General Equilibrium with Price-Making Firms

ISBN-13: 9783540066248 / Angielski / Miękka / 1974 / 247 str.

T. Marschak; R. Selten

Opis

Motivation. That elegant fiction the competitive equilibrium seems still to dominate the frontiers of theoretical microeconomics. We may think of it in a general way as a state of affairs wherein economic agents, responding "rationally" to annoWlced prices, make choices which are consistent and feasible. The prices may also be described as "taken": for one reason or another the agents who respond to them consider them as given. The existence of such a state, its optimality, its robustness against free bargaining among agents when there are many of them, its Wliqueness, its stability when price displacements evoke specified adjustments--all these issues have been studied, and continue to be studied in a variety of settings. Slowly the equilibrium investigated begins to incorporate public goods, externalities of certain kinds, differences in agents' information, and infinitely many time periods. The appeal of such results need not be belabored: the equilibrium studied may sustain an optimal resource allocation, and when it does it sus tains it in a manner that appears to be informationally efficient and to accord well with individual incentives. Therefore it is important to extend the circumstances under which an equilibrium exists, under which it sustains opti mality, and under which it survives displacements as well as free bargaining among agents."

Spis treści

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.