extra1w03 - Ohio State University Department of Economics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Ohio State University Department of Economics Econ. 805 Prof. James Peck Winter 2003 Extra Problems in General Equilibrium Theory (Do not hand in) (1) An allocation is called envy free if every consumer prefers his/her allocation to the allocation of any other consumer. That is, x is envy free if for all h and i, we have u i (x i ) ! u i (x h ) . (a) Will every envy free allocation be Pareto optimal? Explain why or why not. (b) Explain why this economy has at least one envy free allocation that is Pareto optimal. Specify any theorems that your argument relies upon. (Hint: First, redistribute resources so that everyone has the same endowment. Now can you find an allocation that is both envy free and Pareto optimal?) (2) Give an example of a pure exchange economy with two consumers and two commodities, where: (i) each consumer has a utility function that is continuous and strictly increasing, and (ii) the conclusion of the second fundamental theorem of welfare economics is false (that is, there is a Pareto optimal allocation, strictly positive in all components, that cannot be achieved as a competitive equilibrium). A carefully drawn Edgeworth box diagram that is clearly explained is sufficient to answer this problem. (3) Consider an exchange economy with I different "types" of agents, and M agents of each type. In other words, the total number of agents is IM. Any two agents of the same type have the same utility function and the same strictly positive endowments. Assume that all utility functions are strictly monotonic, continuous, and strictly quasiconcave. For each of the following two statements, either show why it is true or find a counterexample. (a)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/17/2008 for the course ECON 805 taught by Professor Peck during the Spring '08 term at Ohio State.

Page1 / 4

extra1w03 - Ohio State University Department of Economics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online