Energy efficiency


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Energy efficiency

  1. 1. Energy Efficiency: A Study in Derived Demand Michael Alexander1 International Innovative Institute ABSTRACT: Examination of the economics of energy efficiency can be unduly complicated by the assumption that the demand for energy is a real demand. However, this paper takes the approach that the demand for energy is not a fundamental demand, but rather a derived demand – derived from the demand for energy services. This approach can greatly simplify the analysis of energy efficiency. Note that although the paper is expressed primarily in terms of the demand for electricity, the same underlying analysis would apply to automotive demand for gasoline, water for irrigation, or any other derived demand. This paper focuses on the Takeback Effect (sometimes called the “Rebound Effect”) as an application of the derived demand approach. Section I of this paper shows some of the problems with using the demand for energy as the basis of analysis, and discusses how looking at the demand for energy services can simplify the analysis. Section II discusses the relationship between the demand for energy services and the demand for energy and shows how one can convert from one to the other. Section III deals with the limitations of traditional supply and demand analysis in analyzing the real world. The Appendix examines the use of the concept of “negawatts” to produce similar results. SECTION I: THE PROBLEMS WITH USING THE DEMAND FOR ENERGY In a traditional economic setting, the equilibrium price and quantity of a good can be determined by a supply and demand curve. 1 The author may be contacted at <> page 1 of 15
  2. 2. Energy Efficiency: A Study in Derived Demand Figure 1: Traditional Supply and Demand In such an analysis, the Consumer Surplus can be thought of as the area between the demand curve and the price line (P0). Figure 2: Consumer Surplus page 2 of 15
  3. 3. Energy Efficiency: A Study in Derived Demand (Note that producer surplus is the area between the supply curve and the price. However, in utility regulation, the producer surplus is usually regulated by a fixed rate of return, and therefore is not relevant to most analyses of energy efficiency involving regulated industries. For that reason, it is omitted from the discussion in this paper.) However, when examining the effects of conservation and the demand for electricity, however, it is clear that this framework requires refinement. A simple example will suffice: Consider a customer who keeps his home heated and air-conditioned to 72 degrees year round, paying a price of 10¢/KWH for electricity. After enrolling in a new government program, the customer’s heating and air conditioning units have their efficiency increased by 10%. (The cost in this example is exogenous to the consumer, and occurs as a one-time cost, not an on-going marginal cost of electricity) Since the consumer is getting the same amount of heating and cooling at for a lower electricity use, one would expect that their demand curve would shift in. Let us assume, for simplicity sake, that in this case the supply of electricity is completely elastic. Since the customer is living in the same 72o house, and paying 10% less in total, logic would dictate that he is better off. However, without changing the assumptions underlying our original analysis we would come to the conclusion that the consumer was not better off, but rather worse off. Figure 3: Misleading Effect of a 10% improvement in Energy Efficiency In the prior situation, his consumer surplus was area CPB, now that is reduced to area CPA, which means that he is somehow area CAB worse off, which is not logical. page 3 of 15
  4. 4. Energy Efficiency: A Study in Derived Demand One solution is to assume that energy efficiency is beneficial if there is a sufficient decrease in the price. Figure 4: Demand Declining While Facing an Upward sloping Supply Curve As we see in figure 4, our theoretical consumer has added to their surplus by area BCED and lost area ADF. Therefore, under this transition, they are better off if and only if BCE is larger than ADF. This is approach gets us half way there; the customer can be better off, but not all the way there; the customer is not definitely better off. In order to deal with this dilemma, Brennoni suggested that “Because energy efficiency increase the amount of energy service one gets, the value consumers gets from initial levels of consumption will increase, not decrease. Thus the effect of energy efficiency investments is not to shift the demand curve down… but to pivot it.” page 4 of 15
  5. 5. Energy Efficiency: A Study in Derived Demand Figure 5: Brannon’s Rotated Demand Curve (from his Figure 4) Unfortunately, the fundamental problem remains that if the price is unchanged at C, then the consumer surplus change is ACD (the new Surplus) minus BCE (the old surplus), and again, even though the customer gets the same temperature, the consumer surplus could actually shrink if BCE > ACD. It is also not clear intuitively why the shift would occur, other than in some specialized cases of “crowding out.”2 The problem with the preceding examples is that they are all set in terms of the demand for electricity.ii But, people do not want electricity, per se. They want the services of electricity. iii Therefore, the demand for electricity is a derived demand, not a primary demand.iv We need to look at the area under the demand for energy services curve if we want to see what is happening, in terms of consumer surplus. The first thing to note is that the demand curve for energy services does not shift with changes in energy efficiency. The pleasure that a person derives from a 72o house (or X lumens of light in the house, etc.) is the same. Therefore, energy efficiency does not shift the demand curve for energy services at all. What does change is to decrease the cost of obtaining those energy services. Looked at in this way, instead of seeing a 10% increase in efficiency as a decline in the demand for energy, we can see it as a 10% decrease in the price of those services. So, the cost free 10% improvement in efficiency at a fixed cost for electricity gives us Figure 3A. 2 I shall discuss crowding out later in the paper. page 5 of 15
