Two utility functions

In French: Deux fonctions d'utilité

The classical economic theory (Debreu, Theory of Value, 1959) is based on three elements: the utility function, the production function, the initial endowment that divides ownership of the goods among actors. Starting from these elements one can deduce the vector of relative prices that, directing the exchange, guides the economy to a Pareto optimum.

The elegant simplicity of this model provides it a great power. The general equilibrium is detailed in partial equilibrium, each market being the scene of a supply and a demand. This can be completed by introducing the time: the production function is then modified by the investment.

In "A Suggestion for Simplifying the Theory of Money" (Oxford University Press, February 1935) John Hicks proposed however to fill a gap in this theory. He noted that each agent has actually two utility functions: one describes the satisfaction that comes from consumption, and the other one describes the satisfaction that gives him the possession of a patrimony.

Assets can be classified according to their liquidity. Money, which is the pure liquidity, is readily usable and implies no risk but provides no income. Illiquid assets provide an interest or a rent, but their price is changing: their possession presents a risk of depreciation.

It would be foolish to prefer to another an asset which is both more risky and less profitable. The ranking of the most liquid assets (currency) to the least liquid (buildings) is normally also a ranking based on performance (less profitable to more profitable) and according to risk (less risky to more risky).

The structure of patrimony which an agent desires is determined by its expectations: the demand for money is explained by the need for a convenient way to pay for daily expenses and also to quickly seize opportunities, it cancels if the agent expects a sharp decline in the purchasing power of the currency. The agent will also desire to own a property, which is illiquid because its sale requires time, if he anticipates a rent or an increase of the price.

The utility of patrimony is not detached from the utility of consumption: it addresses the need to ensure the level of it in the future despite the uncertainties.

Expectations give to the prices of assets a dynamics that differs from that of the price of consumption. For the latter, the interaction of supply and demand results in a price that reflects a static model. By cons the price of assets obeys a powerful dynamic.

If indeed most agents expect that the price of an asset will grow, they wish to acquire it and demand will raise its price: this will strengthen their expectation. A symmetrical evolution occurs if a lower price is anticipated. The change in the price continues until, for often fortuitous reason, anticipation changes sign.

While the price of a product intended for consumption tends to its equilibrium value, the price of an asset will fluctuate widely, the phases of pessimism succeeding to phases of optimism, and cross without stopping the equilibrium level - if one can define it.

If we can assume perfect information of economic actors regarding current prices, it can not be the same for expected prices because the future is inherently uncertain. The inter-temporal equilibrium is a second best equilibrium under the constraint of the law of anticipation p^a = f(p^h) that binds the expected price p^a to the historical prices p^h (Jean-Michel Grandmont, Money and value, 1983). It may happen that this second best equilibrium is so far from the optimum that the economy is experiencing a structural crisis (mass unemployment, under-investment): it is then said to be in a disequilibrium. This is currently the case.

*     *

Keynes (General Theory, 1936) created the concept of disequilibrium by introducing expectations in economic reasoning.

Neoclassical economists believe that expectations are rational, that is to say random but not biased. They assume that the price of assets is as stable as the price of consumer goods, and gives at each moment an accurate measure of their value: the disequilibrium is impossible. However, the volatility of asset prices brings an experimental refutation of their hypothesis.

Other economists (André Orléan, Jean-Noël Giraud) believe instead that the "true value" of a good does not exist, whether it is an asset or a consumer product: the price is according to them a psychological phenomenon or the result of a power struggle.

We can overcome this opposition if we consider that each agent has two utility functions - one for the consumption, one for patrimony - and that the dynamics of the market leads to price stability for the former, to volatility for the latter.