The effect of financial constraints on the optimal design of public transport services

Recent experience with the design of bus services in Santiago, Chile, seems to confirm Jansson's (1980) assertion regarding observed planned bus frequency and size being too low and too large, respectively. We offer an explanation based upon the relation between cost coverage, pricing and optimal design variables. We recall that average social cost decreases with patronage, which generates an optimal monetary fare below the average operators' cost, inducing an optimal subsidy. Then we compare optimal frequency and bus size–those that minimize total social costs–with those that minimize operators' costs only. We show that an active constraint on operators' expenses is equivalent to diminish the value of users' time in the optimal design problem. Inserting this property back in the optimal pricing scheme, we conclude that a self–financial constraint, if active, always provokes an inferior solution, a smaller frequency and, under some circumstances, larger than optimal buses.