Exergy Research.pdf

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Enugy, Vol I, pp. N-178. Pergamon Press 1976. Print ed in Great Brit ain

ENERGY COST OF LIVING?ROBERT HERENDEENS and JERRY TANAKA

Center for Advanced Computation, University of Illinois, Urbana, IL 61801,U.S.A.(Received 1March1976)

AbstractWe evaluate the energy requirements of household expenditures for all products from the 1!960-61Consumer Expenditure Survey of the Bureau of Labor Statistics. We use more detail and employ moreaccurate energy intensities than in a previous, preliminary work (R. Herendeen, Affluence and energydemand, Mechan. Engng, October, 1974), nd also introduce a modest analysis of errors. We find that, withinerror bounds, one universal curve shows the dependence of energy impact of expenditures for householdsof 2 through 6 members. This curve bends down somewhat; that is, it is less than linear. The single-memberhousehold falls below the universal curve, apparently because of reduced purchases of actual energy. Atypical poor household exerts -65% of its energy requirements through its purchases of residential energyand auto fuel; for an affluent household, this fraction drops to 35%. We also find evidence that urban life isapproximately 15% less energy intensive (Btu per dollar expended) than rural non-farm life.

1. INTRODUCTIONOnly one-third of Americas energy is used in residences or the private automobile. Since privateconsumers are responsible for a total of three-fourths of the entire energy budget (the rest beingrequired to support government expenditures and exports), we can say that the averagehousehold consumes more energy indirectly through the purchase of goods and services thandirectly though the purchase of energy itself (see Fig. 1).

Fig. 1. Role of persona1 consumption in U.S. energy demand, l%7. PCE means personal consumptionexpenditures. The direct component includes energy penalty on energy purchases, such as conversion lossesin power plants.In this study, we evaluate empirically the relationship between household expenditures and

total resulting energy requirements (which we call energy cost), with especially detailedtreatment of the non-energy purchases. Particular motivation was given by the often-quotedobservation that, since household-energy purchases tend to saturate with increasing income,increased energy prices must have strongly regressive effects. On the other hand, we noted thatmany non-energy expenditures showed rapid increase with increasing income (housing,education, air travel): these must be energy-costed as well.

To convert expenditures to energy requirement, we use energy input-output analysis.. Thisaccounts for all energy consumed in the economy to support a certain activity, includingcontributions all1along the mining-manufacturing-sales chain. The most recent results divide theeconomy into 357 sectors, but here we aggregate to fewer sectors.tWork supported by the National Science Foundation.SPresent address: Institute of Social Economics, Technical University of Norway, 7034 Trondheim-NTH, Norway.

165


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166 R. HERENDEENnd J. TANAKAOur source of household expenditure data is the Consumer Expenditures Survey of the U.S.Bureau of Labor Statistics (BLQ3 These are extremely detailed, cataloging yearly expendituresdown to the last nickel for 13,000 U.S. households. Since every activity required energy, this

comprehensiveness is necessary. The price we pay for completeness is age; the last BLS surveyfor which results are available was conducted in 1960-61. (A similar survey covering 1972-73should be available in mid-1976.) The results in this study, therefore, must really be interpreted asoffering a baseline.

2. ENERGY COSTINGUse of input-output economics to obtain energy cost has been described before,** and

applications have appeared several times.& It is an empirical approach, based on the U.S.economy for a particular year. It explicitly accounts for the implied (or embodied) energyassociated with any dollar transaction, and traces every consumer product back to its basic rawmaterials, taking into account that different industries pay widely different prices for their fuels.

One question is, of course, if the energy intensities (Btu/$) of different products are reallydifferent. We have found that they differ by as much as a factor of ten when measured at the pointof manufacture (e.g. extruded aluminum vs a haircut). However, the consumer price of mostgoods contains a sizable wholesale and retail markup which tends to push the energy intensitiestowards a common value. But a significant spread still persists (Table 1). We measure energyintensity in primary terms (coal plus crude oil plus gas plus a primary equivalent of hydro andnuclear electricity.) By energy, we mean the enthalpies of combustion. We take no account of theactual specific use (feedstock, low or high temperature heat, motive power, lighting, etc.) and theimplications for substitution these might have.

