General Equilibrium with Price-Making Firms

I. Introduction.- Motivation.- Literature.- The present study.- Notational conventions.- II. General Equilibrium with a Monopolistic Sector: Equilibria of Traditional Type.- 1. “True” General Equilibria of Traditional Type.- 2. General Equilibria of Traditional Type When Monopolists Do Not Sell to Each Other.- 2.1. Notation.- 2.2. A traditional concept of monopolistic general equilibrium.- 2.3. Walras’ Law for monopolistic economies.- 2.4. A basic mapping for existence proofs.- 2.5. The case of a single good for which prices are taken: the “totally monopolized” economy.- 2.6. Economies with many goods for which prices are taken.- 2.7. Unbounded consumption sets and unbounded price-taking firms’ production sets.- 2.8. The case of an economy with a single monopolist.- 2.9. “Epsilon-equilibria”.- 2.10. A retreat from “true” equilibrium: autonomously distributed profits payments or “subsidies”.- 2.11. Restrictions on monopolists’ price choices.- 3. Monopolists Selling to Each Other.- 4. Concluding Remarks.- List of Assumptions.- III. A New Approach to Monopolistic and Other Noncooperative Equilibria: The Theory of “Convolutions” (Rationality-Preserving Response Functions).- 1. Basic Concepts.- 2. Examples.- A two-monopoly economy.- A Bertrand duopoly example.- A class of games with “protected punishing.”.- General equilibrium for an economy in which there is protected punishing in the monopolists’ game.- 3. A Necessary Condition for Existence of a Convolution.- 4. “Weak” Convolutions and the Sufficiency of the Necessary Conditions.- 5. Other Variants.- 6. Concluding Remarks.- IV. Oligopolistic Economies as Games of Limited Information: Description of Equilibria.- 1. Introduction.- 2. A Small Oligopolistic Economy with Set-Up Costs and Nondecreasing Returns.- 2.1. First version of the small economy.- 2.2. Second version of the small economy.- 2.3. Response functions.- 2.4. Constructing a convolution for the first version of the small economy, with set-up costs separable.- 2.5. Stable points for the first version of the economy.- 2.6. A convolution for the second version of the small economy, with set-up costs separable.- 3. A Large Oligopolistic Economy with Each Firm Visualizing a Small Economy: A Concrete Version and an Abstract Generalization.- 3.1. Sustainable states in games with limited information: general abstract framework and a specific example, namely, the large economy with sales as passive variables.- 3.2. First illustration of an admissible assignment rule and a properly sustainable pair: the separable-fixed-cost economy with each firm visualizing only replicas of himself.- 3.3. Second illustration of an admissible assignment rule and a properly sustainable pair: the nonseparable-fixed-cost economy with each firm visualizing an economy containing only “separable versions” of himself.- 3.4. Remarks on the two illustrations.- 3.5. Equilibria.- V. Oligopolistic Economies as Games of Limited Information: Existence of Equilibria.- 1. An Essential Existence Proposition.- 2. Notation and a Mapping Argument for the Basic Existence Proposition.- 3. The Quantities of Goods Required to Produce a Given Final-Good Vector: Existence and Continuity of the Functions g, ?, $$
{\overline f _W}
$$.- 4. Zero-Profit Prices for Intermediate Goods: Existence and Continuity of the Function µ.- 5. The Intersection Point of a ?-Curve and the Offer Surface: Existence and Continuity of the Function $$\ell $$.- 5.1. A continuous curve from “below” D to “above” D intersects D: two versions.- 5.2. Using the two versions in proving the continuity of the function $$\ell $$.- 6. Summary: the Basic Existence Theorem.- 7. Implications of the Basic Existence Theorem for the Existence of Oligopolistic General Equilibria.- 8. Other Equilibria.- 9. A Numerical Example of Oligopolistic General Equilibrium.- VI. Conclusion.- References.