We present a model of car ownership and replacement and use it to evaluate the impact of two policies widely used in the regulation and control of the automobile industry. These are taxes on gas and scrap value for older cars. The two policies are used to either stimulate the sale of new cars or to reduce emissions. Both policies are unlikely to achieve their objectives in this model because they tend to delay the replacement of older cars.


Public authorities regulate the auto industry despite the absence of economic models to explain the workings of the market. The majority of difficulties stem from the interplay between new and used car markets and durability. Nevertheless, market size, emissions from cars, and the impact on economic activity, as well as the environment, are all so important that regulations are often discussed. Most regulation policies are based on the idea that by replacing cars more frequently, the market for new vehicles is active and economic activity, in general, is stimulated. New cars emit less pollution than older models, and rapid replacement also reduces pollution.

By focusing on a simplified picture of the issue, however, some regulatory tools can lead to unexpected outcomes. We want to emphasize the importance of such possibilities. We endogenise consumer replacement decisions and demonstrate that some regulation policies negatively impact this variable. Our model explores two regulation policies. First, we have a tax on gas. The policy is designed to reduce gasoline consumption by increasing the cost of travel. This policy is expected to result in a reduction in pollution. This policy does reduce travel distance, but it has a negative effect on car ownership and replacement. The higher the cost of gasoline is, the longer it takes to replace a car and the older the cars are. The tax has a negative impact on older cars because they are more polluting and less fuel efficient.

Second, we will look at the scrapping premium for old cars. In the last 20 years, a number of European governments have used this instrument, including France 1, to reduce the cost of replacing old cars. This policy assumes that if a person is offered a price higher than the market value of a second-hand car, they will scrap the vehicle to gain the extra money. We demonstrate how the subsidy increases the “value” for old cars. A typical consumer will delay replacing his car, as its price in the future won’t decrease nearly as much. The policy will still increase the value of older cars even if it is only used for a short time. We show that in this case pollution would be increased and that the new car market would be hurt.

The average age of US cars is on the rise. The average age of cars increased from 5.6 to 9.0 in 2001. The increased durability of automobiles may explain this, but we also believe that policies like scrapping premiums or taxes on gasoline play a part. The slow replacement of cars is a source of additional pollution because it results in the use of older (more polluting technologies). In fact, each year, new cars become cleaner, so it’s better to replace old ones with newer models. A user who delays the replacement of their car will generate additional pollution.

Policy makers tend to ignore the replacement time, which is an important aspect. Our analysis shows that taxes on gasoline or scrapping premiums do not always have positive effects on social welfare. It is important to pay attention to the implementation phase. A tax on gasoline should be avoided to the maximum extent possible. It may be more effective to use policies that directly target polluters. The use of devices that can detect excessive emissions in mobile vehicles remotely and outdoors can be very effective. For reasons that remain unclear, this alternative has yet to be seriously considered.

At least two factors are responsible for the difficulty in modeling the automotive market. The dynamic oligopoly of this market makes it difficult to create tractable models, and the theory of dynamic competition is still in its very early stages. The second challenge is the durability of cars and the interaction between the new and used car markets. We abstract from these problems by focusing our model on the consumer’s decision under the two assumptions that we make: (i) price rigidity, and (ii) the used car market is perfectly competitive. The assumptions are not restrictive in terms of our objectives. They have also been used by other literature (see Berry and colleagues, 1995, Yamawaki 2002, Bresnahan 1987, Adda & Cooper, 2000, for example). We derive, under these assumptions, an optimal replacement strategy and demand function for new vehicles for each type of consumer.

The paper is organized as follows. In Section 2, the model is described. In Section 3, we derive the consumer’s decision about buying and replacing a car. In Section 4, we analyze the taxation of gasoline. In Section 5, we discuss the second policy, the scrap value. The final section is the conclusion. The proofs are moved to Appendix A.

Section Snippets

The basic model.

A type th >=0 agent has an instantaneous utility of that when using a vehicle of quality qt. Agents have an infinite lifespan, and time is continuous. In Section 3, we will discuss the more general case (affine transform of t ). The quality of a brand-new car is q0, with q0 >=qt. We assume, without losing generality, that q 0, = 1. The quality depreciates with a rate l and future gains at a b. Start with the date

Consumer decision.

The agent purchases a vehicle if the utility ( t) is greater than the reservation level ( – ). u ( t) > u -. In practice, the value of u – can depend on the available transportation options. Let’s assume that u -=0. Then we will discuss the general case.

We have, em>c/em>(0) = > em>b/em>(0) = ’em>th -/em>/ ’em>b/em>. c(0) > _b(0) _th/ _b. The cost of replacing the with is reduced (positive effect), but the benefit is also decreased (negative effect).

Demand for new cars in relation to gasoline prices.

This section introduces the travel distance as a decision variable. The cost of a certain distance travelled depends on gasoline prices and consumption per kilometer. We examine the impact of an increase in gasoline prices on the decision to replace the car. First, we extend the model. Then, we discuss pollution.

Scrapping premium.

The use of scrapping fees by the public sector has been justified for two reasons. In times of recession, it is a way to stimulate the automotive industry. The second is that by renewing old cars, the average age of the vehicles decreases, resulting in a reduction in emissions. In this section, we consider scrapping old cars as an alternative. We conclude that this does not always achieve both goals.

The scrapping premium increases the value of older cars.


The model was developed to evaluate the impact of the two regulations that regulate the automobile industry. The model’s main innovation is the inclusion of the replacement cycle as an endogenous factor. We conclude that some tools used to regulate the auto market are ineffective because they ignore the effects of the replacement decision.

In general, the increase in gasoline prices is intended to reduce travel.


Thank you to Simon Anderson, Ray Deneckere, and StefProost for their comments and suggestions. Joshua Gans, an anonymous referee, and his comments have been used to improve the revised version. The authors are grateful to the participants of the Workshops held at the University of Melbourne and Catholic University of Leuven, as well as the University of Cergy-Pontoise, which took place on May 22, 2006, during ENPC’s 8th journey of transport. The second author M. Kilani has also been a Visiting scholar at the University of