Table 1. Energy intensities used for the 68 consumption categories. These have been given overall capitaland inflation corrections to account for the fact that Ref. [2] was the basic source of energy intensities inproducers prices; Ref. [2] is based on 1%3 data. The capital factor is 1.053 multiplicative); this assumesthat half of U.S. capital purchases are for maintenance and replacement. The inflation factor is 1.026(multiplicative). Intensities given here are thus in Btu per $ 1%1. Gas rate, electric rate, and split rateindicate that actual national-average rate structures were used. The last two columns refer to error analysis.For coefficient error, 1 denotes best (that is, smallest), 2 denotes medium, and 3 denotes worst. Expenditureerror is defined as P, in Appendix A, and discussed there

Sector Categories Energy intensity Coefficient(Btu per $ 1%1) error Expenditureerror (%)1 Food prep. at home2 Food away from home3 Alcoholic bev.4 Tobacco prod.5 Rented dwelling, total6 Owned dwelling, otherI Owned dwelling taxes8 Owned dwelling repairs9 Owned vacation home, other10 Owned vacation home, taxes11 Owned vacation home, repairs12 Lodging out of home city13 Other real estate14 Water and sanitary service15 Coal and coke16 Wood

17 Kerosene18 Fuel oil19 Other solid and petr. fuels20 Gas21 Electricity22 Gas and elec. combined23 Household oper.24 Laundry supplies25 Cleaning supplies26 Household paper27 Telephone and telegraph28 Household textiles29 Furniture30 Floor coverings

6124050416538073451322981117710721611177107216148575179571407971.5889 [email protected] 10 2

1.2522 lo6 11.13626 101.13626x10Gas RateElectric RateSplit Rate428911115301046355818971096

22

2222222222

2

22

22

0.51.90.50.51.52.12.42.12.12.12.12.12.11.01.01.01.01.01.01.01.01 o1.51.5I.51.51.12.42.42.4


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Energy cost of livingTable 1 Contd)

167

sector Categories Energy intensity Coefficient Expenditure(But per .$%l) error error (%)31 Major appliances32 Small appliances33 Housewares34 Misc. household items35 Clothing materials and services36 Clothing upkeep37 Auto purchase38 Motor gasoline39 Motor oil48 Lube, washing, etc.41 Tires42 Batteries, etc.43 Other operating expenses44 Repairs and parts45 Auto insurance46 Registration and other expenses47 Public transp., home city48 car pool49 Public transp., out of home city50 Other transportation51 Medical care52 Drugs53 Personal care54 Personal care supplies55 Recreation56 Spectator admission57 Reading materials58 Education59 Miscellaneous60 Personal insurance61 Gifts and contributions62 Cash in bank63 Purchase of non-farm dwelling64 Purchase of farm dwelling65 Purchase of other real property66 Investment in business67 Stocks and bonds68 Other assets

r4448.50140510374726580019520247695783897695655501403897636126101271104945520247 2141891 252024741482575175014066082501403010255246580465014036126054050761638247482474

22

2

22

3

1.83.43.95.01.31.83.01.53.03.03.03.03.03.01.33.02.81.51.41.41.11.11.01.01.62.11.74.75.01.32.22.016.016.016.016.016.016.0

3. EXPENDITURE DATABesides the problem of age, the main difficulty with the BLS survey data is in matching theirexpenditure categories with the input-output categories. We used three methods.(1) Matching directly to input-output categories. To convert the energy intensities topurchasers (i.e. consumers) price, we used data on margins from the Bureau of Economic

Analysis (BEA) of the U.S. Department of Commerce.(2) Matching to BEAs personal consumption activity categories. This is different from that in

(1) above; it represents BEAs attempt to convert familiar consumer activities (e.g. a meal in arestaurant) into its component input-output expenditures, as given in their publication PersonalConsumption Expenditures in the 1%3 Input-Output St~dy.~

(3) For a few sectors, use of independent data, e.g. converting expenditures for natural gas toenergy using national average rate structures which explicitly include volume discount pricing.The matching problem is a limiting one; as a result, we have aggregated the BLS expendituredata into 68 categories. Table 1 lists these and the corresponding energy intensities.Documentation is given in Ref. [lo].

