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Change in coal cost



Change in gas cost



Change in coal use



Change in gas use



Table 3 alone does not indicate the net effect of the simulated changes on CO2 emissions: it would obviously depend on the the level of coal and gas consumption to which the percentage changes apply. What appears to be small percentage changes could be significant in absolute terms. In reality, data on consumption levels would be readily available to make accurate predictions of electricity market responses to changes in CO2 prices.


The methodology used in this paper estimates the extent of decarbonisation that can be achieved in accord with cost-minimisation objectives of power-plant operators. It illustrates the potential of individual countries to tap into power systems' fuel-switching capabilities, leading to a further reduction in CO2 emissions. The two preliminary examples demonstrate the flexibility with which US utilities respond to fuel price changes, an indication that a price on CO2 would trigger some fuel substitution and lower CO2 emissions in electricity generation in the near future. The Spanish market, largely liberalised and facing emission caps imposed by the EU ETS, displays cross-price elasticities of a higher value, indicating an even more responsive generation sector. A thorough comparison with the United States would require further analysis.

The framework presented could support further climate-policy analyses. It could, for instance, be combined with new-capacity investment behaviour under uncertainty: to what extent would fuel switching offer a viable 'wait-and-see' approach when the future of climate policy is uncertain and new-capacity investments carry a high risk (see Blyth et al., 2007)? The connection between inter-fossil fuels substitution and increased competition from alternative fuels such as renewables can also be further analysed using this tool. More generally, this estimation method reveals one of the core relationships in electricity markets: the linking of fuel cost and fuel use. As such, it could guide many decisions on climate policy design.


A detailed derivation of equations for interfuel substitution models is outside the scope of this paper, so here we only provide key formulae and ideas. The model is essentially based on estimating the power sector's aggregate "variable cost functions". "Variable" refers to the exclusion of fixed costs of generation, and "cost function" refers to a functional relationship between inputs, such as fuel prices, capacity, amount generated and the cost, after optimisation of costs. Thus, the estimates seek to identify the optimised allocation of fuel inputs in the electricity sector.

The cost function is estimated by first assuming a very generic form called translog, and then estimating its parameters from observed data. The translog cost function takes the form of the following "cost share equation" after applying a lemma and a few transformations:

Si = ai + PiqlogQ + PJogK + aJogPi+ ai2logP2+ ai3logP3 (1)

where Sj are fuel cost shares in the total combustible fuels cost; index i=1,2,3 refers to coal, gas and oil; ai is intercept; Q is electricity generated from fossil fuels; K is generation capacity; Pj are fuel prices; and piq, pik and aij are regression parameters (Soderholm, 1999). Formula (1) consists of three equations, one for each fuel; for each fuel equation we have observations over a period of time. The equations are estimated by adding an error term and applying "seemingly unrelated regression" because the equations are linked (e.g. the sum of shares is one). After the regression parameters are estimated, one can apply known formulae for calculating elasticities.

One important aspect of the methodology is that elasticity changes as cost shares of fuels change with time. The significance of this characteristic is twofold: a high elasticity, such as in the case of the oil-gas elasticity in the US example above, can be due to a low cost share of a fuel in the generation mix; secondly, when one projects a policy effect on fuel switching, one needs to have some assumptions for future cost shares (thus, fuel mix and fuel prices) because they will determine future elasticities. In other words, the underlying estimate of the cost function can be assumed to stay the same, but changing cost shares will affect elasticities and therefore the size of response to carbon prices.

As to values of elascticity, one of the common measures of relationship between the price of one fuel and demand for another fuel is "cross-price elasticity". The simplified definition of cross-price elasticity is:

nx, elasticity of demand of fuel X to the price of fuel Y = [% change in demand of fuel X] / [% change in price of fuel Y]

There is a large body of academic literature on the theoretical and practical aspects of estimating cross-price and other elasticities of substitutable input factors in various sectors of the economy (see Frondel, 2004). For this study we used the flexible translog cost function and excluded the capital-investments variable in order to get short- to medium-term estimates.

Cross-price elasticity is defined for changes in the price of only one fuel (and changes in the use of another fuel). However, since carbon dioxide is emitted by both coal and gas, changes in the price of CO2 simultaneously affect costs of coal and gas generation. We therefore need to use another measure of substitution, and one of the classic definitions, the "behavioural" elasticity of substitution (Frondel, 2004), suits the purpose:

a, elasticity of substitution between fuels X and Y = [% change in relative demand] / [% change in relative price].


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