Understanding General Equilibrium and Welfare Theorems

1. ExchangeChapter 31 Niklas Jakobsson

2. Introduction • So far we have discussed partial equilibrium, that is the market for a single good • General equilibrium analysis study the interaction of several markets 2007

3. The Edgeworth box • Competitive markets • Two consumers and two goods • Pure exchange (no production) 2007

4. The Edgeworth box - Trade • Person A is better off than at the initial endowment at all the bundles above her indifference curve through the initial endowment • Same is true for person B • Both are better off where these regions intersect • Trade to the point M • Doing the same analysis from point M we see that no more trade occurs • This imply pareto efficiency since the region where A is made better off is disjoint from the region where B is made better off. 2007

5. The Edgeworth box – Pareto efficiency • Pareto efficiency: there is no way to make some individual better off without making someone else worse off • If the two curves cross there is a possibility of mutually advantageous trade so the point cannot be pareto efficient (excluding border solutions • The contract curve illustrates all pareto efficient allocations • It goes from A’s origin to B’s origin and the shape depend on the indifference curves 2007

6. The Edgeworth box – Welfare theorems • A competitive equilibrium will exist if each individuals demand function is continuous (convex preferences) or if every consumer is small relative to the size of the market • The first theorem of welfare economics: the equilibrium in a set of competitive markets is pareto efficient • The second theorem of welfare economics: if all agents have convex preferences there will always be a set of prices such that each pareto efficient allocation is a market equilibrium for an appropriate assignment of endowments 2007

7. First theorem of welfare economics • This result is generalizable to much more complex models • The theorem has grand implications for the way to allocate recourses • The theorem follows from: • Agents only care about their own consumption • Agents behave competitively • Agents are small relative to the size of the market 2007

8. First theorem of welfare economics • A private market with each agent maximizing her own utility will result in pareto efficiency • That is, a competitive market ensures pareto efficiency • A competitive market economizes on the information that agents need to posess; only price information is needed 2007

9. Second theorem of welfare economics • Every pareto efficient allocation can be achieved as a competitive equilibrium • Thus, the problems of distribution and efficiency (allocation) can be separated • As long as the taxes are based on the value of the consumer’s endowment of goods there will be no loss in efficiency • When taxes depend on the choices that a consumer makes inefficiency result • Practical problem: how to tax the initial endowment? The endowment is potential labour. Lump sum tax. 2007

10. Second theorem of welfare economics • Prices should be used to reflect scarcity, not to distribute • Lump-sum transfers of wealth should be used to adjust distribution • Do not redistribute through the price mechanism! 2007

11. Critique “The assumptions of perfect competition are not even remotely related to much of the world in which we live…” -Richard Lipsey 2007

12. Informal justification of markets? • The market system is self-organizing and coordinates economic decisions better than any known alternative – not optimally • This is done relatively efficient by producing prices that are influenced by (not determined) relative scarcity • A market economy with institutional underpinnings tend to decentralize power and cause less corruption than more centralized systems • Markets are conductive in growth by encouraging competition of ideas and opportunities 2007

13. Summary • General equilibrium • Edgeworth bow • The welfare theorems • Implications 2007

14. One minute paper • What is the most important thing you learned today? • What is the muddiest point still remaining at the conclusion of today’s class? 2007