each person is proportional to his or her relative preferences, defined as the percent of income spent for a good. For each person, income must equal spending. The general model can be summarized in a set of equations: M A X ~S{3oodl + Y~.SGooa2 + ...

subject to PEnd . . . . . . tl + PEnd . . . . . t2 + "'" +PGoodl + PGood2

+...=1 for each endowment ESEndowment ~ E D E n d . . . . . t

for each good: for a given activity:

So,,,,,,= ( b,)( SE,d,,w,~,,,,,) + ( b2)( SE,,,o,.,~,,,,2) E SGood= E DGood

2. The basic m o d e l

for each person:

The following model represents a closed economy, which is always in market equilibrium, so that

[( DGood, )( PGood I ) ] / [ ( O~ood2)( PGood2) ] / . . -

-= RelPrefGood l/RelPrefGoo,a2/...

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M. Ricker / Ecological Economics 21 (1997) 141-158

( SEndowment I ) ( PEndowment I ) + (SEndowment2) ( PEndowment2 ) + ' ' " = (DGood,)(VGoodl)

+ ( Dc;ooa2)(VGood2)

+''"

where sum in the market (of supply or demand) supply in units of product relative price demand in units of product production coefficient relative preference in percent income paid In words, the following assumptions are made in the model: 1. The market is always in equilibrium, such that there is no excess demand or supply, and production is maximal. 2. Quantities of endowments affect produced quantities of goods linearly. 3. Each person is at the same time producer (supplier of endowments) and consumer (demander of goods). 4. Each person does maintain the same preference for a good in terms of percent income he spends, independent from the quantity produced; or in more technical terms, the consumer utility is of the Cobb-Douglas type with the elasticity of substitution being one. All of these assumptions are somewhat unrealistic, but they are not crucial for the logic which follows. Now I will turn from the general model to specific numerical models. The basic specific model is summarized in Table 1. Assume a world with two persons (or types of persons with the same endowments and preferences). In that world there is only labor, land and oil as fossil energy, which comprise the endowments. All inputs and outputs are weekly fluxes. One person is rich, owning 100 ha land, which he or she rents out, and 80 i / w e e k oil. The other person is poor, owning only 1 ha land. The rich person wants to work 10 h / w e e k and the poor person 15 h / w e e k to obtain two goods, one lowtechnology good and one high-technology good. No other goods will be considered in the basic model. They will spend the money gained from labor, land rent and energy sale completely on these two products. The rich person spends 30% of his or her

E

S P D b RelPref

weekly income on the low-technology good and 70% on the high-technology good. The poor person spends 50% on each. The production is summarized in a production possibilities set with three activities. The low-technology good requires 2 h labor, 80 ha land and 5 1 oil to obtain 10 units (e.g., weekly averages of an agricultural good). For the high-technology good there are two production activities: Both require 28 h labor and 2 ha land, but differ in their energy input and production output (e.g., weekly averages of an industrial good in a production plant). Physical resources needed to produce the products are not considered explicitly as they are obtainable from the land, using labor and energy, and in the model are assumed to be recycled completely from the good with energy. Although theoretically this is possible (see Bianciardi et al., 1993a), in the real world this assumption is a simplification, which is not always realistic (see Bianciardi et al., 1993b). Since there are only two produced goods, a production possibilities frontier can readily be graphed. To calculate its values from the production possibilities set, the following linear optimization has to be carried out for different values of L (or alternatively H, i.e., the quantity produced of one of the two goods) MAX(10)(x) + (8)(y) + (4)(z) subject to (2)(x) + (80)(x) + (5)(x) + (10)(x)

(28)(y) + (2)(y) + (250)(y) +

(28)(z) (2)(z) (80)(z)

~ 25 _< 101 _<80 -L

{labor constraint) {land constraint) {energy constraint) {or(250)(y)+(80)(z)=H)

where production level (explained below) to produce LowTechGood y, Z production levels to produce HighTechGood L quantity produced of LowTechProduct quantity produced of HighTechProduct H The resulting piece-wise linear production possibilities frontier is shown in Fig. 1. The solution for production must lie on the production possibilities frontier, if production is to be optimal. However, the preferences of the involved persons will determine where on the production possibilities frontier the solution will lie. X

M. Ricker / Ecological Ecom~mics 21 (1997) 141-158

The equilibrium situation of the model market, calculated with a computer program, is given in Table 1. The resulting relative prices are $0.0592 per hour labor ($ = money units), $0.0118 weekly land

145

rent per hectare, $0.0188 per liter oil as energy, $0.1152 per unit low-technology good and $0.7951 per unit high-technology good (Note that the sum of all involved relative prices is one, as stated above).

