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Energy and the Israel economy
74
Energy and the Israel economy Avishai B R E I N E R a n d Reuven K A R N I Energy Planning and Policy Research Group, The Management Sciences Research Centre, Faculty of Industrial Engineering and Management, Teehnion-lsrael Institute of Technology, Haifa 32000, Israel Received September 1981 Revised January 1982
The OMER macroeconomic model has been developed in order to examine the interactions between energy and the Israel national economy. This paper presents a description of three sets of scenarios which study the manner in which the 'mix' of industries and their output levels could be affected if a maximal and minimal effort were made to provide the necessary energy requirements for the economy. Several assumptions are also made as to the probable increase in energy prices to the end of the century. In general, the effect of higher energy prices is to spur industrial activity towards exports in order to pay for energy imports, at the expense of private consumption. Thus industry is less affected than private consumption. Nevertheless, a shift is made towards less energy-intensive industries, and the reduction of transportation levels. Finally, if only minimal outlays on energy are made, both energy requirements and growth rates fall to about one-half of those when maximal required outlays are made.
1.
I n t r o d u c t i o n
The OMER (Optimizat~'on Model for Energy Resources) study, sponsored by the Ministry of Energy and Infrastructure in Israel, is intended to provide planners with a consistent analytical framework for studying the energy supply sector and its interactions with the national economy during the period 1980-2000. During this time, the energy sector is expected to change from one based almost entirely on imported oil, to one based on imports of oil, coal and nuclear power, as well as those local energy resources (hydroelectric
power and solar energy) which could be exploited by the end of the century. In the face of such radical change, the OMER energy-economic model has been used to explore the implications of both short and medium range energy-related decisions and scenarios. The OMER model is a linear programming model [1,2,3,5] consisting of the following major components: - energy supply sectors--process type sub-models of activities relating to refining and electricity generation; - industrial (non-energy) sectors of the economy, aggregated into 15 sectors and 7 usage groups--described by means of a Leontieff type input-output matrix; - investments in energy and non-energy sectors-described by means of an investment matrix; - public and private consumption; foreign trade, encompassing exports, imports and the trade balance. The set of scenarios described in this paper is intended to encompass two ends of the possible spectrum of activity in the energy sector and its relation to the national economy--minimum investment in the energy sector and outlay on imported fuels; and optimal investment in the energy sector and imported fuels, consistent with maximum growth in consumption. Thus two objective functions have been used in the analyses: - m a x i m i z a t i o n of discounted gross domestic product (private and public consumption, investment and exports, less imports); minimization of the discounted investment in the energy sector (refining and electricity generation capabilities) and the energy import bill. In view of the energy situation, several constraints are assumed to act on the Israeli economy: - the necessity to diversify energy sources, mainly by introducing coal and nuclear power; the necessity to cope with rising prices of imported oil, coal and nuclear fuel; the necessity to reduce--and even eliminate-the deficit in the balance of trade, and the growth of defence imports; the necessity to reduce the growth of consumption in the public sector. -
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Research was sponsored by the Israeli Ministry of Energy and Infrastructure. The authors are solely responsible for the views expressed here. North-Holland Publishing Company European Journal of Operational Research 13 (1983) 74-87
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0377-2217/83/0000-0000/$03.00 © 1983 North-Holland
75
A. Breiner, R. Karni / Energy and the Israel economy Table 1 Nonenergy industrial sectors in the O M E R model Industrial sector
Sector fraction in total nonenergy output a (percent)
Cost of energy in sector output b (percent)
Energy intensity of sector output c (t.o.e. per 106 IS)
Energy usage group d
Water Chemical, plastics Mining, glass, cement Metals, metal products Machinery, equipment Textiles Wood, paper, print Agriculture Food, beverages, tobacco Diamonds Road transport Sea and air transport, communications Construction Services Trade
0.7 5.0 2.8 5.8 8.1 5.6 4.4 7.6 10.0 3.6 4.3 6.5 12.5 15.0 8.1
30.0 5.3 11.3 2.0 1.5 3.2 2.3 5.0 4.2 0.1 13.1 10.1 3.6 1.5 2.0
305 43 149 16 6 16 19 14 16 1 97 43 9 6 8
4 1 1 2 3 2 2 4 2 3 5 5 6 7 7
a Output share: According to 1975/76 output levels. b Energy share." Based on total i n p u t - o u t p u t coefficients of primary energy sources. c Energy intensity: Based on direct i n p u t - o u t p u t coefficients of electric and non-electric energy, corrected to October, 1980. Energy group." 1: High energy-intensive manufacturing, 2: Medium energy-intensive manufacturing, 3: Low energy-intensive manufacturing, 4: Water and agriculture, 5: Transportation and communication, 6: Construction, 7: Trade and services. Table 2 Energy requirements by consumption sector (percentages for 1975) Consumption sector a
Electricity and refining losses Water Chemical, plastics Mining, glass, cement Metals, metal products Machinery, equipment Textiles Wood, paper, print Agriculture Food, beverages, tobacco Diamonds Road transport Sea and air transport, communications Construction Services Trade Public consumption Private consumption Other Total c
Electricity
Petroleum products b
Total
1.3 17.4 6.1 5.6 4.1 2.9 4.3 2.5 2.1 4.4 0.2 0.1 1.2 0.5 2.0 5.6 9.0 29.2 1.5
11,8 0,4 7.0 12.6 1.4 0.3 1.3 1.9 3.9 3.8 0.0 14.6 7.5 4.3 1.0 0.0 11.5 11.7 5.0
8.2 6.2 6.7 10.2 2.3 1.2 2.3 2.1 3.3 4.0 0.1 9.7 5.3 3.0 1.3 1.9 10.6 17.7 3.9
100.0
100.0
100.0
Breakdown in O M E R model. b Excluding 2.35 x 106 t.o.e, for electricity generation c Total electricity consumption (1975): 8,25 x 109 kWh. Total petroleum product consumption (1975): 6.87 x 106 t.o.e.
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A. Breiner, R. Karni / Energy and the Israel economy
The effects of these constraints on the energy e c o n o m y have been described in detail elsewhere [3]. This paper concentrates on the industrial sectors and private consumption. A schematic and mathematical outline of the model is given in the appendix.
2. Energy consuming sectors The energy consuming sectors have been aggregated into 15 industrial sectors and four final d e m a n d s e c t o r s - - p u b l i c consumption, private consumption, investment and exports. I n p u t - o u t put data for the industrial sectors have been derived from tables issued by the Central Bureau of Statistics for the year 1975-1976, and corrected for energy c o n s u m p t i o n according to the latest data available. The output and energy consumption characteristics of these sectors is detailed in Tables 1 and 2. A further aggregation into seven usage groups has been made, in accordance with the energy intensity of output, and the type of sector. Energy consumption in Israel has the following general characteristics: - A b o u t 35% of all primary energy is used to generate electricity. (Water p u m p i n g - - m o v i n g water from where it is available to where it is n e e d e d - - c o n t r i b u t e s significantly to this high percentage.) As the shift to a mix of oil, coal and nuclear fuels impacts the electricity sector in the main, it is one of the policies of the Ministry of Energy and Infrastructure to move towards raising the electricity share even higher. - The main consumers of electric power are the private and water p u m p i n g sectors. Most water is used for agricultural purposes. Thus, if consumption of electricity is to be reduced, either agricultural activity will have to be c u r t a i l e d - - a t the expense of exports, and possibly, increased imp o r t s - o r the private sector will have to reduce its requirements in some manner. - The main consumer of petroleum products are the chemical and mineral industries, and the transportation sector. Large amounts of energy are required to manufacture petrochemicals, potash, phosphate and cement. The extent of these industries would have to be curtailed in order to decrease petroleum product consumption. In the transportation sector, the provision of fuel for air
and sea purposes constitutes the only likely way of reducing consumption here. - Finally, the public and private sectors are large consumers in both areas. Thus both these sectors are likely to be vulnerable to efforts to reduce overall consumption. As public consumption is set exogenously in the O M E R model, different levels have been assumed for the various scenarios (see Table 3); any further reductions will be at the expense of the private sector.
3. OMER scenarios Three series of scenarios, based upon assumptions on energy prices, trade deficits and public Table 3 Key input assumptions for OMER scenarios - Series I: Series II: Series IIl:
Continuation of current trends in trade balance, public consumption and defense imports Reduction or balancing of trade balance, public consumption and defense imports As for Series II, but with minimization of energy imports and investments, with the growth in private consumption not less than 1% per capita per annum
Fuel
Low price (L)
(all scenario series): Base High price price (a) (H)
Crude oil Coal Nuclear fuel
2% 2% 2%
5% 3% 3%
- A n n u a l p r i c e escalation o f imported fuels
8% 4% 4%
- Foreign trade deficit:
Series I: 2% annual growth to 1985, then no growth Series II, 1II:2% annual decline to 1985, then no decline (II(B),) Series II: 9% annual decline to 1985, then no decline (II(B)z) - Defense imports:
Series I: 2% annual growth Series II, IIl: No growth - Total public sector consumption:
Series I: 4.6% annual growth Series II, III: 4% annual growth - R a t e o f population growth:
1.95% per annum
- Objective:
Series I, II: Maximizediscounted gross domestic product Series III: Minimizediscounted energy imports and investments
A. Breiner, R. Karni / Energy and the Israel economy
77
4. General macro-economic and energy-related results
spending, have been carried out. The key assumptions underlying the scenarios are detailed in Table 3. The six scenarios form a gradation in the severity of the constraints affecting the energy bill and the trade balance, from scenario I(L) which assumes low energy price rises and little constraint on the trade balance, through scenario III(B), which tries to minimize activity in the energy sector, with a minimal rise (1% per capita, or 3% overall in private consumption growth). They thus provide a spectrum of possibilities of the effects of the constraints on the Israel economy and its levels of output and consumption.
