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Relative Price Elasticity of Demand Change: A Case Study for Hydrous Ethanol and Gasoline in Brazil

Paulo Henrique de Mello Sant’Ana
Professor, Center of Engineering, Modeling and Applied Social Sciences
Federal University of ABC (UFABC), São Paulo – Brazil

 

Elasticity is frequently used in economics to analyse how the change of a variable affect others.  Price elasticity of demand and cross price elasticity of demand are often used in energy economics, but these indices have limitations if there are close substitutes for a good with similar prices. The objectives of this paper are to: (1) Calculate price elasticity of demand and cross price elasticity of demand for hydrous ethanol and gasoline for flex-fuel vehicles in Brazil, also showing the limitations of both indices; and (2) Propose an elasticity index that has better results than elasticity of demand and cross price elasticity of demand for the case studied.

1. Introduction 

Elasticity is frequently used in economics to analyse how the change of a variable affect others.  Two of the most used elasticity in energy economics are price elasticity of demand and cross price elasticity of demand. Price elasticity of demand (equation 1) measures the sensitivity of quantity demanded to price change, where p is the price and q is the demand of good x. Cross price elasticity of demand (equation 2) measures the sensitivity of the demand for a good to a change in the price of another good, where p is the price, q is the demand, x and y are goods

[equation 1]

 

                                                    

 [equation 2]
 

Hsiao et Hsiao (1985), Abdel-Khalek (1998), Liu (1983), Bentzen et Engsted (1993),  Boonekamp (2007), Brons et al (2008), He et al (2011), Fan and Hyndman (2011), Fatima  et al (2012) are examples of calculation of price elasticity for energy modelling, market analysis and policymaking. Frondel (2004) calculated cross price elasticity of demand to understand and appreciate energy substitution.

When calculating price elasticity of demand and cross price elasticity of demand for flex-fuel[1] vehicles in Brazil, the results were not consistent with market behavior. The limitation of both indices when analyzing real data was the motivation for the research of another elasticity index.

The objectives of this paper are to: (1) Calculate price elasticity of demand and cross price elasticity of demand for hydrous ethanol and gasoline for flex-fuel vehicles in Brazil, also showing the limitations of both indices; and (2) Propose an elasticity index that has better results than elasticity of demand and cross price elasticity of demand for the case studied.

Section 2 shows how the fuel market for light vehicles works in Brazil. Section 3 describes the limitations of price elasticity of demand and cross price elasticity of demand, calculating these indices for hydrous ethanol and gasoline in the Southwest region of Brazil. Section 4 shows the relative price elasticity of relative demand index created. Furthermore, it explains why it is a better index than price elasticity of demand and cross price elasticity of demand for the case studied.

 

2. Fuel market for light vehicles in Brazil: ethanol, gasoline and flex fuel

The oil crisis of 1973 stimulated the Brazilian government to launch a program to foster ethanol production from sugarcane called PRO-ALCOHOL. PRO-ALCOHOL was launched by the Government in two variants: (1) compulsorily using 10% anhydrous ethanol as an additive to gasoline, not requiring changes in the motors; and (2) voluntarily using 100% hydrous ethanol (95% ethanol + 5% water) in modified Otto cycle motors (Goldemberg, 2006).

The car manufacturers have made a few adaptations, and hydrous ethanol vehicles dominated national sales in the 80s. Hydrous ethanol shortage in the late 80s has reduced customer confidence, drastically reducing hydrous ethanol car sales. In the 90s flex-fuel technology for light vehicles was developed. Flex-fuel vehicles run with gasoline and hydrous ethanol in any rate (from 0% to 100%). According to the National Car Manufacturing Association (ANFAVEA), flex-fuel car sales began in 2003. This technology put hydrous ethanol back in the market. Since then, flex-fuel vehicles owners can choose hydrous ethanol or gasoline in the gas station, depending on their relative price. The harvest of sugar cane officially begins in April, but is harvested primarily between May and November. Ethanol price is usually lower during this period.

In 2011, flex-fuel cars reached 91% of total sales for light vehicles in Brazil. Flex-fuel car fleet reached 45% in 2010 and is expected to increase up to 86% in 2020 (UNICA, 2011). Table 1 shows the evolution of light vehicles sales in Brazil. It is possible to notice that flex-fuel car sales are dominating national sales since 2006, reaching 91% in 2011.

Table 1: evolution of light vehicles sales in Brazil (2005-2011)

 Table 2 shows the evolution of light vehicle fleet in Brazil. Flex-fuel car fleet is expected to increase in the future, since national sales are increasing in a higher rate.

Table 2: evolution of vehicle fleet since 2005 in Brazil.

Section 3 describes the limitations of price elasticity of demand and cross price elasticity of demand. A case study for flex-fuel vehicles in Brazil is used to show these limitations.