Table 1 Model I (basic model) Problem Weekly endowments

Rich person P~or person

Labor (h)

Land (ha)

Energy (I oil)

10 15

100 1

80 0

Preferences (%) LowTechGood

HighTechGood

30 50

70 50

Activity

1

2

3

Labor (h) t,and (ha) ['nergy (1) LowTechGood (units) ttighTechGood (units)

- 2 - 80 - 5 10 0

- 28 - 2 - 250 0 8

- 28 - 2 - 80 0 4

Rich person Poor person Production possibilities set

Solution Prices ($) 1,abor I,and Energy I,owTechGood HighTechGood

0.0592 0.0118 0.0188 0.1152 0.7951

W e e k l y allocation (units) LowTechGood

HighTechGood

8.528 3.905

2.882 0.566

~ctivity

I

2

3

Lcvel

1.2425

0.0556

0.7488

Rich person Poor person Production levels

Weekly income ($) Rich person Poor person Overall Average

3.2760 0.8998 4.1758 2.0879

Inequality (%)

32

146

n . Ricker / Ecological Economics 21 (1997) 141-158

The rich person receives 8.528 units of the lowtechnology good and 2.882 units of the high-technology good per week, while the poor person receives 3.905 and 0.566 units, respectively. The production levels indicate at which level an activity is run in equilibrium. For example, activity 1 has a production level of 1.2425, and therefore 2.48 h labor, 99.4 ha land and 6.21 1 oil are used to produce 12.425 units of the low-technology good in this activity. These numbers are shown at the top in Table 2 for all three activities in model 1.

Next, Table 1 shows an analysis of the modelsociety's weekly income. Income is calculated as the weekly value of the endowments. The value of a given endowment is calculated as its price times its quantity flux. For example, the weekly income of the rich person is ($0.0592)(10 h)+($0.0118)(100 ha) + ($0.0188)(80 !) = $3.2760. The sum of the weekly income from all existing persons gives the modelsociety's economic overall weekly income, which represents all its wealth. In Table 1, 'average' refers to the average economic income per person.

Table 2 Confirmation of the solution of model 1 (Table 1) a Weekly production Activity

1

2

3

Labor (h) Land (ha) Energy (1) LowTechGood (units) HighTechGood (units)

- 2.48 - 99.4 - 6.21 12.425 0

- 1.56 - 0.11 - 13.9 0 0.445

- 20.97 - 1.50 - 59.90 0 2.995

Comparison of production and consumption Labor supply (h) Labor demand (h) Land supply (ha) Land demand (ha) Energy supply (1) Energy d e m a n d ( l ) LowTechGood supply (units) LowTechGood demand (units) HighTechGood supply (units) HighTechGood demand (units)

10 h + 15 h 2.48 + 1.56 100 + 1 = 99.4 + 0.11 80 + 0 = 6.21 + 13.9

= + 20.97 = + 1.50 = + 59.90 =

8.528 + 3.905 = 0.445 + 2.995 = 2.882 + 0.566 =

25 h 25.01 h 101 ha 101.01 ha 80 I 80.01 1 12.425 12.433 3.440 3.448

Comparison of relative consumption with the preferences Rich person

(8.528 unitsX$0.1152)/[(2.882 units)($0.7951)] = 30%/70% =

0.429 0.429

Poor person

(3.905 unitsX$0.1152)/[(0.566 units)($0.7951)] = 50%/50% =

1.000 1

Comparison of income and spending Rich person

(10 h)($0.0592) + (100 haX$0.0118) + (801X$0.0188) = $3.276 (8.528 units)($0.1152) + (2.882 units)($0.7951) = $3.274

Poor person

( 15 h)($0.0592) + (I haX$0.0118) + (0 IX$0.0188) = (3.905 unitsX$0.1152) + (0.566 units)($0.7951) =

a Slight differences are due to rounding errors.

$0.8998 $0.8999

M. Ricker / Ecological Economics 21 (1997) 141-158

Besides income, the inequality of the modelsociety is calculated according to the following index:

Inequality=[i=~(li--IAvg)Z]/[(12Avg)(nZ--n) ], where I income of person i (~v~ average income n number of persons This index is normalized so that it ranges between 0 (all persons have the same income) and 1 (one person has all income, the others none). The first square brackets in the formula calculated an absolute inequality index in the same way as an unexplained sum of squares in a regression is calculated. It sums for each person the square of the deviation of his or her income from the average income. To normalize the result, in the second square brackets the same type of calculation is being made for the highest possible inequality. By dividing the actual absolute inequality index by the worst-case absolute inequality index, a relative, normalized inequality index results. The term in the second square brackets ( = worst case absolute inequality index) is derived in the following way:

[ li--IA~

+ ( 0 - - IAv~)2(n -- 1)

'k[i = I

:([IA,,gl[n]--IA,,g)e+(12A,,g)(n =(l~vg)(n--l)X+(12Avg)(n--1) =[IAv,l[(n--l)e+(n-- l)] =

1)

n)

in Table 1, the inequality is calculated as [($3.2760 - $2.0879) 2 + ($0.8998 - $2.0879) 2]/[($2.0879) 2( 2 2 - 2)] = 0,32 = 32%. In words, this means that the actual inequality is 32% of the highest possible inequality. In Table 1, it is not possible to see that the solution represents indeed an economic equilibrium, fulfilling all model conditions. To show this, some calculations have to be carried out, which is done for model I in Table 2. First, the actual weekly production is shown (calculated as explained above). Then production is compared with consumption, relative

