In transport economic literature you can find two separate definitions of optimal subsidies for public transports. The first comes from a situation where a public transport operator maximises social welfare. As the consequence of both user and producer economics of scale, an optimal investment policy and optimal (marginal cost) pricing will lead to a financial deficit. A lump-sum subsidy to the public transport operator equal to this deficit will then be necessary to let the operator break even. Though the optimality has more to do with optimal investments and optimal pricing the resulting subsidy is sometimes also referred to as optimal. In what follows this lump-sum subsidy will be referred to as the break-even subsidy.

The other definition of optimal subsidies is the one that will be used here. This definition has more to do with the principal-agent theory and optimal incentives, and is valid in a situation where the transport authority, e.g. the local government hands over the provision of transport services to a private transport operator. The primary goal for the local government, (the principal), is to maximise social welfare, although the government may have some other goals as well, as safety or equity. The goal for the private transport operator, (the agent), however, is to maximise his own profit. The operator supplies transport services in a given area or for specific routes, either as the winner of a competitive tendering process or for some other, probably “historic” reasons. The operator is in a monopolistic position, and cannot be assumed to behave socially efficient. In this situation the government may use subsidies, in some way linked to the performance of the operator, to change the operator’s incentives and thereby affect his decisions. Of course the optimal subsidy is no longer a specific sum of money as in the first definition. Instead with optimal subsidies is meant a system of subsidization that will make the profit-maximising behaviour by the operator simultaneously fulfil the conditions for maximising social welfare.