  6. 6. Energy Efficiency: A Study in Derived Demand Figure 3A: Effect of Energy Efficiency in terms of Demand for Energy Services3 Now we see that the effect on consumer surplus of the added efficiency in our simplified example is a clear increase of area PGBA (note that G=90% of P, since we posited a 10% efficiency increase. Further, we have the difference between the amount demanded at A and the amount demanded at B (which is what we expected), which is the intuitive explanation of the takeback effectv (sometimes called the “Rebound Effect”). The actual takeback would be determined by the transformation function which converts energy services to energy demand. Note that the size of the takeback effect will depend upon the change in energy efficiency (the larger the increase in efficiency, the larger the takeback effect) and the slope of the demand curve, with a highly inelastic demand resulting in a small takeback effect, and a highly elastic demand resulting in a large takeback effect. A more complex formulation of the supply curve does not create a problem. Customers would still be demanding energy services, but they get the same services at a cheaper rate. It might be as simple as the 10% reduction seen above, or it might be more complicated, with varying slopes depending upon the degrees of savings, and even an initial increase in cost to pay for the more efficient equipment. 3 In this paper, I will not be using “Heating and Cooling Degree days” the same way as NOAA (National Oceanic and Atmospheric Administration) does, but rather simply to indicate a number of degrees of temperature adjustment for duration of time. In reality the customer’s utility is probably a function of temperature, not change in the temperature. It is also worth noting, in passing, that the cost of heating and the cost of cooling are probably not the same. page 6 of 15
  7. 7. Energy Efficiency: A Study in Derived Demand Figure 7: Effect of Increasing Energy Efficiency Note that in this example, there is an initial cost (A-B) to running the more efficient equipment4 as well as a decreased marginal cost of the energy service (reflected in the change in slope between the two supply curves). Therefore, whether the price of the services increases or decreases (and therefore whether there is a net increase or decrease in consumer surplus, will depend on whether the Demand curve crosses the two supply curves to the left of D (the intersection of the “inefficient” and “efficient” supply curves) or to the right of D. SECTION II: CONVERTING BETWEEN THE DEMAND FOR ENERGY SERVICES AND THE DEMAND FOR ENERGY While customers demand energy services, utilities provide energy. Therefore, it is necessary to look at how to convert from one to the other. In general, this is relatively straightforward if one has good engineering estimates of the energy consumption of the appliances involved in converting energy consumption to energy services. The easiest example would be an automobile which gets x miles per gallon. One could then look at the demand for gasoline, multiply it by x and get the demand for miles driven. Similarly, one could convert the cost of gas to the cost of miles, simply by dividing it by x. While the equations may be more complicated, if we assume that we know the function for the production of energy services (which may require conversations with an engineer, especially if things get complicated), then we know: 4 As mentioned before, the supply curve for regulated utilities is seldom, if ever, the marginal cost of energy, so the reasons that the supply curves take on the shifts and reformations that they do is not a concern for this paper. page 7 of 15
  8. 8. Energy Efficiency: A Study in Derived Demand EQ-1: f(energy consumption) = energy services, and EQ-2: f-1(energy services) = energy consumption. Similarly, if the price of energy is linear5 then: EQ-3: f-1(supply cost of energy)=supply cost of energy services and EQ-4: f(supply cost of energy services) =supply cost of energy. Therefore, if one knows the demand curve for energy, D(p), then one knows the Demand for energy services f(D(p)). If one knows the Supply curve for energy S(p), then one knows the Supply curve for energy services f-1(S(p)). The relationship between the elasticity of demand (εenergy) for energy and the elasticity of demand for energy services (εservices) is relatively easy to establish. Short-term elasticity for energy (εenergy) is defined as the percent change in Quantity of energy services divided by the percent change in price of energy. EQ-5: εenergy = (∆Q/Q)/(∆P/P) Subsituting EQ-1 into EQ-5 EQ-6: εservices = (∆f(Q)/f(Q))/(∆f-1(P)/f-1(P)) If f is a linear function (or linear at the margin), EQ-6 will simplify to: EQ-7 εenergy = εservices Short Term vs. Long Term Elasticity By definition, short term elasticity covers the change in quantity demanded when there is no change in technology. Long term elasticity covers the change in quantity demanded 5 Increasing and decreasing block prices for energy are not consistent with this analysis, but will not be considered in this paper. page 8 of 15