A summary of some economic and energy consumption figures produced by the model, for the six scenarios, are presented in Table 4, 5 and 6, and in Fig. 1. In Table 4, the macroeconomic indicators refer to the general economy, energy consumption patterns, and energy outlays. (A detailed analysis of energy supply characteristics over the period studies is provided in [4]). The Series I scenarios study the effects of energy prices. As the rate of price rises increases, GDP and private consumption
Table 4 Macro-economic indicators for OMER scenarios (annual growth rates unless otherwise stated) Indicator
GDP growth P e r capita consumption growth Industrial output growth Industrial investment growth
Base values (1980) a
Series II
L
B
H
(%)
(%)
(%)
BI
(%)
Series III B2
(%)
B
(%)
145.109 (IS)
5.7
5.3
4.4
4.5
4.4
3.3
22.103 (IS) 230.109 (IS)
4.5 5.8
3.8 5.7
2.1 5.7
3.0 4.7
2.4 4.8
2.5
40.109 (IS)
4.1
4.0
3.8
3.2
3.3
2.4
8.106 (t.o.e.)
5.2
4.8
4.2
3.5
3.4
2.4
15.105 (t.o.e.)
6.1
5.4
3.9
4.7
4.1
2.8
13.109 (kWh)
5.2
4.9
4.7
3.9
3.9
2.8
3.109 (kWh)
5.0
4.4
3.4
3.7
3.3
2.5
0.8.106 (t.o.e.)
7.0
6.2
4.3
4.9
4.1
3.1
Local energy consumption growth Household energy consumption growth Local electricity consumption growth Household electricity consumption growth Household petroleum product consumption growth Electricity consumption within total consumption c Energy import bill growth Energy import share in GDP c Energy investment growth Energy intensiveness growth per unit of output = 7.5 IS. b Fixed exogenously (as lower limit). By the year 2000. a 1 us$
Series I
36% 2.109 (US$) 12% 30.109 (IS) 37 (t.o.e./106IS)
36
37
41
40
1.0 b
41
41
2.8
8.1
10.0
7.1
7.0
5.6
12 6.4
20 6.3
34 6,2
20 4.3
20 4.3
19 2.7
-0.4
-0.8
-1.4
-1.3
-1.3
-
1.2
78
A. Breiner, R. Karni / Energy and the Israel economy
Table 5 Output levels of energy usage groups in the industrial sectors for the years 1980 and 2000 for OMER scenarios Energy usage group (1)
High energy-intensive manufacturing Medium energy-intensive manufacturing Low energy-intensive manufacturing Water and agriculture
Base values (1980) (2) 9.7 26.7 13.6 6.7
Transportation and communication Construction
15.4
Trade and services
19.4
Total
8.4
100.0
Series I
Series II
Series III
L (3)
B (4)
H (5)
BI (6)
BE (7)
B (8)
9.5 (54) 27.4 (84) 16.4 (100) 3.0 (110) 6.5 (113) 13.4 (111) 23.8 (108)
6.3 (100) 33.3 (100) 16.9 (100). 2.8 (100) 5.9 (100) 12.3 (100) 22.5 (100)
4.9 (73) 36.1 (101) 17.9 (100) 2.7 (91) 5.7 (91) 13.3 (102) 19.4 (81)
2.6 (32) 34.8 (83) 21.0 (100) 3.6 (105) 5.6 (77) I 1.0 (71) 21.4 (76)
2.0 (25) 33.0 (78) 21.1 (100) 3.6 (104) 5.3 (72) 11.8 (76) 23.2 (81)
2.4 (22) 27.7 (49) 28.2 (100) 2.9 (61) 4.8 (49) 11.5 (56) 22.5 (59)
100.0 (102)
100.0 (100)
100.0 (94)
100.0 (80)
100.0 (79)
100.0 (59)
Column (1): Energy usage group (see Table 1). Column (2): Percentage output level (IS/Total IS) of the group during 1980. Columns (3)-(8): Percentage output level (IS/Total IS) of the group by the year 2000; and percentage output level (in brackets) of each group relative to its output in Scenario I(B) (the 'standard' scenario), all by the year 2000.
a small reduction in the growth rate of energy consumption occurs, mainly in the private sector, accompanied by a trend towards electricity as the main energy source. Thus higher energy prices, coupled with the shift to cheaper coal and nuclear fuels, encourage the use of electricity, rather than lead to an overall reduction in energy consumption. As can be seen from Table 5, the move to less
growth fall off. Industrial output and investment, however, remain relatively unaffected. As the energy import bill is seen to rise drastically, we may conclude that industrial activity is geared to meeting the level of exports required to meet this bill. (We assume in the model that the level of exports from Israel is insignificant in the world market, so that all required exports will be taken up.) Overall,
Table 6 Relative levels of activity of industrial sectors, private consumption and energy consumption by the year 2000 for OMER scenarios Series I
Industrial sectors Private consumption Energy consumption
Series II
Series III
L
B
H
B~
B2
B
102 (5.8) 115 (7.6) 110 (5.2)
100 (5.7) 100 (6.9) 100 (4.8)
94 (5.7) 67 (5.1) 89 (4.2)
80 (4.8) 76 (6.1) 74 (3.5)
79 (4.7) 75 (5.3) 75 (3.4)
5 (2.5) 58 (4.0) 57 (2.4)
Percentages relative to the 'standard' scenario I(B), and (in parentheses) annual growth rates between 1980-2000.
79
A. Breiner, R. Karni / Energy and the lsrael economy
4007:.
-
Medium_energy-intensive manufacturing 151
i -5
i I Low ener~y-inlensive 'manu[qcturln I L ~! i
,,'
i
,
L
,! il
u
5o7,-
~u~tu~
aQd~ a t e ~ I
I
5
l
~-~ ~
Ill
]Clon!t~c!iln I
25%~¢ ///~///Tr/;p°rt/at/i°n. a/nd/C°~un~
andServices
__Trade
¢q75
Cqdo
T
T
4985
4?9o
T
000
Fig. 1. Relative nonenergy industrial output in base case.
energy-intensive industries allows the level of output to be maintained with some reduction in energy requirement. In order to effect the shift in energy base, the growth rate of investment in energy remains constant, and higher than that for non-energy industry. The proportion of energy import costs in the G D P is expected to double, in the 'standard' case, by the end of the century, and even triple should energy prices rise faster than generally expected. If energy prices increase at the expected rate, but efforts are made to reduce or eliminate the trade deficit (Series II), all growth rates are seen to be depressed, including industrial output, leading to a general slowdown. Nevertheless, only private consumption decreases from one scenario to the
other; other levels remain constant in order to cope with the increased pressure on the trade balance. Again, the shift to a higher degree of electrification is noticeable. Some small reduction is achieved in the growth of the energy import bill. When only minimal investment in the energy sector and energy imports are allowed (Series III), all levels of growth are seen to fall to about one half of the 'standard' rate, indicating the severity of restrictions on energy availability. Private consumption, however, falls to one quarter of the 'standard' rate. The consumption pattern for electricity is maintained, and the energy bill remains at about 20% of the total GDP. Again, the reduction of the energy import bill growth (to 6%) is rather small.
80
A. Breiner, R. Karni / Energy and the Israel economy
5. Energy and the industrial sector Table 5 describes the effects of the various scenario assumptions on the structure of the nonenergy indUstrial sectors by the year 2000. This structure is portrayed in two ways: the percentage output level of each usage group within all groups, and the output index of each group, using scenario I(B) as the standard (index = 100 for each group). Dealing first with the output index, we notice that the total output level is unaffected by increased prices--as we have commented in the previous section--but falls to 80% as trade balance restrictions are introduced, and then to 60% as only minimal energy requirements are met. The output of low-energy intensive manufacturing is maintained throughout, and water/agriculture as well--except for the last scenario. The other groups follow the overall pattern, in general, except for high energy-intensive manufacturing, which, although very profitable when energy prices are low, rapidly become a burden as the price situation changes for the worse, reaching one quarter of their expected level in the worst case. These output levels affect the proportions of each group in the overall structure: high energy-intensive manufacturing drops from 10% to 6% and even 2% of overall non-energy industry, whilst medium energy-intensive manufacturing rises from 27% to 33%, and low energy-intensive manufacturing from 14% to 17% and even 28% in the severe scenario. The proportions of construction (12%) and trade and services (23%) remain relative constant, whilst those of water/agriculture and transportation drop to about one half.
6. Energy consumption, industries and private consumption Table 6 provides a concise summary of overall growth rates and activity levels for the industrial sector, private sector and total energy consumption. For the pricing scenarios (Series I), the private
sector is seen to be the most affected, in order to achieve lower energy consumption levels and growth rates; industry, as we have mentioned, must maintain its level of growth and output for export in order to compensate for the higher energy bill. For the trade balance scenarios (Series II, III), all three factors are, roughly, equally affected; a general slowdown and reduction in consumption is the only way of coping with the financing of the energy bill. In summary, subject to the structure and assumptions inherent in the current OMER model, we see that a significant amount of investment in the energy sector, leading mainly to a higher degree of electricification, is required in order to face up to higher energy prices and increasing difficulties in paying for energy. On the one hand, nonenergy industries will have to increase levels of exports to pay for imported energy; on the other, the private sector will have to 'pull in its belt' in order to reduce consumption and allow for increased investment. Nevertheless, we notice that all growth rates remain positive, and above the level of population growth (1.95% per annum), indicating that, provided the correct policies are carried out (and our model can only make humble recommendations in this respect), some of the worst aspects of the energy crisis can be coped with.
