Maximizing public value for subsidized non-profit firms: a mathematical economic model

In many public service industries, firms are assumed to maximize certain public goals and are not allowed to make any profits. These public service firms are financed by fixed and variable subsidies and fees-for-services paid by users. Standard economic models, such as the profit maximization and cost minimization model, are not suitable for describing the production structure and the economic behavior of these firms. Productivity and efficiency measures derived from these models therefore are not accurate. This paper derives a model that fits this type of firm and its economic context. It derives the exact mathematical relationships between public value, services delivered, (money) revenues, costs, service prices, resource prices and subsidies. In an empirical setting the model can be used as a reference to calculate productivity and efficiency scores. The usability of the model is demonstrated by an application to Social Labor Services in the Netherlands.