# MODELLING NON-PROFIT INSTITUTIONS: THE UNIVERSITY SUPPLY FUNCTION

## ECONOMIC RATIONALITY IN THE NON-PROFIT SECTOR

The problem with optimization models of non-profit organizations lies in the criterion. Profit *by definition* cannot be the criterion. The level of fulfilment of the institution's primary objective comes into consideration. For universities this means, for example, the number of students (or graduates) or the number of research outputs. There is, however, another problem (common to all optimization models) — the optimum lies on the boundary of the set of feasible solutions. This means not only the maximum possible number of students (which is itself unrealistic), but also the tightest possible budget (no reserves), the maximum possible tuition fee (not a cent less than the amount sufficient to fill the university's capacity), the minimum teachers' pay (not a cent more than the amount sufficient to retain the required number of teachers that year) and so on. Such a university would certainly lose its accreditation very quickly, because to keep that accreditation it needs some degree of tradition and stability, not-too-high turnover of teachers (especially elite ones), soundness in meeting financial obligations, and so on. A transient increase in economic indicators in the current year will endanger vitally important parameters for the next year.

That said, economic behaviour is *(again by definition)* optimizing. Economic agents behave in such a way that they choose the best solution from the feasible options. The fulfilment of this subjective optimum definitely certainly shows some common (objective) traits. The agent fulfils such criterion (even if only unconsciously or implicitly) because otherwise it would not succeed in competition with other agents.

Robert H. Frank^{[1]} popularized Milton Friedman's idea comparing the microeconomic model of the firm to the model of play of a skilled billiards player. His play can be neatly described as the application of the law of reflection and the law of conservation of momentum. Yet the player does not mentally construct the angles or compute the momentum; he relies on intuition and experience. However, any player who plays in violation of these laws of physics will not be successful and will not be a member of the set of top players described by the model.

Another example is that of a motorcyclist leaning into a turn so that his angle respects the centrifugal force, the force of gravity and the grip of the road. In the model describing his riding style it would be necessary to sum the vectors of these forces. But the motorcyclist in the model does not sum any vectors. He rides that way because otherwise he would needlessly increase his risk of crashing.

Something similar applies to the firm: profit maximization is not always a day-to-day concern or an explicit management criterion. Nonetheless, a successful firm (one that survives economically in the face of competition) behaves in accordance with profit maximization. It arrives at such behaviour by trial and error. That is why the profit maximization model is an appropriate (and, at a certain level of abstraction, certainly the best) description of the behaviour of a firm in a competitive environment where there is a risk of extinction. We can describe the profit criterion as the “Darwinian” criterion which the firm must respect (even if not explicitly) if it is to be economically successful.

What general criterion can be used for non-profit institutions? As we explained in the introduction to this book, to model non-profit institutions (for which the profit criterion makes no sense) we can apply a more general "Darwinian" criterion — maximization of the probability of survival. This criterion must be respected by every agent operating in an economic environment where there is a risk of extinction. Again, the criterion does not have to be explicit; agents that are successful in a competitive environment implicitly respect it simply because otherwise they would not survive.

We emphasize again that this is a generalization of, notan alternative to, the *homo economicus* paradigm. The standard profit-maximizing agent is a special case of this criterion (for the profit sector in a market economy).

- [1] Frank, R. H.: Microeconomics and Behavior. New York: McGraw-Hill, 2006, p. 6.