7. Energy-output.elasticities A convenient way to specify the degree of coupling between aggregate economic growth and energy demand growth is by means of an energy-output elasticity, relating the ratio of total energy requirement across any two points in time, to the ratio of industrial output at the same two points. The current value for Israel is about unity, indicating that economic growth and energy growth go hand in hand at present. The average elasticity values between 1980 and 2000, derived from the six scenarios, are as follows shown in Table 7.
Table 7
Average elasticity values between 1980 and 2000 Scenario Elasticity
I(L) 0.92
I(B) 0.86
I(H) 0.74
II(B) l 0.74
II(B)2 0.73
Ill(B) 0.69
A. Breiner, R. Karni / Energy and the Israel economy
These values imply a strong ability to adjust to constraints on energy availability and cost, via structural changes in industry and reduction of final demand for energy. However, the degree of flexibility inherent in the OMER model in its present form is a function of the freedom given to the model to expand or contract the level of activity of each individual sector. In linear models as is well known, a sector may be totally eliminated; in the real world this is not usually allowed to happen. In the current version of the model, in order to avoid the introduction of a large number of constraints, the upper limit on the level of activity of each sector has been set exogenously, equivalent to a maximum growth rate of 7.5% per annum relative to the 1975 value; and a lower limit as the 1975 value itself--i.e. 0% growth rate. These upper and lower bounds provide too much flexibility in the Series I(H), II and III scenarios, thus resulting in a large range of elasticity values obtained. More complex bounds on each sector would lead to a much smaller, and more realistic, range of elasticity values.
8. Limitations
of the model
When considering the results produced by the model, it is important to point out certain limitations of the model structure. These limitations influence the type of results obtained, and thus any conclusions that may be drawn from them. The most important drawbacks in the current version of the OMER model are as follows: - The same input-output data for the non-energy industrial sectors (based on the table for 1975/76) is used for all periods from 1980 to 2000. This implies no improvements in technologies (and thus conservation of energy), and no alternative technologies which could be selected (thereby substituting one source of energy--especially coal or electricity--for another). In general, this leads to conservative results, as more 'energy flexibility' is likely to result in less severe effects of energy-related pressures. - The private sector sub-model, also static and based upon data for 1975/6, allows for income elasticity effects, but does not allow for substitution of energy sources in this sector, such as alternative fuels for cooking or heating. Again, this leads to a conservative 'energy inflexibility'.
81
- For all sectors, price elasticity effects are not considered at all. This is probably the most serious drawback (and a general problem with linear input-output models), as general conservation and c a p i t a l / e n e r g y substitution effects are not accounted for. For example, household use of petroleum products (Table 4) is somewhat exaggerated: the effect of higher prices has been to reduce the growth rate to 3-4%, rather than 6% as predicted by the model. - Finally, the exploitation of local renewable and non-renewable energy sources does not find expression in the model. Although these local sources will, to a large extent, remain marginal in the overall energy balance, it is obviously important to include them in the overall energy picture. The lack of elasticity and substitutability, that could otherwise result from both technological and behavioural changes, leads to a higher requirement of energy than expected for any given level of activity; or, correspondingly, a more depressing effect on the Israel economy. In particular, the level of electrification is less than that hoped for by the Ministry of Energy and Infrastructure, which is promoting this energy form as a means of reducing oil dependency. Nevertheless, the inflexibilities in the model do reflect a certain rigidity in the structure of the Israel economy, which is characterized by a high level of governmental intervention in industry, and in the energy and energy-intensive sectors in particular. This leads to a pricing policy for energy,
Table 8 Year
E n e r g y / G D P ratio (1970 = 100.0)
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981
100.0 96.1 93.4 96.4 92.7 90.0 90.0 93.1 94.8 95.1 94.4 90.3 (estimated)
Source: Israel Monthly Bulletin of Statistics 12 ( 1981 ).
82
A. Breiner, R. Karni / Energy and the Israel economy
both as service and feedstock, and for the products of these industries, which is not necessarily related to market factors. Moreover, the manner in which prices and wages are mutually linked to changes in COL indices results in energy and price elasticities which are very small indeed, see Table 8. There is thus little incentive, in the cement, chemical and mineral sectors, for technological improvement; it is the government, rather, which is pressuring these industries to convert to coal-based process heating. However, a movement away from energy-intensive industries towards those such as aviation and electronics is becoming apparent, as predicted by the model. In view of the lack .of energy flexibility, this provides the main mechanism for coping with rising energy prices. As we have used constant input-output data in the models, it is felt that presentation of results in terms of seven usage groups, rather than fifteen industrial sectors, leads to a more realistic prediction of such trends. The current phase of development concentrates on modifications in the above areas. In particular, coal-oil substitution in energy-intensive industries, electricity-oil substitution in the private and public sectors, and implementation of the Mediterranean Sea-Dead Sea hydroelectric project are being incorporated in the model.
9. Conclusions The above results illustrate a portion of the ongoing OMER study on the development of the Israeli economy facing a changing energy picture throughout the rest of this century. These years represent a transition period from an economy based entirely on imported oil and little conservation to an economy in which primary energy sources are more diversified, more substitution will take place, and more conservation will be carried out. It is shown that values of macroeconomic indicators, such as GDP, personal consumption, industrial output and investments will grow at a slower rate than in the last 30 years. The lower rate of growth is more profoundly demonstrated if a high annual increase in the price of oil is assumed, or attempts are made to reduce the trade deficit. The rising absolute and relative cost of energy imports will more than ever force accelerated development of the exporting sectors of the economy. At the same time the share of energy-in-
tensive sectors in the industrial output will have to decrease. Further studies, including improvements in the OMER model, are under way and will be reported as they are completed.
Appendix: A mathematical description of the OMER energy model A. 1. Comments
This appendix describes all the central relationships in the OMER model, excluding a detailed breakdown of the energy sector. A.detailed exposition of the model, covering the extensive sub-models for refining and electricity generation, is currently in preparation. All monetary units for all periods are expressed in million IS base year (first period) current prices. The base year used at present is April 1975 to March 1976. The values generated by the model are thus real, and not inflated, values. All energy units are expressed physically, in 1000 tons or million kWh. All labour units are expressed in 1000 workers. All production and investment coefficients cover inputs from local production and competitive import. A separate vector covers necessary import. All variables express average annual activity levels during the relevant period, not total period values. In mathematical terms, the OMER model is represented by a linear program, consisting of intraperiod relationships expressiong technological and supply-demand dependencies between the activity variables; and interperiod relationships that constitute the linkage between consecutive time periods. The central linking factor is that of capital formation--the replacement or increase of production capacity, necessitated by capital erosion (via obsolescence or wear and tear), or a desired increase in output. Capital formation covers: (i) The depreciated transfer of productive capacity from one period to the next; (ii) The use of productive outputs within the period in order to replace or increase production capacity, rather than be used for private or public consumption; (iii) The maturation of such investments over time--i.e, the time-lagged creation of production capacity within the investment a n d / o r subsequent periods;
A. Breiner, R. Karni / Energy, and the Israel economy
(iv) The relationship between the capital invested and the capital form (production capacity created). As the production capacity available is not necessarily used within the period, a special variable, 'unused capacity', is introduced in order to indicate, in conjunction with the capacity actually used, that capacity, before depreciation, to be transferred to the following period. A particular multiperiod model is constructed of ' T ' periods of ' n ' years each.
A
F
H A.2. Constants A
A'
B
B,
L,
= (aij) intermediate use input-output di-
=
=
=
=
rect coefficient matrix of industry inputs to each industry. Each coefficient describes the physical or monetary quantity of input required from industry i in order to produce one physical or monetary quantity of output from industry j. (a~) input-output coefficient vector of necessary import to all industries. Each coefficient describes the monetary units of necessary import required in order to produce one physical or monetary unit of output from industryj. (bij) capital formation coefficient matrix. Each column describes the input mix required for each unit invested in industry j. Each coefficient describes the monetary units of input required from industry i when investing one monetary unit in industryj. (bj') necessary import capital formation coefficient vector. Each coefficient describes the monetary units of necessary import required when investing one monetary unit in industry j. (lj,) total labour force coefficient vector. Each coefficient describes the total labour units of input required in order to produce one physical or monetary unit of output from industry j, during period
C
H'
Pit
PEt
O, IV, K~
l.
F
= (fj) industrial availability coefficient or 'plant factor' matrix. The reciprocal of each coefficient describes the units of production capacity required in order to produce one unit of output from industry j.
R
83
= (8i) private consumption income elasticity vector--constant term. Each coefficient describes the minimal consumption per capita from source industry i, in physical or monetary units. = (Z) private consumption income elasticity vector--variable term. Each coefficient describes the change in total private consumption from source industry i in physical or monetary units, per monetary unit of private consumption. = (hi) public consumption vector, describing the input mix required for each monetary unit of public consumption. Each coefficient describes the physical or monetary units of industry i required to satisfy one monetary unit of public consumption. = private consumption of necessary import, describing the monetary units of necessary import required to satisfy one unit of private consumption. = public consumption of necessary import, describing the monetary units of necessary import required to satisfy one unit of public consumption. = (Pljt) competitive import price vector. Each coefficient gives the C.I.F. price per physical unit of energy industry j imported, or the relative price per monetary unit of non-energy industry j imported, during period t. = ( P E j t ) export price vector. Each coefficient gives the F.O.B. price per physical unit of industry j exported, or the relative price per monetary unit of non-energy industryj exported, during period t. = population level (thousand persons) during period t. = total labour force availability (thousand workers) during period t. = (kjl) initial production capacity vector. Each coefficient gives the production capacity per annum in physical or monetary units, of industry j, during the initial period. = (t)) output-capital ratio vector. Each coefficient describes the production capacity added to industry j, in physical or monetary units, when one monetary unit is invested in that industry.