4. RESULTS AND ANALYSISThe BLS survey covered some 13,000 households and included data on income, number of

members, location, age of family head, etc. If we had access to the raw data, we could analyzestatistically for the most significant variables. Unfortunately these detailed data are not available;


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168 R. HERENDEEN and J. TANAKAonly various aggregated data are. This limits our analysis to the role of income and of location(urban vs rural) and even introduces uncertainty into these, as we will discuss later.

We call attention to the fact that some of our results contain error bars. We have attempted toaccount for potential errors in both the energy intensities from input-output analysis, and in theexpenditure data from BLS. Still, some errors had to be estimated (see Appendix A). Errors hereare l-sigma; that is, the probability is about 0.69 that the true value falls within the bars.1. Results on total household energy requirements us expenditures

Figures 2a-i show the energy requirements vs expenditures for different household size (oneto six or more members). We plot total expenditures, not income after taxes, since welfarepayments, etc., must be included. (The numerical data used for these curves are given in Table 2).In Fig. 2b, we plot curves for several household sizes on the same axes.From Fig. 2b, we note that the energy required by households of the same income isstatistically the same, regardless of size, except for the single consumer. The single consumerdoes appear to use less energy per dollar, and much of the difference is due to reduced actualenergy purchases. At this point, our aggregated data causes difficulty, since we can not extract,e.g. age effects to try to explain the reduced purchase. Note also that the error bars are large forsingle consumers because of small sample sizes. For households of 2 or more members, a fairlyuniversal energy/expenditure curve seems to emerge. Age, location, etc. effects are buried andcould be significant. For this curve (e.g. Fig. 2a), we can see that energy purchases do tend tosaturate with income, while total energy requirements show a much weaker tendency to level off.Energy purchases account for roughly 2/3 of the energy impact of the lowest income households,while this ratio has dropped to almost l/3 for the most affluent.While the total energy vs expenditure curve does not saturate, it does seem to bend downsomewhat, so that the average energy intensity (Btu/$) does decrease with increasingexpenditures. Roughly, the average energy intensity decreases by about 30% from the poorest tothe richest expenditure class. Average energy intensities are listed in Table 3. Note that these areaverages ; marginal energy intensities (the slope of the curve) would show even a greater change.Whether the total energy vs expenditue curve really does bend down is controversial, so herewe must refer again to the error bars and ask if it is possible statistically that it could be linear. It

I600 -

1600 .1400 -

AVERAGE OF ALL U.S. HOUSEHOLDS

01 0 25 5 7.5 10 12.5 IS 17 5 20 225 25EXPENDITURES ( IO3 196lt 1

Fig. 2(a).


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1600 -

1600 -

1400 -

600 -

400 -

200 -

Energy cost of living

LEGEND- 5 MEMBERS. . . . . 4 MEMBERS---- 2 MEMBERS

- I MEMBER- AVERAGE OF ALL U.S HOUSEHOLDS

169

01 0 25 5 75 IO 12.5 15 175 20 22 5 25EXPENDITURES ( IO3 1961S )

Fig. 2(b).

1600

600

SINGLE CONSUMERS

T /

t

H TOTAL

/$gf $, f , DIRECT ( ,2.5 5 7.5 IO 12.5 15 17 5 20 22.5 25

EXPENDITURES ( IO3 1961$ )

Fig. 2(c).


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170

I800 -

1600 -

1400 -

600 -

400 -

200 -

R. HERENDEENnd J. TANAKA

2 MEMBERS

0 1 I 1 I0 2.5 5 7.5 IO le.5 IS 17.5 20 22.5 25EXPENDITURES ( IO3 l96tS I

Fig. 2(d).

1800 -

1800 -

1400 -

1200 -5

0 1000 -E%iffaE 800-

600 -

4 MEMBERS

01 I ,0 2.5 5 75 IO 12.5 15 17.5 20 22.5 25EXPENOtTURES ( IO l96l$ )


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171

leoo -

1600 -

600 -

400 -

200 -

Energy cost of living

6 OR MORE MEMBERS

010 2.5 5 7.5 IO 12.5 15EXPENDITURES ( IO3 196lt 1

17 5 20 22 5 25

Fig. 2(f).Fig. 2. Household energy requirements vs expenditures for different household sixes. Total refers to allpurchases; direct, to residential heat and light and automobile fuel. Direct includes the energy penalty inrefining, conversion to electricity, etc.

