Short-run pricing strategies to increase corporate average fuel economy.
In 1974 the average fuel efficiency of new automobiles sold in the United States reached a low of 14.2 miles per gallon (MPG). Close on the heels of the Arab-OPEC oil embargo of 1973-74 and the ensuing petroleum price shocks, Congress passed the 1975 Energy Policy and Conservation Act. The Act required each manufacturer to meet sales-weighted corporate average fuel economy (CAFE) standards, beginning with 18 MPG in 1978, and gradually increasing each year to 27.5 MPG in 1985 (Figure 1). The expressed purpose of the CAFE standards was to stimulate the development of technology to improve fuel efficiency. The possibility of raising the relative prices of the least energy efficient models as a strategy to meet the standards was considered, but only as a last resort. (1)
Although there continues to be intense debate as to whether fuel price increases or the CAFE regulations drove the fuel economy improvements of the 1970s and 80s, several studies agree that improvements in automotive engineering and design, rather than pricing strategies, played an overwhelmingly dominant role. (2)
No empirical evidence supports the effectiveness of using pricing strategies to increase the overall level of automotive fuel economy.
Every year since 1985 automobile manufacturers have successfully petitioned the National Highway Traffic Safety Administration, which determines the level of the CAFE standard, to reduce the target (from 27.5 to 26 MPG in 1986-88 and 26.5 MPG in 1989). In each case at least one manufacturer argued that it would be unable to meet the original target with its planned product offerings and would have to resort to other strategies that would result in unacceptable economic costs.
This paper explores a method of estimating the costs of achieving fuel economy goals when pricing strategies are used to alter the distribution of sales. The method employs the closed-form equation for consumers' surplus derived from the multinational logit model of discrete choice discussed by McFadden [1973! and assumes that manufacturers must bear the full cost of meeting the fuel economy target. The estimated cost represents an upper bound on the losses firms would incur by setting prices to minimize loss of profit.
Using econometric estimates of the sensitivity of vehicle choice to vehicle price, together with market shares and fuel efficiencies for 1986, I estimate the costs of short-term improvements in average fuel economy using pricing strategies for General Motors, Ford, and Chrysler. Minor adjustments of up to 1 MPG cost 1-2 percent of the price of a $10,000 car. For improvements of 2 MPG or more, however, pricing strategies become a costly way to improve fuel economy. The technique also estimates the market shares for each car line that correspond to the pricing solution. It thereby identifies which car lines would be most affected.
The technique produces precise price changes and market shares for each car line. Readers should not place too much weight on the apparent precision, but should consider the estimates as an approximation, the usefulness of which lies in measuring the difficulty of meeting fuel economy targets via pricing strategies alone. One can compare the size of these estimates to the fines for failing to meet the standards ($50 per MPG per car) or to typical manufacturer rebates to stimulate sales (often $100 to $2,000 per car).
II. A FORMULATION OF THE PRICING
Faced with the CAFE requirements, a firm can respond with engineering and design improvements or by raising the prices of less efficient models and lowering the prices of those that exceed the standard. Technological improvements generally require a lead time of three to five years. Very large fluctuations in fuel prices have occurred in far shorter perids (Figure 1), creating the risk that a manufacturer's product offering could be out of step with the market. Without the time to alter product lines (and neglecting the possibility of altering consumer tastes through advertising), manufacturers would have to resort to pricing strategies or face prosecution and fines.
Theoretical models of manufacturer behavior given a binding CAFE constraint and assuming profit maximization have been presented by Kleit [1988!, Kwoka [1983! and, earlier, by Stucker, Burright, and Mooz [1977!. Kwoka assumes a monopoly firm selling two models, with linear demand and constant per-unit cost functions. He further assumes that the less fuel efficient car line yields a higher profit to the manufacturer than the more efficient line. Deriving the first-order conditions for profit maximization, he obtains equations for the optimum sales quantities. These equations depend on own- and cross-price elasticities of demand, as well as car line production costs. Kleit's model also assumes linear demand and cost functions, but allows competition between Japanese and American manufacturers and includes five types of automobiles: Japanese basic small, Japanese luxury small, American basic small, American luxury small, and American large. A market solution is derived in which manufacturers set prices to maximize profits. Kleit estimates the economic loss of a 1.5 MPG increase in fuel efficiency achieved via market sales shifts at $3.5 billion. However, by using such broad market classes, Kleit's model misses significant opportunities to improve sales-weighted fuel economy by shifting sales among makes, models, and engine-drive-train configurations. In any case, Kleit [1988, 18! makes an educated guess at industry cost functions since, as he points out, "...no study exists of short-run cost curves in the auto industry."