A. Breiner, R. Karni / Energy and the Israel economy
84
Q,
Ol
N,
Y
,,
= (qj,) relative productivity vector. Each coefficient describes the labour force productivity in industry j, during period t, as the relative output per worker compared with the first period. = (ag) annual depreciation rate vector. Each coefficient describes the annual fractional loss in production capacity, caused by wear and tear and technological obsolescence, in industryj. = investment maturity coefficients. Each coefficient expresses that fraction of the initial investment in industry j, made during period ~-, which matures (is added to the current production capacity) at the beginning of period t. = asymptotic geometric growth rate for production capacity and the objective function during the post-terminal periods. = price of energy product from energy industry j relative to the base price for energy imports. = total input coefficient of energy to nonenergy industry j, representing the 'energy component' in the output of that industry. = discount factor for a time-summed objective function, for period t.
A.3. Variables
X,
v, G,
= (xj,) activity level vector. Each variable describes the annual output of industry j, in monetary or physical units, during period t. = (m j,) competitive import vector. Each variable describes the annual 'output' of (overseas) industry j, in monetary or physical units, during period t. = (ej,) export vector. Each variable describes the annual export from industry j, in monetary or physical units, during period t. = (yj,) investment vector. Each vector describes the annual amount invested in industry j, in monetary units, during period t. = total annual private consumption, in monetary units, during period t. = total annual public consumption, in
monetary units, during period t. = (u j,) unused production capacity vector. Each variable describes the average annual unused capacity of industry j during period t. = trade balance deficit, in monetary units, during period t. A. 4. Technological balances (equafities) For any period, total intermediate uses, private consumption, public consumption, export and investment equals total self use in production and import (A-I)X,-M,+
E,+ B . Y~
+A.O,+F.V,+H.G,=O. Private consumption elasticities are accounted for by the term ( A . 0t + I". Vt) , which expresses private consumption as a function of the population level and the total level of expenditure in each period. A.5. Trade balance (constraints) In the OMER model, prices only appear in the trade balances, which constitute one of the most critical set of constraints in the model. As all imports and exports have some 'energy component', their prices must reflect the imposed changes over time of the base energy price, P~c,. For energy industries j, where activities are expressed in physical units: Plj,
=PI,," P:,."
For non-energy industries j, where activities are expressed in monetary units: P I j , : I + p~( P I . - P , c , ) / P , c t where p~, the total energy coefficient for non-energy industry j, is derived from the industry column and total energy industry row of the inverse matrix ( I - A)- 1 Similar considerations are applied to the export prices. For each period, the total competitive import (to intermediate uses plus final uses--private consumption and public consumption) plus necessary import, less export, gives the trade deficit. The value of this deficit, for each period, can be im-
A. Breiner, R. Karni / Energy and the Israel economy
posed, or left as a constrained variable A'. X, ÷ P,,. M , - PE," Et
+ C " V, + H " G, - D, <~O. A.6. Labour force (constraints) The labour force is characterized by growth in availability over time, and growth in productivity over time. This results from better worker performance, and from the increased use of mechanized and automated methods, resulting in an increased gross output per worker. This is incorporated in the model by adjusting the total labour force coefficient vector
The total labour force constraints become
Lt. X, + L<;,. G, <~ W,. A. 7. Production capacity (equalities) The utilized and unutilized (or total) production capacity during any period equals the depreciated total production capacity from the previous period, plus that capacity resulting from the maturity of investments made during a n d / o r in previous periods. Both utilized and unutilized production capacity are assumed to depreciate equally. The unutilized capacity variables convert the capacity constraints into equalities (as U, >/0). In general, ( 1 / F ) . X , + U, ( ( l / F ) - (1 - n a ) . X t _ , + (1 - na). Ut_,) -r=t
+ ~_, Y , . R . f l : = O . ~-=1
For the first period, the production capacity carried over and the maturation of investments made before this period is not known; thus the constraint is modified to -- gl"
/~:" R + ( l / F ) ' X ,
model is being used. Usually, it is the weighted sum of private consumption, or gross national product. The weight allows a possible discounting factor to be incorporated. Thus we may have (i) Maximum private consumption
(ii) Maximum gross national product
A. 9. Initial and final conditions
L,: L, = L I / Q , .
-
85
+ V1 = K,
where in the initial production capacities K 1 are given exogenously.
A.8. Objective function The composite objective function applied to the model depends on the scenario for which the
A particular instance of a multi-period model is composed of a number of periods representing a time span of 'real' years. Initial conditions must be defined in order to 'start' the model at the correct period. Final conditions must also be defined, as an optimization model acts as if the economy does not exist beyond the final period, and thus requires no carry-over of production capacity. Some of these conditions are ipso facto obtained when actual and projected profiles of population size, labour force size, government spending and trade balance deficits are set exogenously for all periods, and production capacities for the initial period. Control of final conditions presents a more difficult problem. The model provides an optimum solution in accordance with the objective function specified, and thus tends to drive to zero any other factors which may otherwise reduce this optimum. Thus, if private consumption is optimized, no investment is made in the last period(s), as production capacity is utilized for private consumption only. It may even happen that industries are 'closed down' as they are not required after the last period. We make the assumption that the growth rates toward the final period of the model are asymptotically geometric, i.e. that the real world follows a 'golden age' growth path. If this asymptotic property is known, then an approximate solution to the infinite time horizon model is obtained by truncating the time horizon at time T (the model horizon thus extending from t = 1 to t = T). The values of the various variables and the objective functions are computed exactly by the model; the values
86
A. Breiner, R. Karni / Energy and the Israel economy Previous period
RHS
Current period
I X
~
~
x "5
,"
o l
Industrial
Interindust - I
demand balances
l l
3onsumF 2onsump Expantion tion sion
I
I-0
<
NCI Rela-IRelaNCI NCI I profill tive 'itive arofileprofild
Trade balance
~rices l~rices "
-
1
t-
!
Labor
Work force
0
~rofile profile purch.
LaborI inten~ ~ity I
inten-
"-[.... ~ominal Capital formation & I~pre- I[ Depre-I Natur-Ia acit Iclatxonliatio~ i t y ~at pio ( capacity expansion
~turi ity
i
I
Objective (GNP)
P 1 !
l l l
1
i
-1
~llowable ~eficit ~vail~bility
.... i Maximize
J
Fig. AI. Schematicdiagramof the OMER model.
during the post-terminal periods to infinity are approximated by assuming that the growth rates of the variables are equal to the asymptotic growth rates obtained in the model. Thus, for any chosen variable Z, Zr+t=Zr(l+y)
t-r
(t=T+I,T+2
.... )
and this relationship may be applied to any chosen variable in the model. In the OMER model the above analysis applies to two relationships--production capacities and the objective function. (i) Production capacities. We assume that the production capacity in the first post-terminal period is (1 + T) times that during the terminal period; and that the investment in the first postterminal period is at least that (1 + y) times that in the terminal period. Substituting in the balance for period T + 1, we obtain -r=T
((1/F)'Xr+ Ur)(na+nY)- E Y.'R'fl r+] *=1
- Yr "R'~'r+Or+t/l + T) ~<
(The added production capacity generated in period T + 1 is less than or equal to the additional production capacity resulting from the maturation of investments made during the model horizon periods, plus the additional production capacity resulting from the partial maturation of investments made during period T + 1.) (ii) Objective function. The objective function applied to the model will depend on the scenario for which the model is being used. If the function is composed of a growth term for each period, say Z, (such as private consumption, GNP, etc.), then allowing for a possible discount factor we have
Z=~X'Z'+Zr l--Xr(l+y) t
"
We see that the approximation to the infinite horizon objective function results in a modified weighting factor for the contribution in the terminal period: AT[
1 +1(1 -- At)(1 + Y) 1
745
A schematic diagram of the model is given in Fig. A1.
A. Breiner, R. Karni / Energy and the Israel economy
References [1] M. Avriel, A. Breiner, D. Marmur and A. Melnik, A mathematical model for assessing energy-economic options on a national level, Proc. International Conference on Systems Modelling in Developing Countries, Bangkok, Thailand (1978) 183-199. [2] G.B. Dantzig, A PILOT linear programming model for assessing physical impact on the economy of a changing energy picture, Proc, I1ASA Conference '76, Vol. 2, Laxenburg, Austria (1976) 183-200. [3] H, D'Hoop and M.A. Laughton, Survey of present energy
87
models with particular reference to the European Community, in: B.A. Bayraktar, E.A. Cherniavsky, M.A. Laughton and L.E. Ruff, Eds., Energy Policy Planning (Plenum Press, New York, 1981). [41 R. Karni, A. Breiner and M. Avriel, Energy-economic planning in Israel: The OMER study, in: M. Avriel and R. Amit, Eds., Perspectives in Resource Modelling: Energy and Minerals (Ballinger, Boston, MA, 1981). [5] J.G. van Zyl, An approach to the modelling of the South African energy economy, CSIR Publication SWlSK 16, Pretoria (1980).