Table 2. Frequency distribution of energy intensities for 68expenditure categories. Three categories use a rate structure, andtherefore intensity depends on amount purchasedNumber ofEnergy intensity (Btu/$l%l) expenditure categories

09999 310000-19999 32oooo-29999 13oooo-39999 64oooO-4%% 45otJcxLs9999 166oooo-6%% 37ooc4l-7!9999 78oooo-89999 4!Kttw-99999 11~119999 712OOW139999 -

lWOO-19999 21-199999 -2tXxQM99999 -5ooooo-g%%g 3

loooooo-1499999 415m 1w

is not possible to draw a straight line through all of the error bars and it is especially hard if onealso requires that the line go through the origin. In our opinion, the relationship is not linear.All this points to the conclusion that rising energy prices will have (and have had!) a regressiveeffect. It would not be as regressive as one would conclude from only direct energy purchases per

se. To say exactly how much, one would need to know how price increases would be passed on.This should not be interpreted as meaning that the rich would be as hard hit as the poor, of


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172 R. HERENDEENnd J. TANAKATable 3. Energy and expenditure data for several household sizes, andsample error estimates for average of all households(a) Household size-average of all U.S. households; location-urban andrural combined.

Income before Average energytaxes Expenditures Energy intensity(S) (S) (106Btu) (Btu/$)573 1363 151 1110001548 1938 204 105wO2618 2958 302 1020003746 4085 408 999004923 5327 536 1OlOlm6044 6315 643 1020007500 7641 753 986009716 9383 903 9630013583 12758 1160 91200

27750 23056 1840 79700(b) Error calculation for Table 3(a).

CoetBcient error (0s)a1a2ff3Expenditures ($)136319382958

408553276315764193831275823056

-o- -non-zero-0.05 0.10 0.15 0 0.05 0.10 0.150.10 0.20 0.30 0 0.10 0.20 0.300.20 0.30 0.50 0 0.20 0.30 0.50Per cent error in energy3.5 5.7 9.1 8.5 9.2 10.2 12.52.0 3.9 5.9 1.6 2.6 4.2 6.11.8 3.6 5.4 1.0 2.1 3.7 5.5

1.8 3.5 5.3 1.1 2.1 3.7 5.41.7 3.5 5.2 1.9 2.6 4.0 5.51.8 3.5 5.3 2.4 3.0 4.3 5.81.8 3.5 5.3 2.5 3.0 4.3 5.91.7 3.5 5.2 2.3 2.9 4.2 5.71.7 3.3 5.0 2.8 3.3 4.4 5.82.2 3.7 5.9 8.2 8.5 9.0 10.1

(c) Household size-single consumers; location-urban and rural.Income before Average energytaxes Expenditures Energy intensity

(S) (S) (106Btu) (Btu/%)659 10931493 17022686 27793907 37165204 45726307 57817939 71369908 898814494 1658840461 25727

1211702362953514254%62813101440

111000997008480079300769007360069500699007880056100(d) Household size-2 members; location-urban and rural.

Income before Average energytaxes Expenditures Energy intensity(S) (S) (106Btu) (BtulO)644 1638 194 119Ow1573 2127 239 1120002601 2900 317 1090003755 4030 423 1050004993 5029 519 1030006219 6024 609 1010007722 7217 687 952009895 9138 820 8970013986 13114 1080 821002%10 23512 1910 81300


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Energy cost of living 173Table 3. (Contd)

(e) Household size-4 members; location-urban and rural.Income before

taxes(8) Expenditures(8) Energy(106Btu)Average energy

intensitytBtu/$)- 40316232611369148485985743497151380827604

26202338350247095866671080321252622894

34025038649864569980793311601840

130000107ooo110000110008104000101000993009270080400

(f) Household size-6 or more members; location-urban and rural.Income beforetaxes6) Expenditures6) Energy(lo Btu)

Average energyintensity(Btu/$)459 2521 264 105ooo1636 2103 225 1070002511 3304 344 104Ol303549 4399 465 106OCQ4591 6097 609 998005723 6337 710 1120007046 7482 828 111000

9192 9194 1040 10700012822 12048 1220 10100027521 20218 1750 86800

course. The rich would change their vacation plans while the poor would go short on homeheating fuel.If present cross-sectional data can be used as a basis, we also conclude that redistributingbuying power away from the rich towards the poor will increase the energy intensity of personalconsumption expenditures. This result is not as dire as it sounds, however, since theredistribution will result in fewer poor people; as they become richer, their energy intensitychanges. For example, if all households had expenditures equal to the average in Fig. 2a, theirenergy requirements would be only 4.7% higher than the distribution shown in Fig. 2a (seeAppendix B for details of calculation). This is, of course, a steady-state calculation, and ignorestransients.