  9. 9. Energy Efficiency: A Study in Derived Demand after a technological response has taken place. This distinction is not relevant to the demand for energy services, which are unchanged with technology. In effect, long-term elasticity is the sum of short-run elasticity and technological elasticity (the study of the adoption of technological change, endogenously and exogenously supplied is not examined in this paper. Therefore all discussions of elasticity in this paper concern short-run elasticity only.) A Definition of the Takeback Effect What does this mean in terms of the takeback effect? The takeback effect is defined as the difference between the amount of energy used after an improvement in conservation and the savings one would obtain if customers use the same amount of energy services. In other words, if one were to improve the insulation of a home by 10% one would expect to see a 10% change in the energy used for home heating and air conditioning if the customer did not change their heating/cooling behavior. However, because the price of heating and cooling a home is now 10% less (since the same energy consumption will result in more heating and cooling), as the result of the price effect customers would likely increase the amount by which they heated and cooled their homes, which will diminish the energy savings experienced. It has been postulated that that takeback effect could exceed the savings from the energy conservation program. In a simple example with completely elastic supply curves, consider the 10% increase in energy conservation: $/Heating and cooling degree Day A P0 S0 B .9*P0 S1 C D Heating and cooling degree Days Figure 8: Takeback Effect page 9 of 15
  10. 10. Energy Efficiency: A Study in Derived Demand Because of the lower price, however, the consumption of energy services has increased from C to D in terms of energy services. In terms of energy itself, the increase in demand (prior to applying the increase in energy efficiency) would be f-1(D) - f-1(C). After applying the increase in energy efficiency, the takeback would be 0.9*[f-1 (D) - f-1(C)]. Note that by the definition of elasticity: EQ-7 D-C= ∆Q Substituting this into EQ-5, we get: EQ-8: ε = ((D-C)/Q)/(∆P/P) Solving for (D-C)/Q by multiplying both sides by [(∆P/P)], we get: EQ-9: (D-C)/Q= ε*(∆P/P) In other words, in terms of energy services, the takeback effect as a percentage of demand (with Q≈(D+C)/2 is simply elasticity times the percent change in price. Note that the percent change in the price of energy services is 1 minus the increase in efficiency. As an example, if the elasticity of demand for electricity is about 0.25, a 10% increase in efficiency will result in a (0.25*0.10=0.03) 3% takeback effect. Therefore, if a study, such as those surveyed by Gottronvi reports a significantly higher takeback effect, one should suspect that something other than price effects may be going on. If we assume that f(), is roughly linear, then in terms of energy demand, the takeback effect as a percentage of demand is also equal to the same elasticity times the percent change in price. Hence, the higher the price elasticity the higher the takeback effect. In fact, the takeback effect will exceed 100% if EQ-10 1 < ε*(∆P/P) or multiplying both sides by (P/∆P), the takeback effect will exceed 100% if EQ-11 (P/∆P) < ε Note that, if the supply curves are not complely elastic, the same result holds, although (∆P/P) may be more difficult to calculate, especially in a situation, such as that shown in Figure 7 above. page 10 of 15
  11. 11. Energy Efficiency: A Study in Derived Demand SECTION III: PROBLEMS WITH TRADITIONAL SUPPLY AND DEMAND ANALYSIS While Sections I and II dealt with traditional supply and demand analysis, the bread and butter of the micro-economist, there are a number of other possible models of decision making for consumers and they might affect the final results. Consider the following alternatives to the traditional demand curve. • Budget Decision making A consumer may put together a budget for consumption. Therefore, the consumer rule is “I will spend roughly $x for electricity each month.” In this case, the consumer’s total outlay for energy will be the same, and an improvement in the energy efficiency of an appliance will be wiped out with a corresponding increase in energy use either on the same appliance (i.e. more comfortable temperatures), or with an increase in the use of other appliances in the home. The result would be a 100% takeback effect. • Conservation thinking There is reason to believe that customer’s utility functions include a belief that they are saving energy. (And based on imperfect knowledge, that belief may not be accurate.) Therefore, a consumer may say something to the effect of “Since I have better insulated my home, I have done my bit for the environment. Now I can set my thermostat to a more comfortable temperature, etc.” To the degree that the feeling of conserving is not based in actual data, the exact effect may be unknown. • Higher conservation costs drive out cheaper options As an example, consider a person whose windows leak. If that person could install low cost single pane windows, they probably would. However, if the market only offers higher priced dual pane windows, for some customers, the cost of the upgrade might exceed the value for some customers. Looking at Figure 7-a, we see that this could happen on a system wide basis if the demand for energy services crosses the original and increased efficiency supply lines to the left of their intersection point page 11 of 15