Energy and the Israel economy Avishai B R E I N E R a n d Reuven K A R N I Energy Planning and Policy Research Group, The Management Sciences Research Centre, Faculty of Industrial Engineering and Management, Teehnion-lsrael Institute of Technology, Haifa 32000, Israel Received September 1981 Revised January 1982
The OMER macroeconomic model has been developed in order to examine the interactions between energy and the Israel national economy. This paper presents a description of three sets of scenarios which study the manner in which the 'mix' of industries and their output levels could be affected if a maximal and minimal effort were made to provide the necessary energy requirements for the economy. Several assumptions are also made as to the probable increase in energy prices to the end of the century. In general, the effect of higher energy prices is to spur industrial activity towards exports in order to pay for energy imports, at the expense of private consumption. Thus industry is less affected than private consumption. Nevertheless, a shift is made towards less energy-intensive industries, and the reduction of transportation levels. Finally, if only minimal outlays on energy are made, both energy requirements and growth rates fall to about one-half of those when maximal required outlays are made.
1.
I n t r o d u c t i o n
The OMER (Optimizat~'on Model for Energy Resources) study, sponsored by the Ministry of Energy and Infrastructure in Israel, is intended to provide planners with a consistent analytical framework for studying the energy supply sector and its interactions with the national economy during the period 1980-2000. During this time, the energy sector is expected to change from one based almost entirely on imported oil, to one based on imports of oil, coal and nuclear power, as well as those local energy resources (hydroelectric
power and solar energy) which could be exploited by the end of the century. In the face of such radical change, the OMER energy-economic model has been used to explore the implications of both short and medium range energy-related decisions and scenarios. The OMER model is a linear programming model [1,2,3,5] consisting of the following major components: - energy supply sectors--process type sub-models of activities relating to refining and electricity generation; - industrial (non-energy) sectors of the economy, aggregated into 15 sectors and 7 usage groups--described by means of a Leontieff type input-output matrix; - investments in energy and non-energy sectors-described by means of an investment matrix; - public and private consumption; foreign trade, encompassing exports, imports and the trade balance. The set of scenarios described in this paper is intended to encompass two ends of the possible spectrum of activity in the energy sector and its relation to the national economy--minimum investment in the energy sector and outlay on imported fuels; and optimal investment in the energy sector and imported fuels, consistent with maximum growth in consumption. Thus two objective functions have been used in the analyses: - m a x i m i z a t i o n of discounted gross domestic product (private and public consumption, investment and exports, less imports); minimization of the discounted investment in the energy sector (refining and electricity generation capabilities) and the energy import bill. In view of the energy situation, several constraints are assumed to act on the Israeli economy: - the necessity to diversify energy sources, mainly by introducing coal and nuclear power; the necessity to cope with rising prices of imported oil, coal and nuclear fuel; the necessity to reduce--and even eliminate-the deficit in the balance of trade, and the growth of defence imports; the necessity to reduce the growth of consumption in the public sector. -
-
-
Research was sponsored by the Israeli Ministry of Energy and Infrastructure. The authors are solely responsible for the views expressed here. North-Holland Publishing Company European Journal of Operational Research 13 (1983) 74-87
-
-
0377-2217/83/0000-0000/$03.00 © 1983 North-Holland
75
A. Breiner, R. Karni / Energy and the Israel economy Table 1 Nonenergy industrial sectors in the O M E R model Industrial sector
Sector fraction in total nonenergy output a (percent)
Cost of energy in sector output b (percent)
Energy intensity of sector output c (t.o.e. per 106 IS)
Energy usage group d
Water Chemical, plastics Mining, glass, cement Metals, metal products Machinery, equipment Textiles Wood, paper, print Agriculture Food, beverages, tobacco Diamonds Road transport Sea and air transport, communications Construction Services Trade
0.7 5.0 2.8 5.8 8.1 5.6 4.4 7.6 10.0 3.6 4.3 6.5 12.5 15.0 8.1
30.0 5.3 11.3 2.0 1.5 3.2 2.3 5.0 4.2 0.1 13.1 10.1 3.6 1.5 2.0
305 43 149 16 6 16 19 14 16 1 97 43 9 6 8
4 1 1 2 3 2 2 4 2 3 5 5 6 7 7
a Output share: According to 1975/76 output levels. b Energy share." Based on total i n p u t - o u t p u t coefficients of primary energy sources. c Energy intensity: Based on direct i n p u t - o u t p u t coefficients of electric and non-electric energy, corrected to October, 1980. Energy group." 1: High energy-intensive manufacturing, 2: Medium energy-intensive manufacturing, 3: Low energy-intensive manufacturing, 4: Water and agriculture, 5: Transportation and communication, 6: Construction, 7: Trade and services. Table 2 Energy requirements by consumption sector (percentages for 1975) Consumption sector a
Electricity and refining losses Water Chemical, plastics Mining, glass, cement Metals, metal products Machinery, equipment Textiles Wood, paper, print Agriculture Food, beverages, tobacco Diamonds Road transport Sea and air transport, communications Construction Services Trade Public consumption Private consumption Other Total c
Electricity
Petroleum products b
Total
1.3 17.4 6.1 5.6 4.1 2.9 4.3 2.5 2.1 4.4 0.2 0.1 1.2 0.5 2.0 5.6 9.0 29.2 1.5
11,8 0,4 7.0 12.6 1.4 0.3 1.3 1.9 3.9 3.8 0.0 14.6 7.5 4.3 1.0 0.0 11.5 11.7 5.0
8.2 6.2 6.7 10.2 2.3 1.2 2.3 2.1 3.3 4.0 0.1 9.7 5.3 3.0 1.3 1.9 10.6 17.7 3.9
100.0
100.0
100.0
Breakdown in O M E R model. b Excluding 2.35 x 106 t.o.e, for electricity generation c Total electricity consumption (1975): 8,25 x 109 kWh. Total petroleum product consumption (1975): 6.87 x 106 t.o.e.
76
A. Breiner, R. Karni / Energy and the Israel economy
The effects of these constraints on the energy e c o n o m y have been described in detail elsewhere [3]. This paper concentrates on the industrial sectors and private consumption. A schematic and mathematical outline of the model is given in the appendix.
2. Energy consuming sectors The energy consuming sectors have been aggregated into 15 industrial sectors and four final d e m a n d s e c t o r s - - p u b l i c consumption, private consumption, investment and exports. I n p u t - o u t put data for the industrial sectors have been derived from tables issued by the Central Bureau of Statistics for the year 1975-1976, and corrected for energy c o n s u m p t i o n according to the latest data available. The output and energy consumption characteristics of these sectors is detailed in Tables 1 and 2. A further aggregation into seven usage groups has been made, in accordance with the energy intensity of output, and the type of sector. Energy consumption in Israel has the following general characteristics: - A b o u t 35% of all primary energy is used to generate electricity. (Water p u m p i n g - - m o v i n g water from where it is available to where it is n e e d e d - - c o n t r i b u t e s significantly to this high percentage.) As the shift to a mix of oil, coal and nuclear fuels impacts the electricity sector in the main, it is one of the policies of the Ministry of Energy and Infrastructure to move towards raising the electricity share even higher. - The main consumers of electric power are the private and water p u m p i n g sectors. Most water is used for agricultural purposes. Thus, if consumption of electricity is to be reduced, either agricultural activity will have to be c u r t a i l e d - - a t the expense of exports, and possibly, increased imp o r t s - o r the private sector will have to reduce its requirements in some manner. - The main consumer of petroleum products are the chemical and mineral industries, and the transportation sector. Large amounts of energy are required to manufacture petrochemicals, potash, phosphate and cement. The extent of these industries would have to be curtailed in order to decrease petroleum product consumption. In the transportation sector, the provision of fuel for air
and sea purposes constitutes the only likely way of reducing consumption here. - Finally, the public and private sectors are large consumers in both areas. Thus both these sectors are likely to be vulnerable to efforts to reduce overall consumption. As public consumption is set exogenously in the O M E R model, different levels have been assumed for the various scenarios (see Table 3); any further reductions will be at the expense of the private sector.
3. OMER scenarios Three series of scenarios, based upon assumptions on energy prices, trade deficits and public Table 3 Key input assumptions for OMER scenarios - Series I: Series II: Series IIl:
Continuation of current trends in trade balance, public consumption and defense imports Reduction or balancing of trade balance, public consumption and defense imports As for Series II, but with minimization of energy imports and investments, with the growth in private consumption not less than 1% per capita per annum
Fuel
Low price (L)
(all scenario series): Base High price price (a) (H)
Crude oil Coal Nuclear fuel
2% 2% 2%
5% 3% 3%
- A n n u a l p r i c e escalation o f imported fuels
8% 4% 4%
- Foreign trade deficit:
Series I: 2% annual growth to 1985, then no growth Series II, 1II:2% annual decline to 1985, then no decline (II(B),) Series II: 9% annual decline to 1985, then no decline (II(B)z) - Defense imports:
Series I: 2% annual growth Series II, IIl: No growth - Total public sector consumption:
Series I: 4.6% annual growth Series II, III: 4% annual growth - R a t e o f population growth:
1.95% per annum
- Objective:
Series I, II: Maximizediscounted gross domestic product Series III: Minimizediscounted energy imports and investments
A. Breiner, R. Karni / Energy and the Israel economy
77
4. General macro-economic and energy-related results
spending, have been carried out. The key assumptions underlying the scenarios are detailed in Table 3. The six scenarios form a gradation in the severity of the constraints affecting the energy bill and the trade balance, from scenario I(L) which assumes low energy price rises and little constraint on the trade balance, through scenario III(B), which tries to minimize activity in the energy sector, with a minimal rise (1% per capita, or 3% overall in private consumption growth). They thus provide a spectrum of possibilities of the effects of the constraints on the Israel economy and its levels of output and consumption.