2. Details of expenditure patterns with incomeIn Fig. 3, we break down the expenditures of three income classes (poor, average, rich)

into 11 categories for a household of 4 members. We note that, in going from poor to rich, therelative portion of total energy requirements due to energy purchases decreases from 65 to 35%and that the increase of non-energy purchases is dominated by growth in travel, education,housing and investments (investments must also be energy-costed; see Appendix C).3. Efect of urbanization on energy intensityBLSs aggregation of data again causes a problem. The average urban household differs intotal expenditures from the average rural non-farm household, which complicates comparison.In Fig. 4, however, where we plot location data next to the average energy-expenditure curve, aclear trend emerges: the urban household tends to the low energy intensity side of the curve,while the rural farm and non-farm (especially the latter) tend to the high energy intensity side ofthe curve. We attempt to quantify this result in Table 4. We see that the urban householdaverages about 15% less energy intensity than the rural non-farm household and is also lessenergy intensive than the rural farm household; from the error bars in Fig. 4, we conclude that


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174 R. HERENDEEN.nd J. TANAKA

.._ RECR&TlON 1.39%TRANSP.EESIDES AUT? \ 7 XJCATION 0.59%, INVEST.. INSUR.0 PURCH. 8 MAINT

MEDICAL, PERS.CLOTHING

(b)

TRANSP. BESIDES AUTO

MEDICAL, PERS.CARE

Fig. 3. Breakdown of energy requirements into 11 expenditure categories, for poor, average and richhouseholds with four members. (a) Expenditures = $2,620; (b) expenditures = $5,866; (c) expenditures =$22,894.


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Energy cost of living900 -

800 -

700 -

; 600 -k8w0= 500-&5= 400 -:5* 300 -

200 -

IO0 -

INSIDE SMSA :I URBAN NONFARM2 RURAL NONFARM3 RURAL FARM

OUTSIDE SMSA :4 URBAN NONFARM5 RURAL NONFARM6 RURAL FARM

///

I 1AVERAQE OF ALL HOUSEHOLDS

0 ALL URBAN AND RURAL FAMILIESAN0 SINGLE CONSUMERS

A ALL URBAN AND RURAL SINGLECONSUMERS

8 ALL URBAN AN0 RURAL FAMILIESOF 2 OR MORE

0' h I I0 IO 2.0 3.0 4.0 50 60 70 6.0ANNUAL EXPENDITURES ( t IO3 1

Fig. 4. Effect of urbanization on household energy intensity. Data points are for national average sizehousehold, by location. Direct comparison is difficult because of different average expenditures for, say,urban and rural farm households. nergy intensity, however, can be compared with the averageenergy/expenditure curve a point lies on. The dotted line is the average curve from Fig. 2a. A point above thecurve is more energy intensive; a point below is less energy intensive. Energy intensity is expressed in Btuper dollar.Table 4. Comparison of energy intensity of urban and rural households.Listed are the percentage deviations from the average (Fig. 2a) for thatexpenditure

Inside SMSA Outside SMSA

Allhouseholds IUrban -1 +2Rural non-farm +10 +20Rural farm t16 +11

tUrban -26 -IISingle Rural non-farm +28* +19consumers Rural farm -5* +5

*Indicates that error bars are too large for statistical significance.this observation is statistically significant. We are more suspicious of the rural farm resultbecause farms typically have trouble dividing energy bills into farm and non-farm use.Another problem in general is the definition of urban and rural non-farm households. Thedefinitions are given in Ref. [12], pp. 7-15, and it appears that urban includes some householdsone would call suburban.Why is the urban household less energy intensive? In Table 5, we break expenditures into 11categories. The urban household spends at least 20% less of its dollar budget on residentialenergy and automobile fuel than the rural. The resulting reduced energy use is not counteractedby the fact that the urban house hold spends at least twice as much for transportation other thanauto. These data seem to confirm the picture of the urban family as one in which people live ina less-energy demanding dwelling (apartment?) and drive less than the folks in the suburbs andcountry.