147

consumption with preferences and income with spending. Table 2 confirms that the solution is correct; there are only some slight deviations due to rounding errors (the accuracy of the calculations can be chosen to any degree in the computer algorithm). For the following modified models (2-6) these calculations are not shown and the reader would need to carry them out by him or herself to confirm the solution. The general computer algorithm will simultaneously find for any number of goods the correct point on the production possibilities frontier (Fig. 1), determine the prices according to the preferences and distribute the available product quantities according to the ownership of endowments. In this case of two goods, the equilibrium distribution at the determined point on the production possibilities frontier and prices can be demonstrated graphically in an adjusted Edgeworth box (Fig. 2). The X-axis represents all available units of the low-technology good (12.43) and the Y-axis all available units of the high-technology good (3.45) in the market at equilibrium. This available product mix represents one point on the production possibilities frontier (Fig. 1). The lower left comer is the origin for the poor person and the upper right comer the origin for the rich person. To read off the situation for the rich person, one has to look at it after turning around the graph. Different from a usual Edgeworth box, here the two persons are not indifferent between different

"O O O

3.5,

(,9

tO O t.---

g

3. 2.5.

-r-

"6

2.

IE

1.5.

-O O "O

9

1. 0.5.

13..

0

0

~

~

~

1'o

12

14

Produced units of LowTechGood Fig. I. Production possibilities frontier for the low-technology good and the high-technology good in model I (Table 1).

148

M. Ricker / Ecological Economics 21 (1997) 141-158

~;Z[ o o 3.5 co 3 I-2.5 22

"5

O.

1

0.5 0

O_

~0 o I,~'0 -o m

°;t

o

Lz

o

L9-z

g

=-

c-

2

r- 1.5 -.1 c o tn

p o o g q O e l M O q JO sl!un s,uosJed qo!E I 01 ~'L ~ ~'~

........-"'"°

"1"

iiii;

-'-t o

2.5

5

7.5

10

tions are to be fulfilled, then that point must be where the two preference condition lines cross. Furthermore, if the prices of the goods and endowments are correct, then the budget constraint must also go through the equilibrium point. The budget constraint is a straight line and is one and the same line for both persons, because at given production the market will always be cleared, and what one person cannot afford because of limited endowments, will always be affordable by the other person. The budget constraint can be calculated as:

:g'£ O O

12.5

Income = ( PLowTechGood ) (

DLowTechGood )

Poor person's units of kowTechGood + ( PHighTechGood ) ( O HighTechGood )" I .............Budget constr. "...... Poor's pref

--

Rich's pref.

I

I

Fig. 2. Adjusted Edgeworth box for model ] (Tables 1, 2). The poor person wants to spend 50% income on the low-technology good and 50% on the high-technology good. His or her preference line is shown, starting in the lower left comer. The further away from the origin, the more income must be available. The rich person wants to spend a ratio of 30% to 70%. His or her preference line starts in the upper right comer and can be read off better by turning around the graph. Where the two lines meet, each person's preferences are met and the market is cleared completely. The budget constraint for both persons also goes through that point.

proportions of the two available goods and consqeuently there can be no indifference lines. Rather, for each person there is one line, which fulfills the preference conditions for different budget constraints. These lines are drawn for each person starting in their respective origin. For the poor person the preference condition is always (PLowTe~hGood)(Dt.owT~chGood) //[(VHighTechGood)(UHighTechGood)] = 0 . 5 / / 0 . 5

and with the calculated prices from Table 1 DHighTechGoo d =

(0.1449)(

DLowTechGood)"

The same can be done for the rich person to determine another straight line, starting in the upper left corner, which fulfills the rich person's preference condition, i.e., spending 30% for the low technology good and 70% for the high-technology good. If the market is to be cleared, then there can only be one point for both persons and if the preference condi-

Using the calculated prices and income in Table 1, the result for the poor person is DHighTechGood = 1 . 1 3 1 7 - (0.1449)(DLowmechGood). This concludes the presentation of the basic numerical model. Next, I will analyze how changes in this basic model affect overall weekly income as well as inequality.

3. A sequence of model variations affecting income and leading to different types of economic growth Assume that the poor person encounters on his or her hectare of land another source of oil, providing a weekly flux of 120 1. Model 2 in Table 3 shows the impact on the market equilibrium. In comparison with model 1, the price for labor has gone down by 14.4%, the price for land has gone up by 106.8%, the price for energy has gone down by 12.8%, the price of the low-technology good has gone up by 85.3% and the price for the high-technology good has gone down by 12.6%. The rich person buys 29.8% less of the low-technology good and 49.0% more of the high-technology good. The poor person, who has become much richer with the endowment increase, buys 65.1% more of the low-technology good and 250.2% more of the high-technology good. Both persons have become wealthier in monetary terms, the rich person by 30.0% and the poor person by 205.9%. Overall weekly income has increased by 67.9% and the inequality index has decreased from

M. Ricker/Eeological Economics 21 (1997) 141-158

Table 3 Model 2 (new fossil energy found by the poor person) Problem a.b Weekly endowments

Rich person Poor Person

Labor (h)

Land (ha)

Energy (1 oil)

