problem code:080609MICRO

[vishruti]

Let the utility function be u(x1 , x2) = (x1 - a1)^b1 (x2 - a2)^b2 where a's and b's are positive constants. Determine the slope and the curvature of the utility funcion . Under what condition will they represent well behaved prefrences ( downward sloping and convex to the origin) ?

[namrata]

slope=b1(x2-a2)/b2(x1-a1)
d(mrs)/d(x1)<0(to ensure strict convexity of ic..
= )b2(x1-a1)(b1dx2/dx1)-b1b2(x2-a2))/b2(x1-a1)^2<0

[vishruti]

SLOPE = - b1 (x2 - a2) / b2 ( x1 - a1)

CURVATURE = b1 (x2 - a2 ) ( b1 + b2) / [b2(x1 - a1)]^2

CONDITION = x1 > a1 , x2 > a2