Quantum impact and the supply-demand curve

Perhaps the best-known result from neoclassical economics is the 'law of supply and demand'. This depicts markets using curves of supply and demand that intersect at a unique equilibrium, whose value represents a kind of aggregate market decision about price. However, because it is impossible to separate supply and demand in practice, the model has little in the way of empirical backing. In finance, in contrast, the related question of price impact, where a large transaction results in a changed price, has been widely studied. This paper uses a probabilistic approach to obtain a model of price impact in the context of asset pricing. A model based on classical probability is first used to simulate economic decisions to buy or sell, and a quantum version is then developed that better captures the response of the system to perturbations. The result is then extended to the general question of supply and demand. The formula is used to obtain a relationship between price change and volatility which is illustrated using empirical stock market data, and implications for other areas such as option pricing and real estate are discussed.This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 1)'.