10 15

100 1

80 120

Solution

Price ($) Labor Land Energy LowTechGood HighTechGood

0.0507 0.0244 0.0164 0.2135 0.6949

Weekly allocation LowTechGood HighTechGood (units) (units) Rich person Poor Person

5.991 6.447

4.295 1.981

Activity

I

2

3

Level

1.2425

0.7614

0.043 I

Production levels

Weekly income ($) Rich person Poor Person Overall Average

4.2590 2.7529 7.0119 3.5060

Inequality (%)

5

Preferences as in Table I. b Production possibilities set as in Table I. 32% to 5%. I will call this event economic growth based on endowment growth. It is of interest to interpret carefully these changes to understand the underlying system effects. It is easy to comprehend that an increase in the total endowment of energy in the market leads to a decrease in the energy price. This leads to an increase in the production level of activity 2, which is more energy-intensive and a decrease in the production level of activity 3. The high-technology good, which is much more energy-intensive, becomes cheaper. Activity 2 requires 3.5 h labor per produced unit of the high-technology good, while activity 3 requires 7

149

h labor per produced unit. By shifting from activity 3 to activity 2, less labor per produced unit is needed, and at given supply, labor is devaluated. On the other hand, land prices, and with it the price of the low-technology good, go up. The reason for this is that the persons keep the same relative spending preferences, and while more energy supply allows production of more high-technology good, there is no more land supply to allow increasing the production level of the land-intensive activity 1 to produce more low-technology good (note that the production level of activity 1 does not change between model 1 and 2). An increase in the energy endowment flux clearly leads to an increase of the model-society's income, and since the poor person happens to own the additional endowment, inequality goes down. Continued exploitation of non-renewable fossil energy will lead at some point to a decrease in the energy-flux endowment. The subsequent changes can be modeled by going the other way round, from model 2 as the initial state to model 1 as the future state. When the 120 1 oil per week of the poor person are not available anymore as an endowment because they have been depleted, then the energy prices go up and goods dependent on fossil energy, such as here the high-technology good, become more expensive. Next, assume that the model-society's population doubles from two to four persons. One new person brings with him or her 12 h labor and the other 17 h. Model 3 in Table 4 shows the equilibrium changes, given the preferences of the new persons. In comparison with model 2, the price for labor goes down, the price for land up, the price for energy down, the price for the low-technology good up, and the price for the high-technology good goes down. The changes are due to an increase in labor supply and a change of the preferences in the overall market, i.e., relatively less preference for the high-technology good and relatively more preference for the lowtechnology good. While overall weekly income increases by 24.3%, due to the increase in labor endowment and the higher land prices, the average weekly income per person decreases by 37.9%. This is a consequence of the poverty of the new persons, as they only bring with them labor. Population increase without endowment increases (other than own labor) clearly leads to a decrease of

150

M. Ricker/Ecological Economics 21 (1997) 141-158

Table 4 Model 3 (human population increase) a Problem Weekly endowments

Rich Poor New New

person person person 1 person 2

Labor (h)

Land (ha)

Energy (I oil)

10 15 12 17

100 I 0 0

80 120 0 0

LowTechGood

HighTechGood

30 50 40 60

70 50 60 40

Preferences

Rich Poor New New

person person person person

(%) (%) 1 (%) 2 (%)

Solution Prices ($) Labor Land Energy LowTechGood HighTechGood

0.0450 0.0329 0.0148 0.2791 0.6282

Weekly allocation LowTechGood (units)

HighTechGood (units)

5.298 4.462 0.774 1.646

5.492 1.982 0.516 0.487

Activity

I

2

3

Level

1.2166

0.2739

1.5683

Rich Poor New New

person person person 1 person 2

Production levels

Weekly income ($) Rich person Poor person New person 1 New person 2 Overall Average

4.9240 2.4839 0.5400 0.7650 8.7129 2.1782

Inequality (%)

22

a Production possibilities set as in Table 1.

average income per person and therefore to a negative per capita economic growth. In addition, if the new persons do not get an endowment share from existing endowments, then inequality increases strongly (in the model from 5% to 22%). With further increase of a population which owns only labor, and with limited endowments of land and energy, some labor becomes unusable (in the model labor would become a free disposal). This would lead to a marginal price of zero for labor and to unemployment, consequences which are clearly observable in today's world. Another economic change of major importance is an increase in production efficiency. Assume that activity 1 can be improved technologically to produce with the same inputs double output, i.e., 20 units of the low-technology good rather than 10 units. The rest of the production possibilities set remains unchanged. For simplification, in the model there is no research and development cost involved. In reality, an increase in production efficiency can be either cheap, stemming from an easy-to-implement idea, or expensive, stemming from long-term work in a research laboratory. One could model research and development as labor or as an additional good. Table 5 shows this model 4 and its equilibrium solution. In comparison with model 3, the prices for labor, land and energy have gone up, the price of the low-technology good down and the price of the high-technology good up. The production levels remain unchanged and for each person the number of units of the low-technology good has doubled. The relative prices of the inputs labor, land and energy have gone up because these endowments have become more productive; given unchanged quantities of endowments, the model-society's income has gone up. As the low-technology good is now produced more efficiently, i.e., with less inputs per unit, its price goes down. The efficiency of the production of the high-technology good relative to the low-technology good has gone down and therefore its price goes up. An efficiency improvement in the production possibilities set clearly increases overall weekly income (in the model by 14:6%). I will call this event economic growth based on production efficiency growth.

