Businesses have gotten bigger over the decades. The Economist asks, how long will these economies of scale hold up? Having worked with a number of very large firms, anecdotally I can say, there must be a size limit after which a company becomes less efficient, not more.

So are businesses like boats or buildings: are they seeking out economies of scale, or are they too big to be efficient? One way to answer this question is to estimate how output levels influence the costs of production in a competitive industry. This relationship—known as a “cost function”—can be tricky to establish because firms often have multiple inputs and outputs. Take farming. Estimating a cost function requires complex information on how each farm’s outputs (milk, meat and crops) and inputs (labour, energy, feed, capital) interact.