In practice, accurate cost and sales price data are generally unavailable at the level
of car line configurations (engine and transmission combinations) making the market equilibrium approach infeasible. To circumvent this difficulty, I assume that manufacturers will bear the full cost of the sales shifts required to meet the CAFE target. This eliminates the need for price and cost data because the objective becomes zero consumer's surplus loss instead of profit maximization. Although this is not a market solution, it is an efficient solution, given that all costs are allocated to the producers. It is also an upper bound on the costs firms would bear in the market solution. A practical method for estimating this cost using the multinomial-logit random-utility model of consumer choice is presented below.
Any change in car prices to achieve a CAFE target will result in a loss (or gain) of utility by consumers and a loss (or gain) of profits by producers (see, e.g., Varian, [1978, ch. 7.4!). If the unit costs of producing car type i, [c.sub.i!, do not change, the change in producer's profit is
(1) [Mathematical Expression Omitted!
where [P.sub.oi! and [q.sub.oi! indicate the initial price and quantity of car type i, and [p.sub.i.sup.*! and [q.sub.i.sup.*! its new price and quantity. Given a set of product offerings that falls short of the fuel economy standard, the producer chooses a new price vector that minimizes (1), subject to the sales-weighted fuel economy constraint:
(2) [Mathematical Expression Omitted!
where car line efficiency, [e.sub.i!, and the mandated sales-weighted average fuel efficiency, E, are in gallons per mile. Solving the producer's constrained optimization problem requires demand equations, efficiencies, selling prices, and production costs by car line. Because accurate vehicle sales prices and production costs are difficult to obtain, one must find another way of estimating the cost of meeting the fuel economy constraint.
For every allocation of costs between producers and consumers there will be a different efficient pricing solution. the solution at zero consumer's surplus loss is of interest because the producer bears the full cost of meeting the standards. Not only is this an upper bound on the producer's cost at the market solution, but it is related to the compensating variation associated with the consumer bearing the full cost of the standards.
Given a change in price vectors from [Mathematical Expression Omitted! the compensating variation is defined as the change, C, in income, y, required to hold the consumer's utility constant at its original level, U(p,y). That is, C must satisfy.
(3) [Mathematical Expression Omitted!
or, in terms of the expenditure function,
(4) [Mathematical Expression Omitted!
If we can find a price vector that satisfies the fuel economy constraint with no change in consumer's surplus, the C = 0.
If cars were the only items consumers purchased, then the producer's surplus loss, pound, would exactly equal the compensating variation required when consumers bear the full cost of the fuel economy improvement and the producer's surplus loss is zero. Since the producer's profit-maximizing price vector is [Mathematical Expression Omitted!, he will suffer a loss under [Mathematical Expression Omitted! of,
(5) [Mathematical Expression Omitted!
If we assume zero profits in the initial case [p.sub.oi=[C.sub.i!) then (5) becomes,
[Mathematical Expression Omitted!
Thus, the sum of price changes times cars sold, or the average price change times total units sold, equals the amount of producer's surplus lost in a competitive market.
We can choose a constant, k, such that
(6) [Mathematical Expression Omitted!
Multiplying all prices by k does not change reltive car prices and, if we compensate consumers with additional income, C, such that equations (3) and (4) are satisfied, quantities purchased will not change. As a result, consumer expenditures will increase by an amount exactly equal to C = pound. Of course this is only true if consumes spend all their compensated income on cars, and, therefore, it is only an approximation.
The cost of meeting the fuel economy constraint when producers bear all the cost is an efficient solution to the fuel economy constraint problem. It is approximately equal to the compensating variation when consumers bear all the cost, and it is certainly an upper bound on the producer's surplus loss. Unfortunately, it is not necessarily the total social welfare loss, since the market solution will generally not be the same as either. Its chief advantage is that its computation requires sales and efficiency data only, plus a parameter describing the sensitivity of cartype choice to car price. The computation method using the multinomial-logit random-utility model is described below.
