Optimal pricing for travelcards under income and car ownership inequities

Travelcards are used in many parts of the developed world as a form of payment for public transport that is convenient for frequent users. In essence it involves a one-time payment T at the beginning of a period that covers all trips within that period. Carbajo (1988) applies the two-part tariff approach to find the optimal (welfare maximizing) value for T assuming a nil effect of T on the demand schedule of each and every individual (no income effect). Here we deal with an urban area where individual trips increase with income, but where car ownership - correlated with income - makes the public transport share diminish towards high income segments. A theoretical model is developed to find the optimal values (maximum social welfare with a budget constraint) for T and, simultaneously, for a single ticket P, considering the effect of T on available income as well as differences across individuals regarding car ownership. The model is applied using parameters associated with monthly travel in Santiago, Chile, where both income and car ownership are highly concentrated and correlated, and where travelcards do not exist. We obtain that the two richest segments choose to pay for the single ticket and the other eight choose to buy the travelcard, increasing equity. Sensitivity analysis regarding public transport quality, increased car ownership and poverty reduction show relatively marginal changes regarding optimal prices and preferred form of payment.