For a conventional good, an increase in price reduces the consumer surplus of both those who no longer buy the good, and of those who continue to buy it. If, however, consumers must spend real resources to obtain rights for the good, or if the quality depends on the number of other consumers trying to obtain the same good, then a price increase may have different effects. Both these characteristics apply to congestible goods: a consumer's utility decreases in the price he pays and in the number of other persons who use the good. Some users may gain from a price increase which reduces demand. Therefore, even if the revenue is not returned to the users, their welfare can increase.

Payment deterioration models are an important input for the efficient management of pavement systems, the allocation of cost responsibilities to various vehicle classes for their use of the highway system, and the design of pavement structures. This paper is concerned with the development of an empirical rutting progression model using an experimental data set from WesTrack. The data used in this paper consist of an unbalanced panel data set with 860 observations. The salient features of the model specification are: 1) three properties of the mix are sufficient to model the performance of the asphalt concrete pavement accurately, 2) the model captures the effects of high air temperatures at WesTrack, and 3) the model predicts rut depths by adding predicted values of the increment of rut depth for each time period, which is particularly advantageous in a pavement management context. The three mix properties are a gradation index, which is obtained from the aggregate gradation, the voids filled with asphalt obtained for the construction mix in the Superpave gyratory compactor, and the initial in-place air voids. The specified model is non-linear in the variables and the parameters, and is estimated using a random effects specification to account for unobserved heterogeneity. The estimation results and prediction tests show that the model replicates the observed pavement behavior at WesTrack well.

Governmental facilities for such services as education, health, and transportation are often small, of poor quality, and overcrowded, even when the costs are spread among all taxpayers. We also find that governments may subsidize private facilities providing the same services, or may charge admission fees at public facilities. We explain these phenomena with a model which considers two types of people, rich and poor. A majority consisting of poor people may purposely build small and low quality facilities to discourage use by the rich, thereby lowering taxes. For the same reason, the poor may benefit from an admission fee at public clubs, or even from a subsidy to private clubs they do not use.

Consider a consumer who can choose to travel on a congestible fast mode or on a congestible slow mode. Users who most value time will use the fast mode. A toll on the slow mode can induce some people who initially use that mode to switch to the fast mode. A toll on the slow mode with revenue not returned to users then necessarily reduces the welfare of all users. A toll on the fast mode may raise aggregate consumer surplus.  

Consider a consumer who can choose to travel on a congestible fast mode or on a congestible slow mode. Users who most value time will use the fast mode. A toll on the slow mode can induce some people who initially use that mode to switch to the fast mode. A toll on the slow mode with revenue not returned to users then necessarily reduces the welfare of all users. A toll on the fast mode may raise aggregate consumer surplus.

The accurate prediction of rutting development is an essential element for the efficient management of pavement systems. In addition, progression models of highway pavement rutting can be used to study the effects of different loading levels, and thus in allocating cost responsibilities to various vehicle classes for their use of the highway system. Further, such models can be used for evaluating different strategies for design, maintenance and rehabilitation. Finally, if the models contain information about asphalt concrete mixes, they can also provide directions in the proportioning of aggregate, asphalt and air in the mix.

The objective of this paper is to demonstrate the effectiveness of the estimation of rutting models by combining the information from two data sources. The data sources considered are the AASHO Road Test and the WesTrack Road Test. Combined estimation with both data sources is used to identify parameters that are not identifiable from one data source alone. In addition, this estimation approach also yields more efficient parameter estimates.

The results presented in this paper demonstrate that joint estimation produces more realistic parameter estimates than those obtained by using either data set alone. Furthermore, joint estimation allows us to account for the effects of pavement structure, axle load configuration, asphalt concrete mix properties, freeze-thaw cycles and hot temperatures in a single model. Finally, it allows to us to predict the relative contributions of rutting originating both in the asphalt concrete and in the unbound layers in the same model.