2 If the function f x is strictly concave then f x 1 1 XB XA 1 2 XB Where XA and XB are two particular values of x and 0 1 1 A

Question

2 If the function f x is strictly concave then f x 1 1 XB XA 1 2 XB Where XA and XB are two particular values of x and 0 1 1 A certain consumer s utility function is u x 3ln x Let x 100 x 500 and 0 6 a 25 pts Calculate the following quantities u x 1 x and u x 1 U XB b 25 pts Based on your calculations for part a does this utility function appear to be strictly convex or strictly concave on the interval 100 x 500 Briefly explain X c 25 pts Now interpret the weight as a probability and interpret the x values 100 and 500 as possible dollar payoffs associated with a gamble Here is a simple probability distribution p x u x 3ln x 100 0 6 500 0 4 Again using your calculations from part b does the consumer appear to be a risk averter or a

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