M. Ricker / Ecological Economics 21 (1997) 141-158 Table 5 Model 4 (increased production efficiency) P r o b l e m a.b Production possibilities set Activity

1

2

3

Labor (h) Land (ha) Energy (I) LowTechGood (units) HighTechGood (units)

- 2 - 80 - 5 20

- 28 - 2 - 250 0

- 28 - 2 - 80 0

0

8

4

Solution Prices ($) Labor Land Energy Lowtechgood Hightechgood

0.0523 0.0382 0.0173 0.1622 0.7300

W e e k l y allocation (units)

Rich Poor New New

person person person I person 2

LowTechGood

HighTechGood

10.593 8.917 1.548 3.289

5.493 1.982 0.516 0.487

Production levels Activity

1

2

3

Level

1.2166

0.2739

1.5683

W e e k l y income ($) Rich person Poor Person New Person 1 New Person 2 Overall Average

5.7270 2.8987 0.6276 0.8891 10:1424 2.5356

Inequality (%)

22

W e e k l y endowments as in Table 4. t Preferences as in Table 4.

Note that production efficiency growth in the model does not affect production levels and therefore the relative employment of the endowments remains unchanged. Consequently, the prices for the endowments remain the same relative to each other and rather increase proportionally by the same degree

151

(here approximately 16%). In turn, in the model inequality is unaffected by production efficiency growth. Finally, I like to explore the introduction of preferences for new goods. A new good could be truly new and stem from development in a laboratory, or it could be long existing but preference for it is new (e.g., because of marketing). This ambiguity is shown when first a new good is introduced that has the same production characteristics as the low-technology good, and therefore could indeed be the lowtechnology good itself, just stemming from a different production activity. Afterwards, a non-commercial good is introduced to demonstrate that commercial and non-commercial goods are not different, except in their form of being payed for. In the model, the introduction of any new good will always lead to a reduction of income by devaluating existing goods and endowments. To correct for this unwanted devaluation effect, the equilibrium prices have to be adjusted. To understand this, recall that the calculated relative prices for all goods and endowments always sum up to 1. In consequence, a market with one good has an average per unit price of $1, two goods an average per unit price of $0.5, three goods an average per unit price of $0.3333, and so on. The introduction of a new good takes away per unit value from other goods and endowments. However, it seems more realistic that the new good adds per unit value to the already existing goods and endowments, while the relative prices of the existing goods and endowments keep adding up to 1. Mathematically, an adjustment of the type (x)(Pl)+ ( x ) ( P 2) + ... = x causes no problem and one just has to choose x such that the relative prices of all but the new good(s) add up to 1. This will become clearer in the following example (model 5). Assume for the new good that the rich and the poor person each spend a weekly income share of 40%, while the other two persons do not want to obtain it (the proportions of the preferences for the other goods remain the same). The situation is depicted in Table 6 (model 5). The adjusted prices are shown together with the usual calculated prices. For the adjustment, I hold that the prices for labor, land, energy, the low-technology good and the high-technology good should still add up to 1, since the sum of the per unit values of these endowments and

M. Ricker / Ecological Economics 21 (1997) 141-158

152

Table 6 Model 5 (introduction of a new good)

Problem a Preferences (%)

Rich Poor New New

person person person I person 2

LowTechGood

HighTechGood

NewGood

18 30 40 60

42 30 60 40

40 40 0 0

Production possibilities set Activity

I

2

3

4

Labor (h) Land (ha) Energy (1) LowTechGood (units) HighTechGgood (units) Newgood (units)

- 2 - 80 - 5 20

- 28 - 2 - 250 0

- 28 - 2 - 80 0

- 2 - 80 - 5 0

0

8

4

0

0

0

0

20

Solution Prices ($)

Labor Land Energy LowTechGood HighTechGood NewGood

unadjusted

adjusted ( = P / ( 1 - 0.2293)

0.0296 0.0560 0.0105 0.2294 0.4451 0.2293

0.0384 0.0727 0.0136 0.2977 0.5775 {sum up to here is 1} 0.2975

W e e k l y allocation (units)

Rich Poor New New

person person person 1 person 2

LowTechGood

HighTechGood

NewGood

5.288 2.307 0.619 1.315

6.359 I. 189 0.478 0.452

11.755 3.076 0 0

3

Production levels Activity

1

2

Level

0.4758

0.2739

W e e k l y income with adjusted prices ($) Rich person Poor person New person l New person 2 Overall Average

8.7401 2.2836 0.4609 0.6529 12.1375 3.0344

Inequality (%)

41

a Weekly endowments as in Table 4.

