(A) If the utility function is v(c)=c^1/2, where c is income, suppose a person's preference ordering over actions or prospects in a two-state world is give by U(c1,c2; ?1,?2)=?1(c1)^1/2+?2(c2)^1/2, depict the indifference curves in a diagram with c1 on the horizontal axis and c2 on the vertical axis (probabilities held constant). Show that each indifference curve touches the axes and is everywhere bowed toward the origin.

(B)

B) IfU = En,v(C,) and v(.) is a strictly concave function, show that if the individual is indifferent between (c], 62) and (Cj, C2) he will strictly prefer the convex combination (ag + (1 - 2)c, ac + (1 -1)c2). Hence draw a conclusion about the shape of the indifference curves in the (C, $2) plane