A summary of some economic and energy consumption figures produced by the model, for the six scenarios, are presented in Table 4, 5 and 6, and in Fig. 1. In Table 4, the macroeconomic indicators refer to the general economy, energy consumption patterns, and energy outlays. (A detailed analysis of energy supply characteristics over the period studies is provided in [4]). The Series I scenarios study the effects of energy prices. As the rate of price rises increases, GDP and private consumption
Table 4 Macro-economic indicators for OMER scenarios (annual growth rates unless otherwise stated) Indicator
GDP growth P e r capita consumption growth Industrial output growth Industrial investment growth
Base values (1980) a
Series II
L
B
H
(%)
(%)
(%)
BI
(%)
Series III B2
(%)
B
(%)
145.109 (IS)
5.7
5.3
4.4
4.5
4.4
3.3
22.103 (IS) 230.109 (IS)
4.5 5.8
3.8 5.7
2.1 5.7
3.0 4.7
2.4 4.8
2.5
40.109 (IS)
4.1
4.0
3.8
3.2
3.3
2.4
8.106 (t.o.e.)
5.2
4.8
4.2
3.5
3.4
2.4
15.105 (t.o.e.)
6.1
5.4
3.9
4.7
4.1
2.8
13.109 (kWh)
5.2
4.9
4.7
3.9
3.9
2.8
3.109 (kWh)
5.0
4.4
3.4
3.7
3.3
2.5
0.8.106 (t.o.e.)
7.0
6.2
4.3
4.9
4.1
3.1
Local energy consumption growth Household energy consumption growth Local electricity consumption growth Household electricity consumption growth Household petroleum product consumption growth Electricity consumption within total consumption c Energy import bill growth Energy import share in GDP c Energy investment growth Energy intensiveness growth per unit of output = 7.5 IS. b Fixed exogenously (as lower limit). By the year 2000. a 1 us$
Series I
36% 2.109 (US$) 12% 30.109 (IS) 37 (t.o.e./106IS)
36
37
41
40
1.0 b
41
41
2.8
8.1
10.0
7.1
7.0
5.6
12 6.4
20 6.3
34 6,2
20 4.3
20 4.3
19 2.7
-0.4
-0.8
-1.4
-1.3
-1.3
-
1.2
78
A. Breiner, R. Karni / Energy and the Israel economy
Table 5 Output levels of energy usage groups in the industrial sectors for the years 1980 and 2000 for OMER scenarios Energy usage group (1)
High energy-intensive manufacturing Medium energy-intensive manufacturing Low energy-intensive manufacturing Water and agriculture
Base values (1980) (2) 9.7 26.7 13.6 6.7
Transportation and communication Construction
15.4
Trade and services
19.4
Total
8.4
100.0
Series I
Series II
Series III
L (3)
B (4)
H (5)
BI (6)
BE (7)
B (8)
9.5 (54) 27.4 (84) 16.4 (100) 3.0 (110) 6.5 (113) 13.4 (111) 23.8 (108)
6.3 (100) 33.3 (100) 16.9 (100). 2.8 (100) 5.9 (100) 12.3 (100) 22.5 (100)
4.9 (73) 36.1 (101) 17.9 (100) 2.7 (91) 5.7 (91) 13.3 (102) 19.4 (81)
2.6 (32) 34.8 (83) 21.0 (100) 3.6 (105) 5.6 (77) I 1.0 (71) 21.4 (76)
2.0 (25) 33.0 (78) 21.1 (100) 3.6 (104) 5.3 (72) 11.8 (76) 23.2 (81)
2.4 (22) 27.7 (49) 28.2 (100) 2.9 (61) 4.8 (49) 11.5 (56) 22.5 (59)
100.0 (102)
100.0 (100)
100.0 (94)
100.0 (80)
100.0 (79)
100.0 (59)
Column (1): Energy usage group (see Table 1). Column (2): Percentage output level (IS/Total IS) of the group during 1980. Columns (3)-(8): Percentage output level (IS/Total IS) of the group by the year 2000; and percentage output level (in brackets) of each group relative to its output in Scenario I(B) (the 'standard' scenario), all by the year 2000.
a small reduction in the growth rate of energy consumption occurs, mainly in the private sector, accompanied by a trend towards electricity as the main energy source. Thus higher energy prices, coupled with the shift to cheaper coal and nuclear fuels, encourage the use of electricity, rather than lead to an overall reduction in energy consumption. As can be seen from Table 5, the move to less
growth fall off. Industrial output and investment, however, remain relatively unaffected. As the energy import bill is seen to rise drastically, we may conclude that industrial activity is geared to meeting the level of exports required to meet this bill. (We assume in the model that the level of exports from Israel is insignificant in the world market, so that all required exports will be taken up.) Overall,
Table 6 Relative levels of activity of industrial sectors, private consumption and energy consumption by the year 2000 for OMER scenarios Series I
Industrial sectors Private consumption Energy consumption
Series II
Series III
L
B
H
B~
B2
B
102 (5.8) 115 (7.6) 110 (5.2)
100 (5.7) 100 (6.9) 100 (4.8)
94 (5.7) 67 (5.1) 89 (4.2)
80 (4.8) 76 (6.1) 74 (3.5)
79 (4.7) 75 (5.3) 75 (3.4)
5 (2.5) 58 (4.0) 57 (2.4)
Percentages relative to the 'standard' scenario I(B), and (in parentheses) annual growth rates between 1980-2000.
79
A. Breiner, R. Karni / Energy and the lsrael economy
4007:.
-
Medium_energy-intensive manufacturing 151
i -5
i I Low ener~y-inlensive 'manu[qcturln I L ~! i
,,'
i
,
L
,! il
u
5o7,-
~u~tu~
aQd~ a t e ~ I
I
5
l
~-~ ~
Ill
]Clon!t~c!iln I
25%~¢ ///~///Tr/;p°rt/at/i°n. a/nd/C°~un~
andServices
__Trade
¢q75
Cqdo
T
T
4985
4?9o
T
000
Fig. 1. Relative nonenergy industrial output in base case.
energy-intensive industries allows the level of output to be maintained with some reduction in energy requirement. In order to effect the shift in energy base, the growth rate of investment in energy remains constant, and higher than that for non-energy industry. The proportion of energy import costs in the G D P is expected to double, in the 'standard' case, by the end of the century, and even triple should energy prices rise faster than generally expected. If energy prices increase at the expected rate, but efforts are made to reduce or eliminate the trade deficit (Series II), all growth rates are seen to be depressed, including industrial output, leading to a general slowdown. Nevertheless, only private consumption decreases from one scenario to the
other; other levels remain constant in order to cope with the increased pressure on the trade balance. Again, the shift to a higher degree of electrification is noticeable. Some small reduction is achieved in the growth of the energy import bill. When only minimal investment in the energy sector and energy imports are allowed (Series III), all levels of growth are seen to fall to about one half of the 'standard' rate, indicating the severity of restrictions on energy availability. Private consumption, however, falls to one quarter of the 'standard' rate. The consumption pattern for electricity is maintained, and the energy bill remains at about 20% of the total GDP. Again, the reduction of the energy import bill growth (to 6%) is rather small.
80
A. Breiner, R. Karni / Energy and the Israel economy
5. Energy and the industrial sector Table 5 describes the effects of the various scenario assumptions on the structure of the nonenergy indUstrial sectors by the year 2000. This structure is portrayed in two ways: the percentage output level of each usage group within all groups, and the output index of each group, using scenario I(B) as the standard (index = 100 for each group). Dealing first with the output index, we notice that the total output level is unaffected by increased prices--as we have commented in the previous section--but falls to 80% as trade balance restrictions are introduced, and then to 60% as only minimal energy requirements are met. The output of low-energy intensive manufacturing is maintained throughout, and water/agriculture as well--except for the last scenario. The other groups follow the overall pattern, in general, except for high energy-intensive manufacturing, which, although very profitable when energy prices are low, rapidly become a burden as the price situation changes for the worse, reaching one quarter of their expected level in the worst case. These output levels affect the proportions of each group in the overall structure: high energy-intensive manufacturing drops from 10% to 6% and even 2% of overall non-energy industry, whilst medium energy-intensive manufacturing rises from 27% to 33%, and low energy-intensive manufacturing from 14% to 17% and even 28% in the severe scenario. The proportions of construction (12%) and trade and services (23%) remain relative constant, whilst those of water/agriculture and transportation drop to about one half.
6. Energy consumption, industries and private consumption Table 6 provides a concise summary of overall growth rates and activity levels for the industrial sector, private sector and total energy consumption. For the pricing scenarios (Series I), the private
sector is seen to be the most affected, in order to achieve lower energy consumption levels and growth rates; industry, as we have mentioned, must maintain its level of growth and output for export in order to compensate for the higher energy bill. For the trade balance scenarios (Series II, III), all three factors are, roughly, equally affected; a general slowdown and reduction in consumption is the only way of coping with the financing of the energy bill. In summary, subject to the structure and assumptions inherent in the current OMER model, we see that a significant amount of investment in the energy sector, leading mainly to a higher degree of electricification, is required in order to face up to higher energy prices and increasing difficulties in paying for energy. On the one hand, nonenergy industries will have to increase levels of exports to pay for imported energy; on the other, the private sector will have to 'pull in its belt' in order to reduce consumption and allow for increased investment. Nevertheless, we notice that all growth rates remain positive, and above the level of population growth (1.95% per annum), indicating that, provided the correct policies are carried out (and our model can only make humble recommendations in this respect), some of the worst aspects of the energy crisis can be coped with.