4 1.5683

0.7409

goods has not declined. This is achieved by dividing all prices by (1 - 0.2293), where 0.2293 is the unadjusted price for the new good. The calculation neither affects the market equilibrium nor the inequality index, but it does affect the income results. As a consequence of the introduction of the new good, in comparison with the situation in model 4, the price of labor goes down by 26.6%, the price of land goes up by 90.3%, the price of energy goes down by 21.4%, the price of the low-technology good goes up by 83.5% and the price of the hightechnology good goes down by 20.9%. These changes are due to the relatively high land-requirement of the new good, which raises demand for land and therefore drives land prices up. With the higher land prices the rich person, who owns most of the land, becomes richer relative to the other persons and inequality goes up. Overall weekly income goes up by 19.7%. I will call such an event economic growth due to changes in preferences. If overall weekly income increases or decreases with the introduction of a new good, depends on the effect it has on endowment prices, which in turn depends on the mix of endowments employed for its production. For the non-commercial good, assume that the model-society has discovered its taste for wilderness area. Model 6 in Table 7 shows the different preferences of the persons to pay (in whatever form) for the non-commercial good. Activity 5 uses 1 ha of land to produce 1 ha of wilderness. Again this is a new good and again the prices have to be adjusted as in model 5. In comparison with model 5 in Table 6, the price for labor goes down, the price of land up and the price of energy down. Land prices go up, because land is more demanded and as a consequence, the land-intensive low-technology good and NewGood become more expensive. The energy price goes down, because relative to land, energy is less demanded and with it the high-technology good becomes cheaper. The rich person as the major land owner becomes much richer, while the other persons become poorer, and inequality goes up. Overall weekly income goes up by another 12%. Note that the price for land used for production and land used for wilderness is identical. This must be so, because the price of the endowment 'land' is independent of its use. This example shows that the general equilibrium model does not treat non-commercial goods differ-

M. Ricker / Ecological Economics 21 (I 997) 141-158

153

Table 7 Model 6 (introduction of a non-commercial good) Problem

a

Preferences (%)

Rich Poor New New

person person person 1 person 2

LowTechGood

HighTechGood

NewGood

NonCommGood

12.6 24 36 54

29.4 24 54 36

28 32 0 0

30 20 10 10

1

2

3

4

5

- 28 - 2 - 250 0 8 0 0

- 28 - 2 - 80 0 4 0 0

- 2 - 80 - 5 0 0 20 0

0 - I 0 0 0 0 I

Production possibilities set Activity Labor (h) Land (ha) Energy (I) LowTechGood (units) ItighTechGood (units) NewGood (units) NonCommGood (units)

- 2 80 - 5 20 0 0 0

Solution

Prices ($)

Labor Land Energy LowTechGood HighTechGood NewGood NonCommGood

unadjusted

adjusted ( = P/(1 - 0.3306)

0.0188 0.0654 0.0074 (I.2653 0.3124 0.2652 0.0654

0.028 I 0.0977 0.01 I1 0.3963 0.4667 {sum up to here is 1} 0.3962 0.0977

Weekly allocation

Rich person C'nor perslm XIcw pcrson I ~,lew person 2

LowTechGood (units)

HighTechGood (units)

NewGood (units)

NonCommGood (ha)

3.478 1.121 0.307 0.652

6,892 0,952 0.391 0.369

7.731 1.495 0 0

33,599 3.789 0.346 0.490

,~roduction levels ~ctivity

1

2

3

4

5

Lcvcl

0.2773

0.2719

1.6043

0.4607

38.2128

Weekly income with adjusted prices ($) Rich person Poor person New person I New pcrson 2 O~ erall A~erage

10.9352 1.8455 0.3370 0.4774 1.5952 3.3988

Inequality (%)

56

a Weekly endowments as in Table 4.

154

M. Ricker / Ecological Economics 21 (1997) 141-158

ently from commercial goods. Only their interpretation is different: non-commercial goods are demanded goods (or values) that cannot be purchased on a market, because they are collectively consumed. While generally the government a n d / o r non-profit organizations have to secure their supply, the possibilities and limitations for contributing to wealth and economic growth are the same for non-commercial goods as is the case for commercial goods.

14"

12. 69-

r.- 10.

E 0 0 C ~ 2~ Ill I1~

8. 64"

1

4. Discussion

2

3

4

5

6

Model number

I used a computable general equilibrium model to demonstrate the dependence of society's income on its endowments, production possibilities and preferences. The model simplified a closed economy in market equilibrium, in which two to four persons or consumer groups depend completely on labor, land and energy. The only existing wealth consisted of the peoples' weekly income. Non-commercial goods can be and were treated in the same way as commercial goods, except that in the real world payment for them occurs via taxes, donations or foregone income. I defined economic growth as the growth of the value a society puts in monetary terms on all commercial and non-commercial goods and values it possesses during a certain period. In the model, economic growth was equal to increased overall weekly income. Fig. 3 shows the changes of income during the sequence of economic changes, presented in models 1 to 6 (Tables 1-7). Model 1 represented the basic model. In model 2, income increased after new energy endowment was found. In model 3, population increase brought with it new income from labor, but decreased average income. In model 4, production efficiency, and in models 5 and 6 the introduction of preferences for new goods with favorable effects on endowment prices, made the overall income grow further. Fig. 4 shows for the same sequence for the corresponding changes in the inequality index. Inequality goes down, when the poor person obtains more energy endowment, goes up with population growth without endowment growth or redistribution, remains the same with increased production efficiency and increases with the introduction of preferences for