III. A MULTINOMIAL LOGIT METHOD FOR
ESTIMATING THE "COST" OF PRICING
The multinomial logit model expresses the probability of a consumer choosing car
line configuration i as a function of the indirect utility derived from the choice of i, [U.sub.i!, and of all other alternatives, [U.sub.j!, j = 1, ..., N:
(7) [Mathematical Expression Omitted!
The multinomial logit model can be interpreted either as a disaggregate model in which [U.sub.i! contains a random component distributed according to the extreme value distribution, as derived by McFadden [1973!, or as a model of a representative consumer with a preference for diversity in consumption as in Anderson, de Palma, and Thisse [1988!. Since I will be using aggregate sales data, the representative consumer interpretation is more appropriate, although issues of aggregation bias remain (for a discussion see Train [1986, ch. 6!).
Williams [1977! and Small and Rosen [1981! have shown that for the multinomial logit model the change in consumer's surplus resulting from a change in options available to the consumer is
(8) [Mathematical Expression Omitted!
where U (*1) is the utility of new choices, and N1 and N2 indicate that the number of choices may also change. The parameter (-1/B) is the dollar value of an additional unit of utility and, therefore, B is the coefficient of car price in the utility function U. As Varian [1978, 209! points out, it is very unlikely that the marginal utility of income is ever constant, and thus equation (8) constitutes an approximation of consumer's surplus.
The problem of holding consumer's surplus constant (S = 0) while meeting the fuel economy standard requires a nonlinear, constrained minimization procedure, in which a penalty function captures the efficiency constraint. I minimize the square of consumer's surplus for simplicity it has a minimum of zero when S = 0 and increases symmetrically as S deviates from zero in either direction. If the CAFE standard is 1/E MPG, and the efficiency of each car line is [E.sub.i!, then the average efficiency of a manufacturer's sales is
(9) [Mathematical Expression Omitted!
The "penalty" function I minimize equals the sum of the squared change in consumer's surplus plus a penalty weight, or scaling factor, [sigma!, times the squared deviation of average fleet fuel economy from the CAFE target:
(10) [Mathematical Expression Omitted!
Scaling fuel efficiencies in terms of gallons per thousand miles allows greater computational precision as the squared deviation from the CAFE standard becomes very small.
IV. CALIBRATING THE MODEL
Since only the prices of cars change, we can write [U.sub.i! as,
(11) [Mathematical Expression Omitted!
where [D.sub.i! is the price increase or decrease for model i required to meet the CAFE standard, and [A.sub.i! is the utility of car line i otherwise. This does not necessarily imply a linear utility function, but only that the marginal utility of income is approximately constant. Although not attempted here, one can specify a different [b.sub.i! for each car line if information is available on how marginal utilities vary across car lines. Otherwise, only one parameter, namely B, need be known since we can estimate the [A.sub.i! using actual market sales and a normalization rule.
First I compute market shares for each car line using sales data for 1986. Since the number of purchases is in the millions, it is reasonable to assume that the shares equal the probabilities of choice for each alternative, [P.sub.i!. Given that initially all the [D.sub.i!=O,
(12) [Mathematical Expression Omitted!
Since [&P.sub.i!=1, a normalization rule must be chosen to uniquely determine the [A.sub.i!. The rule [&A.sub.i!=0 is useful in that it insures a certain degree of comparability across calibrations. Since any valid normalization rule will cause the [A.sub.i! to differ by a constant, it is clear from (7) or (8) that it does not matter what rule we choose. Using (12) and the normalization rule the [A.sub.I! are determined by
(13) [Mathematical Expression Omitted!
(14) [Mathematical Expression Omitted!
Given the [A.sub.i!, one needs only the value of B to complete the multinomial logit car line choice model.