7. Energy-output.elasticities A convenient way to specify the degree of coupling between aggregate economic growth and energy demand growth is by means of an energy-output elasticity, relating the ratio of total energy requirement across any two points in time, to the ratio of industrial output at the same two points. The current value for Israel is about unity, indicating that economic growth and energy growth go hand in hand at present. The average elasticity values between 1980 and 2000, derived from the six scenarios, are as follows shown in Table 7.
Table 7
Average elasticity values between 1980 and 2000 Scenario Elasticity
I(L) 0.92
I(B) 0.86
I(H) 0.74
II(B) l 0.74
II(B)2 0.73
Ill(B) 0.69
A. Breiner, R. Karni / Energy and the Israel economy
These values imply a strong ability to adjust to constraints on energy availability and cost, via structural changes in industry and reduction of final demand for energy. However, the degree of flexibility inherent in the OMER model in its present form is a function of the freedom given to the model to expand or contract the level of activity of each individual sector. In linear models as is well known, a sector may be totally eliminated; in the real world this is not usually allowed to happen. In the current version of the model, in order to avoid the introduction of a large number of constraints, the upper limit on the level of activity of each sector has been set exogenously, equivalent to a maximum growth rate of 7.5% per annum relative to the 1975 value; and a lower limit as the 1975 value itself--i.e. 0% growth rate. These upper and lower bounds provide too much flexibility in the Series I(H), II and III scenarios, thus resulting in a large range of elasticity values obtained. More complex bounds on each sector would lead to a much smaller, and more realistic, range of elasticity values.
8. Limitations
of the model
When considering the results produced by the model, it is important to point out certain limitations of the model structure. These limitations influence the type of results obtained, and thus any conclusions that may be drawn from them. The most important drawbacks in the current version of the OMER model are as follows: - The same input-output data for the non-energy industrial sectors (based on the table for 1975/76) is used for all periods from 1980 to 2000. This implies no improvements in technologies (and thus conservation of energy), and no alternative technologies which could be selected (thereby substituting one source of energy--especially coal or electricity--for another). In general, this leads to conservative results, as more 'energy flexibility' is likely to result in less severe effects of energy-related pressures. - The private sector sub-model, also static and based upon data for 1975/6, allows for income elasticity effects, but does not allow for substitution of energy sources in this sector, such as alternative fuels for cooking or heating. Again, this leads to a conservative 'energy inflexibility'.
81
- For all sectors, price elasticity effects are not considered at all. This is probably the most serious drawback (and a general problem with linear input-output models), as general conservation and c a p i t a l / e n e r g y substitution effects are not accounted for. For example, household use of petroleum products (Table 4) is somewhat exaggerated: the effect of higher prices has been to reduce the growth rate to 3-4%, rather than 6% as predicted by the model. - Finally, the exploitation of local renewable and non-renewable energy sources does not find expression in the model. Although these local sources will, to a large extent, remain marginal in the overall energy balance, it is obviously important to include them in the overall energy picture. The lack of elasticity and substitutability, that could otherwise result from both technological and behavioural changes, leads to a higher requirement of energy than expected for any given level of activity; or, correspondingly, a more depressing effect on the Israel economy. In particular, the level of electrification is less than that hoped for by the Ministry of Energy and Infrastructure, which is promoting this energy form as a means of reducing oil dependency. Nevertheless, the inflexibilities in the model do reflect a certain rigidity in the structure of the Israel economy, which is characterized by a high level of governmental intervention in industry, and in the energy and energy-intensive sectors in particular. This leads to a pricing policy for energy,
Table 8 Year
E n e r g y / G D P ratio (1970 = 100.0)
1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981
100.0 96.1 93.4 96.4 92.7 90.0 90.0 93.1 94.8 95.1 94.4 90.3 (estimated)
Source: Israel Monthly Bulletin of Statistics 12 ( 1981 ).
82
A. Breiner, R. Karni / Energy and the Israel economy
both as service and feedstock, and for the products of these industries, which is not necessarily related to market factors. Moreover, the manner in which prices and wages are mutually linked to changes in COL indices results in energy and price elasticities which are very small indeed, see Table 8. There is thus little incentive, in the cement, chemical and mineral sectors, for technological improvement; it is the government, rather, which is pressuring these industries to convert to coal-based process heating. However, a movement away from energy-intensive industries towards those such as aviation and electronics is becoming apparent, as predicted by the model. In view of the lack .of energy flexibility, this provides the main mechanism for coping with rising energy prices. As we have used constant input-output data in the models, it is felt that presentation of results in terms of seven usage groups, rather than fifteen industrial sectors, leads to a more realistic prediction of such trends. The current phase of development concentrates on modifications in the above areas. In particular, coal-oil substitution in energy-intensive industries, electricity-oil substitution in the private and public sectors, and implementation of the Mediterranean Sea-Dead Sea hydroelectric project are being incorporated in the model.
9. Conclusions The above results illustrate a portion of the ongoing OMER study on the development of the Israeli economy facing a changing energy picture throughout the rest of this century. These years represent a transition period from an economy based entirely on imported oil and little conservation to an economy in which primary energy sources are more diversified, more substitution will take place, and more conservation will be carried out. It is shown that values of macroeconomic indicators, such as GDP, personal consumption, industrial output and investments will grow at a slower rate than in the last 30 years. The lower rate of growth is more profoundly demonstrated if a high annual increase in the price of oil is assumed, or attempts are made to reduce the trade deficit. The rising absolute and relative cost of energy imports will more than ever force accelerated development of the exporting sectors of the economy. At the same time the share of energy-in-
tensive sectors in the industrial output will have to decrease. Further studies, including improvements in the OMER model, are under way and will be reported as they are completed.
Appendix: A mathematical description of the OMER energy model A. 1. Comments
This appendix describes all the central relationships in the OMER model, excluding a detailed breakdown of the energy sector. A.detailed exposition of the model, covering the extensive sub-models for refining and electricity generation, is currently in preparation. All monetary units for all periods are expressed in million IS base year (first period) current prices. The base year used at present is April 1975 to March 1976. The values generated by the model are thus real, and not inflated, values. All energy units are expressed physically, in 1000 tons or million kWh. All labour units are expressed in 1000 workers. All production and investment coefficients cover inputs from local production and competitive import. A separate vector covers necessary import. All variables express average annual activity levels during the relevant period, not total period values. In mathematical terms, the OMER model is represented by a linear program, consisting of intraperiod relationships expressiong technological and supply-demand dependencies between the activity variables; and interperiod relationships that constitute the linkage between consecutive time periods. The central linking factor is that of capital formation--the replacement or increase of production capacity, necessitated by capital erosion (via obsolescence or wear and tear), or a desired increase in output. Capital formation covers: (i) The depreciated transfer of productive capacity from one period to the next; (ii) The use of productive outputs within the period in order to replace or increase production capacity, rather than be used for private or public consumption; (iii) The maturation of such investments over time--i.e, the time-lagged creation of production capacity within the investment a n d / o r subsequent periods;
A. Breiner, R. Karni / Energy, and the Israel economy
(iv) The relationship between the capital invested and the capital form (production capacity created). As the production capacity available is not necessarily used within the period, a special variable, 'unused capacity', is introduced in order to indicate, in conjunction with the capacity actually used, that capacity, before depreciation, to be transferred to the following period. A particular multiperiod model is constructed of ' T ' periods of ' n ' years each.
A
F
H A.2. Constants A
A'
B
B,
L,
= (aij) intermediate use input-output di-
=
=
=
=
rect coefficient matrix of industry inputs to each industry. Each coefficient describes the physical or monetary quantity of input required from industry i in order to produce one physical or monetary quantity of output from industry j. (a~) input-output coefficient vector of necessary import to all industries. Each coefficient describes the monetary units of necessary import required in order to produce one physical or monetary unit of output from industryj. (bij) capital formation coefficient matrix. Each column describes the input mix required for each unit invested in industry j. Each coefficient describes the monetary units of input required from industry i when investing one monetary unit in industryj. (bj') necessary import capital formation coefficient vector. Each coefficient describes the monetary units of necessary import required when investing one monetary unit in industry j. (lj,) total labour force coefficient vector. Each coefficient describes the total labour units of input required in order to produce one physical or monetary unit of output from industry j, during period
C
H'
Pit
PEt
O, IV, K~
l.
F
= (fj) industrial availability coefficient or 'plant factor' matrix. The reciprocal of each coefficient describes the units of production capacity required in order to produce one unit of output from industry j.
R
83
= (8i) private consumption income elasticity vector--constant term. Each coefficient describes the minimal consumption per capita from source industry i, in physical or monetary units. = (Z) private consumption income elasticity vector--variable term. Each coefficient describes the change in total private consumption from source industry i in physical or monetary units, per monetary unit of private consumption. = (hi) public consumption vector, describing the input mix required for each monetary unit of public consumption. Each coefficient describes the physical or monetary units of industry i required to satisfy one monetary unit of public consumption. = private consumption of necessary import, describing the monetary units of necessary import required to satisfy one unit of private consumption. = public consumption of necessary import, describing the monetary units of necessary import required to satisfy one unit of public consumption. = (Pljt) competitive import price vector. Each coefficient gives the C.I.F. price per physical unit of energy industry j imported, or the relative price per monetary unit of non-energy industry j imported, during period t. = ( P E j t ) export price vector. Each coefficient gives the F.O.B. price per physical unit of industry j exported, or the relative price per monetary unit of non-energy industryj exported, during period t. = population level (thousand persons) during period t. = total labour force availability (thousand workers) during period t. = (kjl) initial production capacity vector. Each coefficient gives the production capacity per annum in physical or monetary units, of industry j, during the initial period. = (t)) output-capital ratio vector. Each coefficient describes the production capacity added to industry j, in physical or monetary units, when one monetary unit is invested in that industry.