4. CONCLUDING REMARKSWe have been able to draw conclusions about total energy cost because of our inclusion of theenergy cost of all goods and services. But we repeat that the data are old and aggregated, and that

EGY Vol. I, No. 2-E


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176 R. HERENDEENnd J. TANAKATable 5. Detailed energy and expenditure data for urban and rural households(averaged over all household sizes). Listed are the percentages of total householdrequirement. Figures with parentheses are expenditures in dollars; figures without arethe resulting energy

Household type, inside SMSARuralUrban non-farm Rural farmResidential energyAuto fuelAuto purchase, maint.Transp. besides autoFoodHousingClothingMedical, personal careEducationRecreationSavings, investments,insurance, Misc.

29.1 (3.7) 34.2 (4.7) 43.315.1 (2.7) 17.3 (3.6) 15.86.5 (8.3) 5.7 (8.6) 5.83.5 (1.5) 2.6 (0.8) 0.814.2 (23.8) 11.2 (21.8) 10.115.5 (28.2) 17.1 (32.7) 7.84.7 (8.9) 3.6 (7.8) 3.54.1 (8.0) 3.4 (7.7) 4.01.1 (1.8) 0.7 (1.4) 0.61.7 (3.5) 1.4 (3.3) 1.04.6 (9.8) 2.7 (7.5) 7.4-----loo.1 (100.2) 99.9 (99.9) 100.1

(5.6)(3.7)(9.8)(0.3)(21.5)(17.8)(8.5)(10.4)(1.3)(2.5)

(18.7)(100.1)

Relative energy intensitywith respect to average(from Table 4) 0.93 1.10 1.16

possible specific technological changes in the efficiency of use of energy in the society are simplynot part of our model. Neither are changes in energy use due to increasing prices.Our intent has been to allocate energy requirements to final consumers. Many arbitrary

decisions are inherent in our approach. One example is business travel. We considered this to bea part of industry and commerce and hence allocated it to final consumer products. On the otherhand, it does seem to be a close antecedent of high income; indeed, it is often considered a fringebenefit of a high-paying job. We would also speculate that a good portion of it is actuallydiscretionary. And the great majority of it is by plane, the most energy intensive mode. It caneasily exceed personal discretionary travel. An informal survey of five Ph.D-holding energyresearchers at the University of Illinois showed that, on the average in 1974, each one traveled8000 miles for personal use (i.e. paid for with personal funds), of which most was by car and nonewas by plane. In contrast, each one traveled 13,000 miles for business purposes (i.e. paid for bysomeone else) and 92% was by plane.

Table 6. Per-household business and convention travel, 1972.Conversion to energy at 11,200Btu/passenger mile, whichassumes air travel and includes the indirect energy require-ments as well as the airplane fuel. Passenger mile data arefrom the 1972Census of Transportation, Vol. I, p. 20. Theywere converted to a per-household basis by using data fromStatistical Abstracts of the United States, 1972 Edn; p. 322,1973Edn; pp. 40,320,322

Household income ($) Business Energypassenger miles (lo Btu)Less than 5,ooO 325 3.65001-7500 620 7.07501-10,000 775 8.710,001-15,ooo 1378 15.4More than 15,000 1860 20.8

The general trend in business travel with income is indicated in Table 6; the dependence issteeper than linear. Today, the average per household is still not that large; it amounts to 21million Btu per year for a relatively affluent family vs about 1700 million already allocated. Butthe trend is insidious, as evidenced by the apparent fact that energy researchers travel much morethan average.

This is just one example of a possible, different allocation scheme.