  12. 12. Energy Efficiency: A Study in Derived Demand Figure 7a: Effect of Increasing Energy Efficiency As a result, that customer will use less efficient windows than they might have. As a result one will see a rotated demand curve for electricity looking like the one in Figure 5 above: Figure 9: More Expensive Conservation Measures Crowd Out Conservation at Some Points page 12 of 15
  13. 13. Energy Efficiency: A Study in Derived Demand This means that for some customers, the amount of energy they use might actually be above the APPENDIX: NEGAWATTS AND THE TRADITIONAL ANALYSIS The proponents of the “Negawatt” view of energy efficiency would call increases in energy efficiency an increase in supply rather than a decrease in demand. In order to graph this in a traditional Supply and demand curve, one would leave the demand curve unchanged, but generate a supply curve S2, which is the sum of the tangible energy (from S1 the supply curve of “tangible” electricity) and the number of negawatts produced. One would then look at the intersection of the demand curve and S2. Figure A-1: The “Negawatt” View In the Negawatt view of the universe, the actual reduction in energy demand is the quantity demanded at D minus that demanded at F consumers are made better off by energy conservation, since when S0 shifts out to S1, their surplus rises from ABD to ACE. Producers see a new surplus, instead of BGE, they now see, CGE, which might be an increase or a decrease. Although it is clear that total surplus has increased by DEF, so (costless) energy efficiency is a benefit both to consumers and to society. The actual amount of energy demanded in this analysis was J before the increase in efficiency. K is the amount of “tangible” and negawatts of energy, of which H are real and need to be generated. If one looks at J, the amount of energy plus negawatts generated to meet the old equilibrium level, one can see that L is the amount of tangible electricity generated, and J-L is the amount of negawatts “consumed”. H-L would be the take-back effect. It would not be possible, with a non-increasing demand curve and a non-decreasing supply curve for H-L to exceed J-L, so at no point can the takeback effect exceed the savings from a demand curve. The exceptions would occur if the traditional supply/demand rules do not apply as mentioned in section III. page 13 of 15
  14. 14. Energy Efficiency: A Study in Derived Demand In the model above, can we estimate the takeback effect, given that we know the price reduction B-C? Had there been no change in the quantity of electricity demanded, the total demanded would be J. That demand would be made up of L megawatts and J-L negawatts. However, because the price of electricity is lowered (held down), by the introduction of conservation, the new quantity demanded is K (Note that K-J can be determined using the price elasticity: η*J*(B-C)/B). The sum of the megawatts and negawatts demanded is where the demand curve crosses the Supply curve, in this case K. The price for the quantity K demanded is C. At price C, H units of real electricity (megawatts) will be consumed and K-H negawatts will be consumed. The takeback effect is the increase in real megawatts, therefore, the takeback effect, in this case is H-L. Figure A-1 may be complicated if one assumes that there is an initial cost (M) to adopting these energy conservation measures. The Negawatt version of the model, unfortunately, cannot be graphed if supply is completely elastic, although the analysis can be reconstructed without particular difficulty. The concept of negawatts, unfortunately, is not directly compatible with the concept of derived demand. For instance, if we assume a basic linear supply curve: EQ-12: P=mQ + G Improving efficiency by (1-x)6 would result in the negawatt world in an equation of the form EQ-13: Pn = x*mQ + G In other word, the price for Q=0 would be the same (G), and would diverge from there. However, in terms of energy services, an increase in efficiency of (1-y)7 would result in an instantaneous decrease in the cost of energy services, resulting in an equation of the form EQ-13a: Pd = y*mQ + y*G In other words, while a graphical representation might intersect at a single point, at all other points Pn ≠ Pd. REFERENCES 6 (0<x<1) 7 (0<y<1) page 14 of 15
  15. 15. i Brennan, Timothy, “Energy Efficiency: Efficiency or Monopsony”, presented at the Center for Research in Regulated Industries Western Conference, June 18, 2009 ii Bently, W.G., C. E. Cosgrove, and P. W. Stallcup, "Integrating Econometric and End-Use Models: A Realistic Approach to Conservation Programs," Proceedings of the Third EPRI Load-Forecasting Symposium March 25-27, 1981, July 1982, pp. 44-76 iii Crew, Michael and Spiegel, Menahem, “Price Caps, Demand Side Management and Public Goods”, presented at the CRRI Western Conference, June 18, 2009 iv Becker, G.S. "A Theory of the Allocation of Time", Economic Journal, Vol 75, No. 299 (September 1965) pp 493-517. v Alexander, Michael, The Effect of Changes in Technology of Derived Demand The Takeback Effect in Energy Conservation Programs, Doctoral Dissertation, University of Minnesota, December 1997, available upon request to the author <>. vi Gottron, Frank, “Energy Efficiency and the Rebound Effect: Does Increasing Efficiency Decrease Demand?” CRS Report for Congress, Congressional Research Service, Library of Congress, Order Code RS20981 (July 30, 2001), available at