micro-fall2007-17 - y B ) u B ( B derives a utility of at...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
General Equilibrium Pure exchange economy Economy: Two goods: x , y Two consumers: A , B Preferences: u A ( x A ; y A ) ; u B ( x B ; y B ) Initial endowments: ( ¯ x A ; ¯ y A ; ¯ x B ; ¯ y B ) Allocation: ( x A ; y A ; x B ; y B ) Ani Guerdjikova ECON 313 Fall 2007 172 / 181
Background image of page 1

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

View Full DocumentRight Arrow Icon
General Equilibrium Edgeworth-box 6 6 - 6 6 ? 0 A 0 B x A y A x B y B r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IC A ¯ x A ¯ x B ¯ y A ¯ y B IC B ............................................................. Ani Guerdjikova ECON 313 Fall 2007 173 / 181
Background image of page 2
General Equilibrium Individual Rationality An allocation ( x A ; y A ; x B ; y B ) is called individually rational if u A ( x A ; y A ) u A ( ¯ x A ; ¯ y A ) and u B ( x B ; y B ) u B ( ¯ x B ; ¯ y B ) Ani Guerdjikova ECON 313 Fall 2007 174 / 181
Background image of page 3

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

View Full DocumentRight Arrow Icon
General Equilibrium Pareto-Optimality An allocation ( x A ; y A ; x B ; y B ) is Pareto-optimal if it is feasible there is no other feasible allocation which would increase the utility of (at least) one consumer without decreasing the utility of any other consumer. Ani Guerdjikova ECON 313 Fall 2007 175 / 181
Background image of page 4
General Equilibrium Finding Pareto-optimal allocations The solution of the following optimization problem is a Pareto-optimal allocation: max x A ; y A ; x B ; y B u A ( x A ; y A ) , s.t. u B ( x B ; y B ) u B ( ˆ x B ; ˆ
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y B ) u B ( B derives a utility of at least u B ) and x A + x B = x A + x B y A + y B = y A + y B ( feasibility of the allocation ( x A ; x B ; y A ; y B ) ) Solution: The contract curve is the geometric place of all Pareto-optimal allocations. Ani Guerdjikova ECON 313 Fall 2007 176 / 181 General Equilibrium Example u A ( x A ; y A ) = x A y A u B ( x B ; y B ) = 4 x B + y B 6 6-6 & 6 ? A B x A y A x B y B IC A q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x A x B y A y B @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ l l l l l l l l l l l l & & & & & & & & & & & IC B CC Ani Guerdjikova ECON 313 Fall 2007 177 / 181...
View Full Document

Page1 / 6

micro-fall2007-17 - y B ) u B ( B derives a utility of at...

This preview shows document pages 1 - 6. Sign up to view the full document.

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