The theory of household behaviour under rationing

This paper simplifies and extends the theory of household behaviour under rationing, using duality and the concept of ‘virtual’ prices. Slutsky-type equations, decomposing the derivatives of the rationed demand functions into income and substitution effects, are derived, and these derivatives are related to the corresponding derivatives of the unrationed demand functions for finite as well as infinitesimal ration levels. The results imply that the Keynesian demand multiplier is more likely but the Barro Grossman supply multiplier is less likely to exceed unity the further the household is from its unconstrained equilibrium