This classic paper by David Kreps and Jose Scheinkman is quite possibly my favourite economics paper of all time. It’s easy to explain and understand, but still makes a very deep point that connects two of the most famous economic models in a simple way.

Way back in 1838, Antoine Augustin Cournot wrote what is, I believe, the first mathematical model of competition between firms. The model makes reasonable predictions that are, in a broad sense, supported by empirical observations. One of these predictions is that as more firms enter a market it should become more competitive and prices should decrease.

However, the Cournot model has one deeply unsatisfactory dimension: firms set the quantity that they wish to sell, and then the market determines the price at which that quantity can be sold. This is most certainly not how firms actually make decisions; when a customer goes shopping, the store posts a price and the customer decides how much to buy.

In 1883, Joseph Bertrand came along and wrote a model where firms set prices, and then the market determines the quantity that will be sold at that price. This is a much more satisfactory foundation for a model of firm behaviour. Unfortunately, the Bertrand model generates very poor predictions. One of the implications of the Bertrand model is that two firms are enough to generate extremely intense competition and low prices. Another implication is that adding more firms to the market doesn’t change the outcome. Neither of these implications are compatible with empirical observations.

So we have one model with good assumptions but inaccurate implications, and one model with poor assumptions but reasonable implications. Is there a way that we can resolve this tension?

It took 100 years, but in 1983 Kreps and Scheinkman found the resolution: they key is to use a two stage model. In the first stage, firms install production capacity. Then, in the second stage, the firms compete over prices ala Bertrand. But here’s the kicker: the outcomes that are produced by this model are exactly the same as the Cournot model.

So we now have a model with both good assumptions and reasonable implications. Of course, this model is still highly stylised and leaves a lot of potentially important features unmodelled, but it does provide an extremely compact way of reconciling two very important economic models. Pretty neat.

Additional notes for economists

One of the things that I really like about this paper is that it can be taught at different levels. For an introductory level class, students can be introduced to the very intuitive story presented above. For an intermediate level class, where the students have a working knowledge of differential calculus, the analysis can be shored up with a derivation of the outcome that occurs along the equilibrium path.

For a more advanced class (perhaps honours level or first year graduate students) a full derivation of the equilibrium can be provided. Providing the full equilibrium is not appropriate for lower level classes because classifying equilibrium strategies off the equilibrium path (when firms install differing quantities in the first stage) introduces some complications.