Fix Price Equilibria in Distribution Economies

In this paper we consider a distribution economy which is dictated by the conditions of the non-substitution theorem for linear economic models of production. Although flexible prices in the consumption section are perfectly compatible with the conclusions of the non-substitution theorem, rigid prices are likely if the production sector has sufficient say over the economy. We study some existence and efficiency properties of fixed-price equilibrium in distribution economies. Subsequently, we turn to an economy with a produced public good and show that all voluntary and efficient allocations for such an economy must be ratio equilibrium allocation, thus establishing the inherent non-optimality of rationing schemes in mixed economies. It is observed that the case for a distribution economy rests solely on the assumption of a numeraire good in terms of which all value and costs can be measured, whereas the general validity of the non-substitution theorem (and thus of uniquely defined fixed prices arising out of the production sector) depends on additional mathematical structure of the cost function. Thus, if the underlying conditions of production invalidate the non-substitution theorem, fixed prices can be considered as a policy instrument available to a social planner in order to implement a desired distribution of resources in the consumption sector.