Principles of the toll roads pricing


  • Piotr JAWORSKI University of Warsaw, Institute of Mathematics, Warsaw, Poland Author
  • Kamil LIBERADZKI Warsaw School of Economics, Institute of Finance, Warsaw, Poland Author
  • Marcin LIBERADZKI Warsaw School of Economics, Institute of Finance, Warsaw, Poland Author



PPPs, toll roads, Engel curves, Tőrnquist function


In this paper the authors refer to the method of commercial provision of road infrastructure called BOT (build-operate-transfer) under Public-private partnerships (PPPs) scheme. First we present the investment criteria for transportation PPP projects as well as application of price theory. Then we recognize that the different participants in PPP projects have distinct goals and requirements that must be met in order for them to be able to participate in an effective partnership. The main challenge for the toll road pricing is to determine the economically viable toll rate that takes into consideration the diverse and sometimes conflicting interests of different stakeholders involved in the project. The main objective is to review the theory of economic principles for optimal toll roads pricing and to review the existing approaches to transportation projects appraisal. Then the authors show how to formally derive the condition for toll rate that meets 2 criteria: 1) is socially optimal and 2) covers operator’s costs. For this purpose we use II type Tőrnquist function, a member of an Engel family of functions. This function models the relationship between income and consumption of inferior and normal goods. Tőrnquist function is a mathematical representation of the well-known Engel curves. These curves record the relationship between the quantity of goods purchased and total income. They are not necessarily straight lines. The demand for some “luxury” goods may increase proportionally more rapidly than income, whereas the demand for “necessities” may grow proportionally less rapidly than income. The precise shape will depend on the individual’s preferences for goods as reflected in the indifference curve map. We deem the highway trip to be a “second necessity good”. There is number of economists who apply the Tőrnquist function for microeconomic analysis. The extremely simple form of the Tőrnquist function allows to get the solution in a closed form.


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Original articles

How to Cite

JAWORSKI, P., LIBERADZKI, K., & LIBERADZKI, M. (2018). Principles of the toll roads pricing. Archives of Transport, 45(1), 53-62.


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