The CAFE standard constrains each manufacturer to individually meet the MPG standard. However, consumers may choose not to buy vehicles from a manufacturer who raises prices. My formulation of this problem recognizes that a manufacturer may lose customers if he rearranges his price structure to meet a CAFE goal. But, a pricing strategy consistent with equation (10) will not change the manufacturers market share. Consider firm X whose share of the total market is (1 - p) X 100 percent. Clearly there are some additional exp([U.sub.i!) terms missing from equations (7), (8), and (9) representing the product offerings of firm X's competitors. These terms do not affect the efficiency constraint (9) since all sets of weights proportional to sales are identical when normalized. If the other firms do not change the utility level of their product offerings (which would be likely if only one firm failed the CAFE standard) then equation (8) can be written as
(15) [Mathematical Expression Omitted!
C is the sum of terms for the other producers which, by assumption, is constant:
(16) [Mathematical Expression Omitted!
Although this changes the value of the term whose logarithm is taken, it does not change the conditions for the minimization of (10). S is minimized when S = O, which occurs when the numerator and denominator in (15) are equal. That equality, together with the assumption that C is constant, implies that firm X's total share of the market remains unchanged. As a result there is no change in the number of cars sold, only in the types.
A convenient property of the multinomial logit model described above is that one can carry out partial analyses for each manufacturer in isolation, without having to consider the product offerings of other manufacturers. This property of the multinomial logit model has been termed the "independence from irrelevant alternatives property," and its realism has been debated at length. Train [1986, 18-24! provides a good discussion.
Finally, we require an estimate of the marginal utility of income. The literature on automobile demand contains over a dozen estimations of multinomial-logit automobile-choice models, beginning with the seminal paper by Lave and Train [1979!. In most of these studies the price coefficient is not a constant but rather depends on household characteristics as well. Most commonly, vehicle price is divided by income so that the marginal utility of income decreases as income increases. Greene and Liu [1988! survey ten studies of automobile choice and conclude that a reasonable midpoint estimate of B is -0.00056. They also calculate an estimate for a typical U.S. household based on the Lave-Train model of -0.00066. Both of these are in 1985 dollars. Since parameter B is crucial to the analysis, it is sensible to try a wide range of values, say from -0.0003 to -0.0008. (3)
V. COSTS AND PRICE CHANGE ESTIMATES
Analyses of sales distributions and fuel economy have shown that sales shifts among car lines and engine-transmission combinations within car lines have a greater impact on sales-weighted fuel economy than sales shifts among size classes. (4) Thus, car line and engine-transmission combinations should be treated as alternatives. The Environmental Protection Agency collects and maintains both efficiency and sales data at the required level of detail (see EPA [1988!). Counting only domestically manufactured makes and models (the CAFE law requires that firms' domestic and imported fleets individually meet the standard), Chrysler offered 76, Ford 74, and General Motors 179 combinations of car lines, engines and transmissions in 1986. The number of these can be reduced by combining "twins," car lines with the same body and engine options, such as the Ford Taurus and Mercury Topax or General Motors Abody cars. Twin configurations were not combined if their estimated fuel economy differed by more than 0.1 MPG. After combining twins, Chrysler had 27 configurations, Ford 42, and General Motors 74.
I first estimated the surcharges and rebates necessary to improve each manufacturer's sales-weighted efficiency by 1, 2, 3, and 4 miles per gallon. The average price change multiplied by the total number of cars sold equals the firm's losses due to the CAFE constraint, under the condition that total consumer satisfaction remains unchanged. These average subsidies also indicate how hard it would be to achieve a given increase in fuel economy. All of the numbers in Table I and Figure 2 were computed using the "typical" value of B=-0.00056, suggested by Greene and Liu [1988!.
From the results shown in Figure 2 it appears that increases in fuel economy of less than 1 MPG can be achieved relatively easily using pricing strategies. Manufacturers seem to have considerable leeway to make up a few tenths of a mile shortfall by means of marketing strategies. The estimated average subsidy for a 0.25 MPG gain for Ford, for example, is $17, and for Chrysler is only $7. An improvement of 0.5 MPG is estimated to cost General Motors $51. Compare these costs to the $5 per 0.1 MPG fine prescribed by law for failure to meet the CAFE standard.