 

3. Limitations of price elasticity of demand and cross price elasticity of demand   

Southwest region is the business-economic center of Brazil. It’s was the responsible for 70% of hydrous ethanol and 47% of gasoline consumption in 2011 (ANP, 2012).

All gas stations sell hydrous ethanol and gasoline in Brazil. Hydrous ethanol (called just ethanol from this part of the paper) has a lower heating value (LHV) of 5.097 kcal/l. Gasoline with 20% of anhydrous ethanol has a LHV of 7.254 kcal/l. Table 3 shows the evolution of gasoline and ethanol sales and prices in the Southwest region of Brazil. Sales are shown in cubic meters. Prices are shown in current Brazilian Real per litre (R$/l), and also in current 10,000 x Real per kilocalories (10,000 R$/kcal). The conversion is made to consider the LHV, since gasoline and ethanol have different energy amount per litre.

Flexible fuel car fleet in Brazil is shown in the same table. The higher this number, the greater the propensity of flex-fuel consumers to switch fuel when there are changes in relative prices of gasoline and ethanol.

The difference between the price of ethanol and gasoline, in terms of LHV, is also in Table 3. It shows the propensity of flex-fuel vehicles owners to switch fuel. If this difference is zero, it means that the price of ethanol and gasoline is equivalent in energy terms.

The percentage in total sales of ethanol is in the last column of Table 3. This number shows how fuel price changes reflect the consumer’s choice. Values highlighted in the last column mean that the total variation from one period to the next is greater than 1.0% in modulus. This means that the flex-fuel vehicles owners have changed from one fuel to another significantly within a month. The other values mean that total variation from one period to the next is equal or lower than 1.0% in modulus.

It’s possible to notice in Table 3 that if price difference is close to zero, a small change in the relative price leads to a significant change in the percentage of ethanol in total sales. This result is reasonable because there is a considerable flex-fuel fleet since 2009 in Brazil, as shown in Table 2. As flex-fuel vehicles fleet increases in Brazil, this fact tends to increase as the relative price between fuels is close to zero and price changes occur.

A conclusion that can be inferred from Table 3 is that when price difference between fuels is high (positive or negative), the change in the relative price don’t affect significantly the percentage of ethanol in total sales from one month to another. However, if price difference between fuels is low (close to zero), the change in the relative price usually affect the demand structure from one month to another. Highlighted values help to check it. 

Price elasticity of demand and cross price elasticity of demand should show that this situation was supposed to happen. However, next section shows that the results were not reasonable.

 

Table 3: market data for ethanol and gasoline in Brazil

Price elasticity of demand for gasoline and ethanol and cross price elasticity of demand for gasoline (x) – ethanol (y) and ethanol (x) – gasoline (y) were calculated to analyze the response of demand to variation in prices of both fuels. The indices consider the values of price and demand in the same row and the next one.

Table 4 shows the results on a monthly basis, together with the price difference between gasoline and ethanol in terms of LHV and the percentage of ethanol in total sales in the Southwest region of Brazil. Values highlighted in the elasticity columns are elastic (> 1.0).  The last column of Table 1 is explained in the next section.

Highlighted values in grey means that market should show an elastic behaviour, because the variation from one period to another is greater than 1,0% in modulus. White cells mean that the percentage of ethanol in total sales column should be inelastic, because the variation from one period to another is equal or less than 1,0% in modulus. Highlighted values only indicate how the market should behave, but doesn’t reflect any scientific method.

From January to August 2009, the high price difference between gasoline and ethanol didn’t change the percentage of ethanol in total sales significantly. Price elasticity of demand and cross price elasticity of demand data is not consistent with market behavior in this period. The numbers should be inelastic, but the majority is elastic.

From September 2009 to April 2010, the low price difference between gasoline and ethanol made the market more sensitive to relative price changes, reflecting the percentage of ethanol in total sales. Price elasticity of demand for gasoline and cross price elasticity of demand for ethanol (x) – gasoline (y) are elastic in this period. It reflects market behaviour. However, from May 2010 to August 2010 these indices should be inelastic, but they are not.

Price elasticity of demand for ethanol data is consistent from September 2009 to November 2010, with just a few exceptions (September 2009, June 2010 and September 2010). Cross price elasticity of demand for gasoline (x) - ethanol (y) shows some consistent data from September 2009 to November 2010, but it’s not for September 2009, December 2009, January 2010, February 2010, April 2010, June 2010, September 2010 and November 2010.

From December 2010 to January 2012, market was supposed to be more sensitive to relative price changes in most of the period, because the price difference between gasoline and ethanol is low. It can be seen in Table 4 that most of the indices are consistent, except for cross price elasticity of demand for gasoline (x) - ethanol (y). However, price elasticity of demand for gasoline and cross price elasticity of demand for ethanol (x) - gasoline (y) are volatile. Both indices have high average numbers and high standard deviation.

