In an economy with an arbitrary number of consumers and an arbitrary number of commodities, some public and some private, I propose a generalization of Lindahl's equilibrium solution, and prove an existence theorem for it. A particular generalization of the of an exchange equilibrium to an economy with public goods is proposed, and it is shown that a Lindahl equilibrium allocation is also a core allocation.

The problem of specifying asset market equilibrium conditions in a macroeconomic model is studied. Two specifications are proposed: "beginning-of-period" and "end-of-period" formulations in period models. In each case the limit of the model as the time period is shortened is rigorously calculated. It is shown that the two formulations are internally consistent, but consistent with each other only under assumptions of perfect foresight. A brief review of the liquidity preference versus loanable funds literature shows that theorists have used these models without explicitly noting the differences and inconsistencies.

Duncan K. Foley, Martin F. Hellwig; Asset Management with Trading Uncertainty12, The Review of Economic Studies, Volume 42, Issue 3, 1 July 1975, Pages 327