Using pricing strategies to make large improvements in average fuel economy costs far more than engineering and design improvements. Green and Liu estimate the total cost of technologically-based fuel economy improvements since 1978 at less than $500 for an improvement of over 8 MPG, or $6 per 0.1 MPG per car. I estimate the cost of an improvement of only 4 MPG via pricing strategies at between $700 and $1900, or $18-$48 per 0.1 MPG per car. Furthermore, the estimated cost of each mile per gallon increment goes up at an increasing rate (asymptotically to infinity) as the limit of the most efficient configuration offered is approached. This result is intuitively plausible, since each additional consumer dissuaded from his desired choice is less willing to switch that the last.
Just as important as the price changes is the elimination of certain car lines by the extreme sales shifts required for gains of 3 and 4 miles per gallon. For example, Chrysler's big cars (Diplomat, Gran Fury,
New Yorker, Town and Country, Newport, and Fifth Avenue) sold over 200,000 units in 1986, over 20 percent of Chrysler's total auto sales. To achieve a 3 MPG increase in sales-weighted fuel economy, these car lines would have to shrink to 4.2 percent of Chrysler's sales, less than one-fifth of their previous volume. Another mile increase reduces their share to less than 2 percent, with the Diplomat, Gran Fury, Newport, and Fifth Avenue car lines essentially eliminated. The same result holds for General Motors whose sales of Caprice, Bonneville, Gran Prix, Regal, Cutlass Supreme, Parisienne, Delta 88, LeSabre, Riviera, Tornado, Electra, Olds 98, and Cadillac DeVille, Seville, and El Dorado would all be decimmated by the sales shift required for even a 2 MPG improvement. Ford's adjustment would be somewhat less severe, but still serious. The LTD Crown Victoria and Grand Marquis lines drop from over 13 percent to less than 4 percent of sales to meet an improvement of 4 MPG.
The estimated costs of pricing strategies differ considerably among the three manufacturers. General Motors would have the greates difficulty improving average fuel economy by sales-mix adjustments. Even an improvement of 1 MPG calls for nearly a $200 per car subsidy. From that point on it costs General Motors nearly twice what it costs Ford or Chrysler for a given increase in fuel economy. Chrysler, often portrayed as a restricted line manufacturer of smaller cars, actually falls between General Motors and Ford. Ford, it appears, has the most flexible product line. The ease with which fuel mileage can be increased depends not only on the range of fuel efficiency in makes and models offered, but also on their market success. That is, a manufacturer must not only have fuel thrifty cars available, but they must also sell well. Plotting cumulative sales versus fuel consumption illustrates the point (Figures 3-5). The three curves show that Ford has a far greater fraction of its sales in low consumption (low GPM) makes and models. Ford's curve also shows more slope than either General Motors' or Chrysler's. Consistent with the results described above, General Motors curve is quite steep. With so much of its sales within a small range of fuel efficiency, General Motors has little flexibility to affect its sales-weighted average with changes in sales-mix.
Finally, the estimated costs of improved fuel efficiency strongly depend on the value of B, the price sensitivity parameter. To quantify this sensitivity, I recalculated the costs of a 1 MPG improvement for each manufacturer using three values for B (-0.0003, -0.00056, -0.0008). The resulting cost estimates were less affected by decreases in the value of B (greater absolute value and greater price sensitivity) than by increases (Table III, Figure 6). Increasing B to -0.0003 nearly doubled the average subsidies required for a 1 MPG increase. Changing B did not change the relative position of the manufacturers. General Motors' sales-weighted fuel mileage remains very resistant to change by pricing strategies. Ford and Chrysler seem to have much greater flexibility.
Which value of B is most appropriate? According to Green and Liu, -0.00056 is a reasonable median value for 1985. Still, this may underestimate the price changes necessary to achieve fuel efficiency increases for two reasons. First, as noted above, the marginal utility of income is not likely to be constant across all car buyers. In fact, in nearly all automobile choice models it is inversely related to income. If buyers of inefficient cars tend to have higher incomes and are thus less sensitive to price, then use of a typical value should underestimate the magnitude of price changes required. The second caution applies to small changes in the fuel efficiency standard. Although economic models often assume that consumers are sensitive to the smallest price signal, it may well be that auto taxes or rebates on the order of $10-$20 would have no effect on consumers at all. That is, there may be a threshold for price changes to have any effect on car choice. If this is the case, the estimated price subsidies for changes of less than 1 MPG could be too small.