A. Breiner, R. Karni / Energy and the Israel economy
84
Q,
Ol
N,
Y
,,
= (qj,) relative productivity vector. Each coefficient describes the labour force productivity in industry j, during period t, as the relative output per worker compared with the first period. = (ag) annual depreciation rate vector. Each coefficient describes the annual fractional loss in production capacity, caused by wear and tear and technological obsolescence, in industryj. = investment maturity coefficients. Each coefficient expresses that fraction of the initial investment in industry j, made during period ~-, which matures (is added to the current production capacity) at the beginning of period t. = asymptotic geometric growth rate for production capacity and the objective function during the post-terminal periods. = price of energy product from energy industry j relative to the base price for energy imports. = total input coefficient of energy to nonenergy industry j, representing the 'energy component' in the output of that industry. = discount factor for a time-summed objective function, for period t.
A.3. Variables
X,
v, G,
= (xj,) activity level vector. Each variable describes the annual output of industry j, in monetary or physical units, during period t. = (m j,) competitive import vector. Each variable describes the annual 'output' of (overseas) industry j, in monetary or physical units, during period t. = (ej,) export vector. Each variable describes the annual export from industry j, in monetary or physical units, during period t. = (yj,) investment vector. Each vector describes the annual amount invested in industry j, in monetary units, during period t. = total annual private consumption, in monetary units, during period t. = total annual public consumption, in
monetary units, during period t. = (u j,) unused production capacity vector. Each variable describes the average annual unused capacity of industry j during period t. = trade balance deficit, in monetary units, during period t. A. 4. Technological balances (equafities) For any period, total intermediate uses, private consumption, public consumption, export and investment equals total self use in production and import (A-I)X,-M,+
E,+ B . Y~
+A.O,+F.V,+H.G,=O. Private consumption elasticities are accounted for by the term ( A . 0t + I". Vt) , which expresses private consumption as a function of the population level and the total level of expenditure in each period. A.5. Trade balance (constraints) In the OMER model, prices only appear in the trade balances, which constitute one of the most critical set of constraints in the model. As all imports and exports have some 'energy component', their prices must reflect the imposed changes over time of the base energy price, P~c,. For energy industries j, where activities are expressed in physical units: Plj,
=PI,," P:,."
For non-energy industries j, where activities are expressed in monetary units: P I j , : I + p~( P I . - P , c , ) / P , c t where p~, the total energy coefficient for non-energy industry j, is derived from the industry column and total energy industry row of the inverse matrix ( I - A)- 1 Similar considerations are applied to the export prices. For each period, the total competitive import (to intermediate uses plus final uses--private consumption and public consumption) plus necessary import, less export, gives the trade deficit. The value of this deficit, for each period, can be im-
A. Breiner, R. Karni / Energy and the Israel economy
posed, or left as a constrained variable A'. X, ÷ P,,. M , - PE," Et
+ C " V, + H " G, - D, <~O. A.6. Labour force (constraints) The labour force is characterized by growth in availability over time, and growth in productivity over time. This results from better worker performance, and from the increased use of mechanized and automated methods, resulting in an increased gross output per worker. This is incorporated in the model by adjusting the total labour force coefficient vector
The total labour force constraints become
Lt. X, + L<;,. G, <~ W,. A. 7. Production capacity (equalities) The utilized and unutilized (or total) production capacity during any period equals the depreciated total production capacity from the previous period, plus that capacity resulting from the maturity of investments made during a n d / o r in previous periods. Both utilized and unutilized production capacity are assumed to depreciate equally. The unutilized capacity variables convert the capacity constraints into equalities (as U, >/0). In general, ( 1 / F ) . X , + U, ( ( l / F ) - (1 - n a ) . X t _ , + (1 - na). Ut_,) -r=t
+ ~_, Y , . R . f l : = O . ~-=1
For the first period, the production capacity carried over and the maturation of investments made before this period is not known; thus the constraint is modified to -- gl"
/~:" R + ( l / F ) ' X ,
model is being used. Usually, it is the weighted sum of private consumption, or gross national product. The weight allows a possible discounting factor to be incorporated. Thus we may have (i) Maximum private consumption
(ii) Maximum gross national product
A. 9. Initial and final conditions
L,: L, = L I / Q , .
-
85
+ V1 = K,
where in the initial production capacities K 1 are given exogenously.
A.8. Objective function The composite objective function applied to the model depends on the scenario for which the
A particular instance of a multi-period model is composed of a number of periods representing a time span of 'real' years. Initial conditions must be defined in order to 'start' the model at the correct period. Final conditions must also be defined, as an optimization model acts as if the economy does not exist beyond the final period, and thus requires no carry-over of production capacity. Some of these conditions are ipso facto obtained when actual and projected profiles of population size, labour force size, government spending and trade balance deficits are set exogenously for all periods, and production capacities for the initial period. Control of final conditions presents a more difficult problem. The model provides an optimum solution in accordance with the objective function specified, and thus tends to drive to zero any other factors which may otherwise reduce this optimum. Thus, if private consumption is optimized, no investment is made in the last period(s), as production capacity is utilized for private consumption only. It may even happen that industries are 'closed down' as they are not required after the last period. We make the assumption that the growth rates toward the final period of the model are asymptotically geometric, i.e. that the real world follows a 'golden age' growth path. If this asymptotic property is known, then an approximate solution to the infinite time horizon model is obtained by truncating the time horizon at time T (the model horizon thus extending from t = 1 to t = T). The values of the various variables and the objective functions are computed exactly by the model; the values
86
A. Breiner, R. Karni / Energy and the Israel economy Previous period
RHS
Current period
I X
~
~
x "5
,"
o l
Industrial
Interindust - I
demand balances
l l
3onsumF 2onsump Expantion tion sion
I
I-0
<
NCI Rela-IRelaNCI NCI I profill tive 'itive arofileprofild
Trade balance
~rices l~rices "
-
1
t-
!
Labor
Work force
0
~rofile profile purch.
LaborI inten~ ~ity I
inten-
"-[.... ~ominal Capital formation & I~pre- I[ Depre-I Natur-Ia acit Iclatxonliatio~ i t y ~at pio ( capacity expansion
~turi ity
i
I
Objective (GNP)
P 1 !
l l l
1
i
-1
~llowable ~eficit ~vail~bility
.... i Maximize
J
Fig. AI. Schematicdiagramof the OMER model.
during the post-terminal periods to infinity are approximated by assuming that the growth rates of the variables are equal to the asymptotic growth rates obtained in the model. Thus, for any chosen variable Z, Zr+t=Zr(l+y)
t-r
(t=T+I,T+2
.... )
and this relationship may be applied to any chosen variable in the model. In the OMER model the above analysis applies to two relationships--production capacities and the objective function. (i) Production capacities. We assume that the production capacity in the first post-terminal period is (1 + T) times that during the terminal period; and that the investment in the first postterminal period is at least that (1 + y) times that in the terminal period. Substituting in the balance for period T + 1, we obtain -r=T
((1/F)'Xr+ Ur)(na+nY)- E Y.'R'fl r+] *=1
- Yr "R'~'r+Or+t/l + T) ~<
(The added production capacity generated in period T + 1 is less than or equal to the additional production capacity resulting from the maturation of investments made during the model horizon periods, plus the additional production capacity resulting from the partial maturation of investments made during period T + 1.) (ii) Objective function. The objective function applied to the model will depend on the scenario for which the model is being used. If the function is composed of a growth term for each period, say Z, (such as private consumption, GNP, etc.), then allowing for a possible discount factor we have
Z=~X'Z'+Zr l--Xr(l+y) t
"
We see that the approximation to the infinite horizon objective function results in a modified weighting factor for the contribution in the terminal period: AT[
1 +1(1 -- At)(1 + Y) 1
745
A schematic diagram of the model is given in Fig. A1.
A. Breiner, R. Karni / Energy and the Israel economy
References [1] M. Avriel, A. Breiner, D. Marmur and A. Melnik, A mathematical model for assessing energy-economic options on a national level, Proc. International Conference on Systems Modelling in Developing Countries, Bangkok, Thailand (1978) 183-199. [2] G.B. Dantzig, A PILOT linear programming model for assessing physical impact on the economy of a changing energy picture, Proc, I1ASA Conference '76, Vol. 2, Laxenburg, Austria (1976) 183-200. [3] H, D'Hoop and M.A. Laughton, Survey of present energy
87
models with particular reference to the European Community, in: B.A. Bayraktar, E.A. Cherniavsky, M.A. Laughton and L.E. Ruff, Eds., Energy Policy Planning (Plenum Press, New York, 1981). [41 R. Karni, A. Breiner and M. Avriel, Energy-economic planning in Israel: The OMER study, in: M. Avriel and R. Amit, Eds., Perspectives in Resource Modelling: Energy and Minerals (Ballinger, Boston, MA, 1981). [5] J.G. van Zyl, An approach to the modelling of the South African energy economy, CSIR Publication SWlSK 16, Pretoria (1980).