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Redistributive Effects of Gasoline Prices

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Abstract

Consumers face significantly different gasoline prices across gas stations. Using gasoline price data obtained from 98,753 gas stations within the U.S., it is shown that such differences can be explained by a model utilizing the gasoline demand of consumers depending on their income and commuting distance/time, where the pricing strategies of both gas stations and refiners are taken into account. The corresponding welfare analysis shows that there are significant redistributive effects of gasoline price changes among consumers, where the welfare costs of an increase in gasoline prices are found to be higher for lower income consumers.

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Notes

  1. See Foote and Little (2011) for a survey of recent studies.

  2. Similarly, Ma et al. (2011) have shown that doubling gasoline prices results in 20% decrease in monthly shopping trips, 14% decrease in monthly purchase volume, or 6% decrease in monthly expenditure.

  3. The highest gasoline price of $4.86 was observed at Mobil Gas Station located at 10 Airport Rd, Nantucket, MA 02554 while the lowest price of $2.58 was observed at Sinclair Gas Station located at 16854 E Highway 20, Claremore, OK 74019. The source and other details of these data are provided in the data section of this paper.

  4. This is similar to studies such as by Jian et al. (2018) who emphasize the importance of considering the demand for commuting services (e.g., carsharing) in the calculation of optimal price.

  5. See Oke et al. (2018) for the interaction between crude oil and refined gasoline based on a network analysis.

  6. See Yilmazkuday and Yilmazkuday (2016) for an alternative (spatial) investigation of gasoline price dispersion based on an unbalanced panel data obtained from gas stations within the U.S. They emphasize the importance of having a gas-station level analysis by showing that about half of the price dispersion in the panel data is due to time effects, while the other half is due to spatial factors. However, their analysis lacks any information on the welfare effects of gasoline price dispersion.

  7. An exception is a pure empirical study by Hosken et al. (2008) who focus on the time dimension of gasoline price differences across 272 stations in Northern Virginia; however, they do not have any welfare analysis on consumers as in this paper.

  8. This is consistent with studies such as by Jiménez and Perdiguero (2011) who show that no rational consumer should travel further than the nearest petrol station in search of lower prices.

  9. Also see studies such as by De Palma and Lindsey (2004), Fujii and Kitamura (2004), Sabir et al. (2011), and Xiao et al. (2011), where commuting behaviour of individuals are investigated in more details.

  10. We downloaded the gasoline price data at midnight of each day from http://gasprices.mapquest.com/. For example, the gasoline price data for September 8th has been downloaded at 12am on September 9th.

  11. Focusing on other topics, earlier studies such as by Abrantes-Metz et al. (2006), Doyle and Samphantharak (2008), and Chandra and Tappata (2011) have also used this data set.

  12. In order to be consistent with the frequency of the gasoline price data, we convert commuting time in minutes to days in the estimation (by dividing them by 60 × 24).

  13. The year of 2011 was the latest year for which such data were available at the time of this study.

  14. In order to be consistent with the frequency of the gasoline price data, the annual wage data have been converted to daily wages (by dividing the annual wages by 365).

  15. Nevertheless, this result is opposed to some other studies such as by Myers et al. (2011) who show that retail gasoline prices are higher in poor neighborhoods; one reason for this deviation may be the spatial coverage of gasoline prices which consists of only three cities within the U.S. in Myers et al. (2011), while this paper covers almost all cities within the U.S..

  16. http://www.wsj.com/articles/SB10001424052702303299604577323661725847318

  17. http://www.nacsonline.com/YourBusiness/FuelsReports/GasPrices_2014/Documents/2014NACSFuelsReport_full.pdf.

  18. In particular, the demand for gasoline is calculated according to \( g_{z}=\varphi d_{z}-\frac {{p_{z}^{g}}}{2w_{z}}\); and cz = nz = yz, where \(y_{z}=\frac {1}{4}+\sqrt {\frac {1}{16}+\frac {{p_{z}^{g}}g_{z}}{2w_{z}}}\).

