ppt of Chapter 5.ppt

Chapter 5 Choice Chapter 5 Choice Chapter 5 Choice Mathematical Characterization ? max U(x 1 ,x 2) 1x 1 +p 2x 2 =m x 1 ,x 2≥0 Optimal Choice ? Optimal choice is at the point in the budget line with highest utility. ? Given monotonicity , optimal choice is the set which is on the highest indifference curve. Tangency Condition ? MRS = – p1 / p2 ? Solution: Two Equations p 1x 1 +p 2x 2 =m p1 / p2=MU 1 /MU 2 (-p 1 /p 2 =MRS) Exercise:Cobb -Douglas Preference ? Implication of the MRS Condition Is tangency condition necessary? ? Kinky tastes (. u(x 1 ,x 2 )=max(2x 1 +x 2 ,x 1 +2x 2) AB UEX1 X2 O ? Boundary Optimum Is tangency condition necessary? A' B' U X1 X2 O 端点解Ⅰ E A BX 1 X 2? Boundary Optimum Is tangency condition necessary? A B U X1 X2 O E 端点解Ⅱ Some Examples ? Perfect Substitutes: u(x 1 ,x 2 )=ax 1 +bx 2 m/p1 ,when a/b>p 1 /p2 ? X1= 0<x1<m/p1 when a/b=p1/p2 0,when a/b<p1<p2 ? Perfect Substitutes: u(x 1 ,x 2 )=ax 1 +bx 2 m/p1 ,when a/b>p 1 /p2 ? X1= 0<x1<m/p1 when a/b=p1/p2 0,when a/b<p1<p2 Some Examples ? Perfect Complements:u(x 1 ,x 2 )=min(ax 1 ,bx 2) ? Two Equations: p 1x 1 +p 2x 2 =m x 2 /x 1 =a/b ?x 1 =mb/(p 1 b+p 2 a) x 2 =ma/(p 1 b+p 2 a) Some Examples ? Bads and Neutrals (Good 2) x 1 =m/p 1 x 2 =0 ? Cobb-Douglas Preference (Mentioned)