It’s possible to draw two general conclusions with the elasticity indices calculated in the case studied.

The first is that a fuel may be elastic or inelastic in different periods, because it depends on the price difference of its direct substitute. If the price difference is high, price elasticity of demand tends to be inelastic. However, if the price difference is low, price elasticity of demand tends to be elastic.

The second is that price elasticity of demand and cross price elasticity of demand don’t take into account seasonal effects from one period to another. This fact may affect one or both variables. For example, in the case studied, there are months that customers use more or less their vehicles because of the number of days or vacation. This fact would change the demand from one period to another for both fuels, even if price wouldn’t. This would cause high elastic numbers from one month to another in price elasticity of demand and cross price elasticity of demand. 

Next section proposes an elasticity index that overcomes seasonal effects, considering the relative changes of price and demand. 

Table 4: elasticity indices for ethanol and gasoline in Brazil

 

4. Relative price elasticity of relative demand change: a better index for market analysis 

The elasticity index proposed in this section considers the market seasonality of both products from one period to another. Furthermore, it considers the relative changes of price and demand of two goods.  The elasticity index is called relative price elasticity of relative demand (εrp). Equation 3 shows the created index, where p is the price, q is the demand, x and y are goods. It doesn’t matter which variable is x or y, because the results are the same in modulus.

Values of  εrp  between 0 and 1 are inelastic. It means that relative changes in the demand and price of any goods have a relatively small effect on the quantity of the goods demanded. 

Values of  εrp  above 1 are elastic. It means that relative changes in the demand and price of any goods have a relatively large effect on the quantity of the goods demanded. 

 

                                        

[equation 3]

The last column in Table 4 shows the results. Values highlighted are elastic (> 1.0).

From January to August 2009, market indicated that numbers should be inelastic, as explained in the section 3. Relative price elasticity of relative demand for ethanol and gasoline (εrp ) data is consistent with market behavior, except in February 2009 and July 2009.

From October 2009 to August 2010, εrp  data is consistent, except in November 2009. However, εrp   is lower than other elasticity indexes in this month. From September 2010 to February 2012, εrp  data show better results than other elasticity indexes.

Table 5 shows in the second column the market move, which is the percentage of hydrous ethanol sales to total sales movement from one period to another times 100. Third column shows the index created index relative price elasticity of relative demand change. Fourth, fifth, sixth, seventh and eighth columns are the price elasticity of demand for gasoline; price elasticity of demand for ethanol; cross price elasticity of demand for gasoline (x) – ethanol (y); and  cross price elasticity of demand for ethanol (x) – gasoline (y), respectively.  

εrp has the best correlation with market move if compared to the other indices. Both cross price elasticity of demand have negative correlation indices, which does not reflect market behavior. It also happens with price elasticity of demand for gasoline. Price elasticity of demand for ethanol has a positive result, but with a low correlation number if compared to εrp.

 

Table 5: market move and the elasticity indices for ethanol and gasoline in Brazil
 

 

Figure 1: market move and the elasticity indices for ethanol and gasoline in Brazil

 

Figure 1 shows graphically the evolution of market move and the elasticity indices for ethanol and gasoline in Brazil. εrp follows market behavior better than other indices.In general, εrp index has better results than elasticity of demand and cross price elasticity of demand for the case studied. Relative price elasticity of relative demand (εrp) may be useful in econometrics, input-output model and market analysis.

 

5. Conclusion

Price elasticity of demand and cross price elasticity of demand are often used in energy economics, but these indices have limitations if there are close substitutes for a good with similar prices.

The case study of ethanol and gasoline for flex-fuel vehicles in Brazil shows that a fuel may be elastic or inelastic in different periods, depending on the price difference of its direct substitute. If the price difference is high, price elasticity of demand tends to be inelastic. However, if the price difference is low, price elasticity of demand tends to be elastic. Another finding is that price elasticity of demand and cross price elasticity of demand don’t take into account seasonal effects from one period to another.

The elasticity index proposed overcomes two problems of price elasticity of demand and cross price elasticity of demand. The first is the price difference of direct substitutes that may be elastic or inelastic in different periods and the second is market seasonality.

εrp  index has better results than elasticity of demand and cross price elasticity of demand for the case studied. εrp has the best correlation with market move if compared to the other indices. It considers the relative demand change of relative price change, which the price elasticity of demand and cross price elasticity of demand indices do not consider.  

Relative price elasticity of relative demand (εrp) may be useful in econometric modeling and market analysis. The variable “x” may be also a basket of goods, comparing it with the relative change of “y”. A natural sequence of this work would be the study of three or more variables in an expanded  εrp index, building a matrix of relative demand and price changes.

 

6. Notes and References 

[1] Flex-fuel vehicles runs with hydrous ethanol and gasoline in any rate (from 0% to 100%)

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