I [z"~'~ Rich pet's. ~

Poor pors. l

New #'

~ ] ~ New #2

I

Fig. 3. Changes of the individual and overall weekly income in the sequential economic changes from model I to 6 for the four persons involved (see Tables 1-7). Model I is the basic model. In model 2, income increased after new energy endowment was found. In model 3, population increase brought with it new income from labor, but decreased average income. In model 4, production efficiency and in models 5 and 6 the introduction of preferences for new goods with favorable effects on endowment prices, made the overall income grow further.

new goods, which cause changes in the prices of the endowments. While one can discuss oversimplifications in the model, the real world economies depend in the same way on endowments, production possibilities and preferences. For discussing limits to economic growth, we must discuss limits to the growth of the endowments, to improvements in the production pos100" 90' 80'

o~

70

•-

60

-~ ::3 D" C

50" 40

-- 3 0 ~ 20

":

Y

10 0

Model number Fig. 4. Changes of the inequality index in the sequential economic changes from model I to 6 (compare Fig. 3).

M. Ricker / Ecological Economics 21 (1997) 141-158

sibilities and to favorable changes of people's preferences. Environmentalists have traditionally pointed to limited endowments, while economists have stressed possible changes in the production possibilities. It is common sense that on earth all physical endowments are ultimately limited. It has been generally less emphasized that energy as an endowment m the economic process is of superior importance (see Faucheux, 1993). Using energy, most matter can be recycled (Bianciardi et al., 1993a; Bianciardi et al., 1993b) and hand labor can be substituted. Energy-dependent economic growth is necessarily limited. Using fossil energy, accumulated millions of years ago, means using the earth's solar energy savings from the past. While in the real world up to the present days, more and more sources of fossil energy have been found, it is clear that the overall stock of fossil energy is limited and that the world's fossil energy endowment is decreasing (see Miremadi and Ismail, 1994). Even maintaining fossil energy fluxes is impossible in the long run and therefore economic wealth dependent on constant fluxes of fossil energy can only be temporary. Once fossil energy is mostly used up, we will rely on the daily solar energy and possibly on nuclear energy (see Rietjens, 1991). Nuclear energy represents savings of energy in matter. Its reserve is huge (in particular when fusion is employed (Rietjens, 1991)), but its employment is also dependent on input of fuel elements and output of harmful waste. Its use is of great political difficulty and therefore may be unwise (compare Nilsson and Abrahamson, 1991). This leaves us with a secured daily influx of solar energy. Given the world's present energy consumption of about 11 TW (1 tera watt = 10 ~2 watt), the available energy power from the sun with 120,000 TW plus 405 TW from wind, waves, geothermal sources and ocean tides, still represents an enormous power reserve. At present estimates, we still have about 100 years with fossil fuel energy before we have to be completely adapted to solar energy use (if not to deuterium-deuterium fusion) (Rietjens, 1991). Much scientific progress has still to be made. For example, Pimentel et al. (1994) estimate that currently 40% of the U.S. energy consumption could be produced employing solar energy technologies, but would still require about 20% of all U.S. land. Despite climatic fluctuations in the long term, we

155

have to consider solar energy as an approximately constant flux of energy, and cannot build economic growth on an increase of the solar-energy endowment. Assuming that one day worldwide energy consumption will be on the long-term average constant because we depend on the daily solar influx, it follows that the equilibrium between resource consumption and recovery must be constant, given a constant energy share for the resource's use as long as depletion is undesired. Then the world's economy could only grow if societies took advantage of energy-independent economic growth. Increasing production efficiency is energy-independent (in the sense that it can be increased without increasing the energy endowment). Nevertheless, thermodynamics dictates upper limits for increasing production efficiency. Any production process requires input of energy and increases entropy when analyzed as an isolated system (second law of thermodynamics, see Moore, 1972). Consequently, it is impossible to have a production process that produces an infinite number of units, whose energy could be used in turn to fuel the production process: The perpetual motion machine is impossible (as physical goods, the units necessarily contain some energy). Economic growth based solely on increasing production efficiency is necessarily limited as is economic growth based solely on increasing the endowments. After having considered endowments and production efficiency improvements, the last option to look for growth possibilities is to look at changes of preferences. To analyze the limits to income growth from preference changes, I consider that all preferences are reflected ultimately in the prices. Looking on the general equilibrium model, one finds that it has numerically an upper limit of obtainable overall income, when maximizing with endowment fluxes being fixed, and with endowment prices as variables. Recall that income is determined by the quantities of the endowments times their respective relative prices. In model 1 (and similarly in any general equilibrium model), the upper bound of overall income can be calculated as the following linear programming problem: MAX(25 h)(PLbo~) + (101 ha)(PL,,,a) + (80 l) (PE,,~rg,)