A practical tool for approximating the costs of short-term pricing strategies to improve sales-weighted average fuel economy is developed and tested using 1986 data for the "big three" U.S. manufacturers. The method is not based on a market equilibrium solution, but rather calculates a set of price changes that hold consumer's surplus constant while meeting the fuel economy requirements. The manufacturers absorb all of the loss in welfare associated with the fuel efficiency constraint, so that the estimated cost represents an upper bound estimate of the cost they would suffer in a market solution. The method not only calculates the average cost and magnitude of price changes, but indicates the impact on market shares of individual car lines. I wish to emphasize that the method deals with short-run pricing strategies only. In the long run manufacturers have the opportunity to improve the fuel efficiency of all makes and models through improved technology and design changes. The costs of such improvements depend on the nature of existing technology and the ease with which innovative new technologies can be discovered.
Analysis of 1986 data suggests that relatively small increases in fuel efficiency can be obtained fairly cheaply by means of pricing strategies. Improvements of less than 0.25 MOG cost from $3 to $10 per 0.1 MPG, depending on the manufacturer. Large improvements, on the other hand, are very expensive. Improvement of 2 MPG cost $11 to $33 per 0.1 MPG, and 4 MPG increments cost an average of $18 to $48 per 0.1 MPG. These compare with an estimated average cost of less than $6 per 0.1 MPG for engineering and design changes to increase energy efficiency and to the fine of $5 per 0.1 MPG for failure to comply with the CAFE law. The marginal cost of fuel efficiency improvements via pricing strategies increases at an increasing rate as the value to the consumer of gains in fuel efficiency decreases. For Chrysler, the first increment costs $80 to go from 3 MPG higher to 4 MPG higher costs $670. These results depend on the sensitivity of consumer choice to vehicle price, on the mathematical form of the model, and on the manufacturer's position in the market.
Even moderately large improvements in mileage devastate certain inefficient car lines. It appears that an increase of only 2 MPG would eliminate some previously important car lines. The caveats noted above apply here as well.
This analysis indicates that achieiving higher average fuel economy by short-run pricing strategies alon can be effective only for small improvements. A manufacturer faced with a shortfall of one- or two-tenths of a mile per gallon (and possibly higher) should be able to effectively use price incentives or other marketing strategies to eke out compliance with the legally mandated standard. Meeting shortfalls numbered in whole miles per gallon by means of short-run pricing strategies, however, would be burdensome. The nearly three billion dollar subsidy General Motors would need to raise its 1986 sales-weighted average fuel efficiency from 26.4 to 28.4 MPG illustrates the point (almost $700 per car times 4.4 million cars). These results do not apply to the long-run effects of "gas-guzzler" taxes on inefficient cars and rebates for more efficient cars since engineering, design, and technological responses are not considered.
(*1) Senior Research Staff, Oak Ridge National Laboratory. This paper was written while I was on assignment in the Office of Policy Integration, U.S. Department of Energy, Washington, D.C. I wish to thank Dr. Carmen Difiglio, U.S. Department of Energy for directing me towards this research and my anonymous referees for comments that led me to significantly improve on earlier drafts. Views expressed are mine and not necessarily those of the Department of Energy or Oak Ridge National Laboratory.
(1.) See U.S. Dept. of Transportation [1977!.
(2.) See Greene [1987!, Heavenrich, Murrell, Cheng, and Loos [1985!, U.S. Dept. of Transportation [1982!, and Greene, Hu, and Till [1985!.
(3.) The minimization program was implemented using the Broyden-Fletcher-Goldfarb-Shanno variant of the Davidon-Fletcher-Powell variable metric algorithm as implemented by Press, Flannery, Teukolsky, and Vetterling [1987!. The FORTRAN driver program for this implementation is available from the author. Cambridge University Press holds the copyright for the numerical subroutines. Solution of the problem occurs if and only if L = 0. T he ability of the algorithm to find the minimum was sensitive to the choice of [alpha!. Values of in the vicinity of 0 to 100 worked when fuel efficiency was given in gallons per 1,000 miles.
(4.) See Patterson [1982!, and Greene, Hu, and Till [1985!.
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|Author:||Greene, David L.|
|Date:||Jan 1, 1991|
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