Monetary Systems and MIU Approach

Hahn argues that in a general equilibrium model, the value of money has to be zero in equilibrium. However, in the real world, money has a positive value. This paper critically analyses the Money-in-Utility approach, which attempts to solve the problem within this framework. In a general equilibrium model, if there are n-good markets, all markets clear with just n-1 real conditions (Walras Law). Money has no role to play. It is like a barter economy.

Hahn derives a set of conditions with n goods of which, the zero-th good has price zero. With this set of conditions, if we start with excess supply of this zero-th good, it is possible to derive equilibrium in a general equilibrium model. Hahn goes on to assign this zero-th good to ‘fiat money’. He believes that all the properties of this good are satisfied by fiat money itself- it has a value of zero and still continues to be circulated in the economy. In this model at equilibrium, money has no value.

However, Patinkin believes that we must start with a positive value of money. This is because of uncertainty of the exact instant of sales and purchase in a given time period. He assumes that no transaction is possible without the intermediate role of money.

Patinkin proposes the neutrality of money in the presence of expectations and the Cambridge constant ‘k’ actually being variable according to the following equation:

Referring to the Quantity Theory of Money, M= kPY;

Given output, neutrality of money is ensured only when the Cambridge constant ‘k’ is a constant. Under this, we need to assume unit price expectations. This implies that there will be no finite value of money; hence further need of the assumption of flexible prices, which goes beyond the framework.

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...y (MIU) approach, which attempts to solve this problem within this framework, suffers from unwarranted assumptions. It is unclear why household actually hold positive amounts of money and how does it provide a positive utility to them. Also, even though Patinkin and Walsh argue for a positive value of money in equilibrium in the MIU model, it does not solve this conundrum.

Works Cited

Hahn, F. (1965): On some problems of proving the existence of an equilibrium in a monetary economy," in The theory of interest rates, ed. by F. Hahn, pp. {126-135}, Macmillan London.

Obstfeld, Maurice, and Kenneth Rogoff (1983). "Speculative Hyperinflations in Maximizing Models: Can we Rule Them Out?" Journal of Political Economy 91, 675-687

Patnaik, P. (2009): The Value of Money, Columbia University Press

Walsh, C. (2003): Monetary theory and Policy, The MIT Press