ericbarrett
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- Joined
- Feb 10, 2010
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- 1
Let U(x,y)=x+2*y^(1/2); read x plus two times the square root of y. I want to prove that a linear combination between two indifferent baskets A=(x0,y0) and B=(x1,y1), mainly C=[a*x0+(1-a)*x1, a*y0+(1-a)*y1], provides a greater U than that at point A or B. Thus U(C)>[U(A)=U(B)] (where a is a number between 0 an 1).
How can I prove it using the fact that the non-linear term is strictly concave??
Part of the solution I have is that the non linear part is f(y)=y^1/2, and that this is supposed to imply that ==> [a*y0+(1-a)*y1]^(1/2)>a*y0^(1/2)+(1-a)*y1^(1/2) but i really don't understand where this comes from, although it's obviously true.
How can I prove it using the fact that the non-linear term is strictly concave??
Part of the solution I have is that the non linear part is f(y)=y^1/2, and that this is supposed to imply that ==> [a*y0+(1-a)*y1]^(1/2)>a*y0^(1/2)+(1-a)*y1^(1/2) but i really don't understand where this comes from, although it's obviously true.