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Energy cost of living 117REFERENCES

I. C. Bullard and R. Herendeen, Proc. IEEE, Vol. 63, No. 3 (March 1975).2. R. Herendeen and C. W. Bullard, CAC Document No. 140, Center for Advanced Computation, University of Illinois at

Urbana. Urbana, II. 61801 (Nov. 1974); A shortened version is C. W. Bullard and R. Herendeen, Energy Policy 3(4) (Dec.1975).3. Consumer xpenditures and Income, Suppl. 3, Part A to EL.9 Report No. 237-93, U.S. Department of Labor, Bureau ofLabor Statistics, (May 1966).4. E. Hirst, Science 184, 134 (1974).5. R. Bezdek and B. Hannon, Science 185, 669 (1974).6. B. Hannon, Science 189, 95 (1975).7. R. Williams (Ed.), The Energy Conservation Papers. Ballinger, Cambridge, Mass. (1975).8. Input-Output Structure offhe U.S. Economy, 1%7. Data tape available from US. Department of Commerce, Bureau of

Economic Analysis. The tape contains margin data unavailable in published versions.9. Personal Consumption Expenditures in the 1963 Input-Oufpuf Study. Survey of Current Business, Jan. 1971, p. 31. This

is at the 83Sector level. A similar study at the 368 level (unpublished) is available from BEA (see Ref. (8]).10. J. Tanaka. Formulation of computer programs for the energy cost of living model, CAC Tech. Memo. 5X. Center for

Advanced Computation, University of Illinois, Urbana, IL. 61801 (July 1975).I I. Eva Jacobs (Telephone conversations). U.S. Department of Labor, Bureau of Labor Statistics.I?. Consumer Expenditures and Income: Survey Guidelines Bulletin 1684. U.S. Department of Labor, Bureau of Labor

Statistics, (G.P.O. Document 2901-0652) (1971).13. Consumer Ewing ndicators. Current Population Reports Series P-65, No. 33, U.S. Department of Commerce, Bureau of

the Census. 16 Oct. (1970).

Error analysisAPPENDIX A

All energies are obtained from a sum of products of energy intensities times expenditurest:

E = 2 CY,.I IWe assume the errors in the Cs and the Ys are independent; then

4C(A(:Y,)+~(~,AY,))!@=AE c C,Y#where AC, and AY, are the respective errors. We express the errors as fractions; viz. AC, = a,C,. AU, = p,Y,; then

AE J(c c~Y.(a.~+B:))_=AE c C


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178 R. HERENDEEN and J. TANAKATable 7. Relative contributions of errors in energy intensity (o) andexpenditures @I). Errors shown here apply to all U.S. families andsingle consumers, urban and rural, from Table 3

Income classPercent error in energyFrom Fromenergy intensity expenditures combined

5.7 8.5 10.23.9 1.6 4.23.6 1.0 3.73.5 1.1 3.73.5 1.9 4.03.5 2.4 4.33.5 2.5 4.33.5 2.3 4.23.3 2.8 4.43.7 8.2 9.0

APPENDIX BCalculation of e#ect of income redistribution

Energy For Total ExpenditureExpenditures Energy No. Householdsm This Class For This Class(8) (lo Btu) (W (IO=Btu) (8 107

1363.42 1Sl1937.79 2042957.79 3024084.95 4085327.40 5366314.91 6437640.60 7539382.71 90312752.45 116023055.79 1840

2.052 309.9 2.985.628 1148.1 10.916.112 1845.8 18.086.530 2664.2 26.677.338 3933.2 39.097.012 4508.7 44.288.352 6289.1 63.817.423 6703.0 69.653.742 4340.7 47.721.118 2057.1 25.78

55.307 33799.8 348.97(a) from Table 3; (b) from Ref. [3].

household with this expenditure is 640x lo Btu. The total if all were average is55.307 10 640x lo6 = 35.40x lOI Btu

which is 4.7% greater than 33.80 10 Btu, the total given above, without redistribution.

Investment-energy intensityAPPENDIX C

The energy coefficients used here are based on the assumption of steady state. Capital expenditures by industry neededfor replacement have been accounted for, but not those for growth (we estimate the latter to require about 5% of the nationsenergy in 1%3). People who invest are thus stimulating growth capital purchases; a dollar lent to a bank or spent for stocksoon finds its way into a construction project, new business, and so on.The average energy intensity of all capital purchases in 1963was 71,300Btu/$. There is some dilution, undoubtedly, sowe use 50,CKlOtu/$ for the energy intensity of investment, and assign to it our worst error assumption, 230%. This value ischanged slightly by additional capital and inflation corrections; see Table 1).

Exergy Research.pdf

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