  19. The U.S. government has been supporting consumer purchase of hybrid vehicles in the forms of federal income tax credits since 2006, but this is achieved across all consumers rather than just low-income consumers. See Beresteanu and Li (2011) for more details.

  20. The price elasticity of demand is implied as \(-{p_{z}^{g}}/\left (2w_{z}g_{z}\right ) \) which is consistent with studies such as by Liu (2014) who show that there is strong evidence of heterogeneous gasoline demand elasticities across states and over time. Also see Lin and Prince (2013) who show that gasoline price volatility also affects the elasticity of demand for gasoline. Havranek et al. (2012) achieve an excellent quantitative survey of the estimates of elasticity reported for various countries around the world.

  21. Instead of the simple case of consumers purchasing gasoline from the closest gas station, in an alternative case, we could have a mass of consumers (say, hz) and a mass of gas stations (say, mz) in each zip code z. In such a case, assuming homogenous consumers/producers, in equilibrium, we would have the condition of \({q_{z}^{g}}=h_{z}g_{z}/m_{z}\), where the gasoline demand of each zip code (i.e., hzgz) is equally shared among the gas stations in that zip code. This case would result in the very same pricing strategy as in Eq. 5.

  22. This result also proposes a theoretical background to empirical studies of “kitchen sink” approach such as by Hosken et al. (2008).

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Correspondence to Hakan Yilmazkuday.

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Appendix: The Model

Appendix: The Model

1.1 Consumers

A typical consumer residing in zip code z gets utility from consuming gasoline combined with commuting and other goods, while she gets disutility from supplying labor. In formal terms, she has the following quadratic utility function:

$$ u_{z}=\varphi d_{z}g_{z}+c_{z}-\left( {g_{z}^{2}}+{c_{z}^{2}}+n_{z}\right) /2 $$
(1)

where φ > 0 is a utility parameter, dz is the commuting distance/time, gz represents the gallons of gasoline purchased from the closest gas station to the consumer residence, cz is the consumption of the goods other than gasoline, and nz is the labor supplied. Such a utility function is imposed to have a linear function representing the demand for gasoline, which is useful to have a clear empirical investigation, below. The budget constraint is given by:

$$ {p_{z}^{g}}g_{z}+p_{z}c_{z}=w_{z}n_{z} $$
(2)

where \({p_{z}^{g}}\) is the price of gasoline, pz is the price of cz, and wz represents wages.

The optimization results in the following demand for gasoline:

$$ g_{z}=\varphi d_{z}-\frac{{p_{z}^{g}}}{2w_{z}} $$
(3)

where the demand increases with the commuting distance/time dz and wages wz, while it decreases with the price of gasoline \({p_{z}^{g}}\).Footnote 20

1.2 Gas Stations

Any gas station g in zip code z produces gasoline according to the following production function:

$${q_{z}^{g}}={r_{z}^{g}} $$

where \({r_{z}^{g}}\) is the gasoline purchased from the closest refiner. Cost minimization results in the following marginal cost of production:

$$ {c_{z}^{g}}={p_{r}^{g}} $$
(4)

where \({p_{r}^{g}}\) is the price of gasoline charged by the refiner. The profit maximization is given by:

$$\max {\pi_{z}^{g}}={q_{z}^{g}}\left( {p_{z}^{g}}-{c_{z}^{g}}\right) -{f_{z}^{g}} $$

subject to the demand for gasoline coming from consumers for whom the gas station is the closest (i.e., Eq. 3),where \({f_{z}^{g}}\) represents fixed costs of the gas station.Footnote 21 The optimization results in:

$$ {p_{z}^{g}}=\varphi d_{z}w_{z}+\frac{{p_{r}^{g}}}{2} $$
(5)

where we have also used Eq. 4. Therefore, the price of gasoline increases with the commuting distance/time dz, wages wz, and costs charged by refiners \({p_{r}^{g}}\). The markups (per gallon) are implied as follows:

$$\begin{array}{@{}rcl@{}} {\mu_{z}^{g}} &=&{p_{z}^{g}}-{c_{z}^{g}}=\varphi d_{z}w_{z}-\frac{{p_{r}^{g}}}{2} \end{array} $$
(6)
$$\begin{array}{@{}rcl@{}} &=&2\varphi d_{z}w_{z}-{p_{z}^{g}} \end{array} $$

where the last equality of the first line has used Eq. 4, and the second line, which will be used to obtain markup estimates after the empirical analysis, has been obtained by using Eq. 5.