156

M. Ricker / Ecological Economics 21 (1997) 141-158

subject to

eLabor + BLand + eEnergy + BLowTechGood + eHighTechGood = l BLabor, BLand, BEnergy , BLowTechGood, eHighTechGood >__0 The condition that the five relative prices add up to 1 means that there is a fixed amount of value for the five units (having one unit of each endowment or good), which is divided to assign each unit individually a relative value, i.e., a price. To say that the total value is l is arbitrary, but that the total value is fixed represents the reference point to determine all prices relative to each other. The solution consists in an upper bound for overall weekly income of $101 with a price of $1 for land (or in general the numerically largest endowment), and a price of $0 for each labor, energy and the two goods (or in general all remaining endowment and goods). This is an unrealistic outcome, but is could be approximated in the real world. In words, this result means that people could prefer those economic activities which make use just of that endowment which is largest in available quantity flux and produce high quantities of goods at very low prices. That would lead them to the ultimate maximum of economic income. Note that the above income maximization does not change when one considers the introduction of new goods with adjusted prices, as in models 5 and 6. With adjusted prices, the condition that the five original prices add up to 1 remains unchanged when new goods are introduced. Consequently, the highest income is still obtained with a price of $1 per unit of that endowment which numerically is in largest quantity. As a result of the analysis, I conclude that all economic growth as measurable in monetary terms, is limited. To predict in the real world the limits to economic growth is a much more complex enterprise than in this model. Not knowing the true stocks of endowments, all production possibilities and all technologies to improve them, it is not possible to determine the real world limits to economic growth. Nevertheless, I have shown that such an upper limit must exist as long as the endowments are limited.

Despite the existence of limits to economic growth, we might still have much room before we get close to them. There should be consensus that economic growth based on production efficiency growth is highly desirable. Manipulating preferences is not really a choice in a free society, but providing information on goods from efficient and environmentally sound production can lead and has led to a kind of responsible shopping. The most heavily discussed aspects of economic growth have been the non-inclusion of non-commercial goods and the increased exploitation of natural resources, i.e., unsustainable endowment growth. The first aspect concerns the indicator of measurement of economic growth. It would be possible to measure and include in an indicator some of the non-commercial spending in terms of taxes spent for such goods and donations given; in some cases it is also feasible to measure forgone income. If the smog level can be decreased in, say, Mexico City, one could add the saved costs of people being sick from smog to the value of a commercial indicator such as gross national product; these saved costs represent the wealth increase in monetary terms. Such an improved indicator of economic growth would also help to put into perspective mining and exploitation of non-renewable resources. Those activities frequently have tremendous externalities in the form of landscape destruction and pollution. If those environmental costs entered the indicator as a reduction of non-commercial goods, the true economic value of recycling would become much more obvious. This concludes the discussion on economic growth. However, so far we have left out another interpretation of the general equilibrium model. There are some changes of economic nature which don't lead to income changes in the model and therefore don't lead to economic growth, but which do lead to an increase of society's utility ( = happiness or satisfaction). I will call all those events pure utility growth to contrast it with economic growth. All forms of pure utility growth have in common that they cannot be measured in monetary terms because there is no absolute reference point: 1. The simplest form of pure utility growth is achieved when all people become happier with what they have; this would be some kind of psychological event and it would be of interest to

M. Ricker/Ecological Economics 21 (1997) 141-158

know what type of information can trigger such a process. For example, experiencing poverty makes one appreciate much more given wealth. 2. Assume that in the general equilibrium model all activities remain the same, but in each a more appreciated good is produced, while the endowments and preferences remain unchanged. That process constitutes a form of economic advance without any numerical changes in the model: All have increased utility, but no relative economic adjustments are required. We could be less stringent on the timing, and say all goods are replaced by more appreciated ones, although not exactly at the san~e time. Then there would be continuous adjustments in the model, which however in the long term would nevertheless lead to the same outcome: A society with higher utility. An example are the medical advances over the last century. This leads to a discussion on the importance of the advancement of knowledge and values, which can not simply be included in an indicator of economic growth. Pure utility growth is obviously of great interest. While it is hardly feasible to measure it objectively, we can nevertheless try to advance it by forwarding technology and knowledge, and discuss values.

5. Conclusions The computable general equilibrium model has led in an intuitive way to the following conclusions: • Societies should start to use appropriate indicators for true economic growth, rather than just for commercial growth as measured by gross national product; 2. All types of economic growth are limited, no matter if based on endowment growth, production efficiency growth, or changes in preferences; 3. Economic growth should be oriented more towards increasing production efficiency and less towards using more natural resources; 4. Human population growth puts at risk the possibilities for average economic growth per person; 5. We should get better prepared to use solar energy in the future;

157

. Besides economic growth, there exists pure utility growth, which is not measurable in monetary terms; it includes much of scientific progress in the long run and is of great importance even though it cannot be included in an indicator of economic growth.

Acknowledgements I am indebted to Professor Herbert E. Scarf (Dept. of Economics, Yale University), who taught me theory and application of the general equilibrium model in his class on mathematical economics, as well as in many discussions. He also kindly provided a computer program for the calculations. I am grateful to Professor Robert O. Mendelsohn (School of Forestry and Environmental Studies, Yale University) who taught me much of my knowledge on natural resource and environmental economics. Professor Martin O'Connor (UFR de Saint-Quentin-enYvelines, France) and one anonymous reviewer gave very helpful comments.

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