A note on cost-share equilibrium and owner-consumers
The contributions of J. Farrell (Econ. Letters 19, 1985, 303–306) and A. Mas-Colell and J. Silvestre (J. Econ. Theory 47, 1989, 239–256) have studied the implications of two unanimity principles when a firm is owned by the consumers. Interestingly, both approaches lead to what J.E. Roemer and J. Silvestre (The proportional solution for economies with both public and private ownership, mimeo, University of California, Davis, 1991) call proportional allocations. We compare these approaches and analyze how well they serve as equilibrium foundations for proportional allocations. In a nutshell, the conclusion is that Farrell's unanimity principle is simpler than Mas-Colell and Silvestre's, but (assuming that the cost function is convex) the latter always works (i.e., equilibrium exists and yields proportional allocations) while the former may not (equilibrium may not exist, in other words, proportional allocations may not be supportable as equilibria).