1.3 Refiners

A typical refiner r has the following production of gasoline:

$$r_{r}=\left( o_{r}\right)^{\alpha} $$

where or represents oil input. Cost minimization results in the following marginal cost of production:

$$c_{r}=\frac{{p_{r}^{o}}\left( r_{r}\right)^{\frac{1}{\alpha} -1}}{\alpha} $$

where \({p_{r}^{o}}\) represents the price/cost of oil that is faced by the refiner. Note that the marginal cost depends on the amount of gasoline produced rr (as long as we have non-constant returns to scale through α≠ 1; this will be tested empirically, below).

The refiner achieves profit maximization at the gas-station level:

$$\max {\pi_{r}^{g}}={r_{r}^{g}}\left( {p_{r}^{g}}-c_{r}\right) -{f_{r}^{g}} $$

subject to the demand coming from the gas station g located in zip-code z :

$${r_{r}^{g}}={q_{z}^{g}} $$

where \({f_{r}^{g}}\) represents fixed costs of the refiner. The optimization results in:

$$ {p_{r}^{g}}=\varphi d_{z}w_{z}+\frac{{p_{r}^{o}}\left( r_{r}\right)^{\frac{1}{ \alpha} -1}}{2\alpha} $$
(7)

As is evident, the gasoline price \({p_{r}^{g}}\) charged by the refiner for a gas station located in zip code z positively depends on the commuting distance/time dz and wages wz (of consumers around the gas station), price of oil po, and the overall amount of gasoline produced by the refiner rr.

1.4 Final Expression for Gas-Station Gasoline Prices

Substituting Eq. 7 into Eq. 5 implies the following expression for the gasoline price charged by the gas station g in zip-code z:

$$ {p_{z}^{g}}=\frac{3\varphi d_{z}w_{z}}{2}+\frac{{p_{r}^{o}}\left( r_{r}\right)^{\frac{1}{\alpha} -1}}{4\alpha} $$
(8)

As is evident, gas-station gasoline prices are positively related to the commuting distance/time dz and wages wz in the same zip code, oil prices/costs \({p_{r}^{o}}\) faced by the closest refiner, and gasoline production level of that refinery rr.

Similarly, substituting Eq. 7 into Eq. 6 results in the following expression for markups:

$$ {\mu_{z}^{g}}=\frac{\varphi d_{z}w_{z}}{2}-\frac{{p_{r}^{o}}\left( r_{r}\right)^{\frac{1}{\alpha} -1}}{4\alpha} $$

where they increase with commuting distance/time dz and wages wz but decrease with costs charged by refiners \({p_{r}^{g}}\).Footnote 22

1.5 Closing the Model

In zip code z, optimization of any consumer (given by Eqs. 1 and 2) results in the following demand for the consumption of the goods other than gasoline:

$$ c_{z}= 1-\frac{p_{z}}{2w_{z}} $$
(9)

which are produced (using labor only) according to the following expression:

$$ y_{z}=n_{z} $$
(10)

Hence, the market clearing condition for the goods other than gasoline is given as follows:

$$ c_{z}=y_{z} $$
(11)

which implies through the quadratic equation solution of the combination of Eqs. 2 and 9 that:

$$ y_{z}=\frac{1}{4}+\sqrt{\frac{1}{16}+\frac{{p_{z}^{g}}g_{z}}{2w_{z}}} $$
(12)

where we have used yz > 0.

Finally, zero-profit conditions for gas stations and refiners imply that their fixed costs are covered by their respective profits.

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Yilmazkuday, D., Yilmazkuday, H. Redistributive Effects of Gasoline Prices. Netw Spat Econ 19, 109–124 (2019). https://doi.org/10.1007/s11067-018-9435-9

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