Question

2. A market with perfectly complementary goods. All individuals in an exchange economy have preferences represented by the function min{x1,x2}; n, of them have the initial bundle (1,0) and the remaining nz have the initial bun- dle (0,1), where n. 12. a. Show that the allocation in which each individual holds the bundle (ni/n, +nz), n2/(ni + n2)) is Pareto stable.

Answer 1

I)sha Page Perfectly complementary Goods ; min {x, ,x2} utility functions individuale have initial bundle (10) (o, 11 Total amount of Good is available = n, x1 Total amount of Good & available XI = N2 Pareto optimal set of allocation when goods is complementary perfectly represented by x=x2 => n = n2 are 7 Goodx2 sequation (1) ideo E 4 3 Ez 2 E. E o 2 4 Ex Good x etc. represent Pareto Points & E2, E3, E4 stable outcomes. Now; are ni Since N2 n, + n2 goods nitna stable will be perfect complements, pareto

Date // Shailza Page Me mi n+n2 ni + 12 → n N2 I which we (1) } already have from equation Hence, the bundle , 12) is mi+n2 nitn2 Pareto stable.