A student propose a utility function as follows:

?(?1,?2)=?21+?22U(x1,x2)=x12+x22

** Part a (10 marks)

Graphically show that this proposed utility function violates average is better than extreme. Hint: draw an IC by fixing the utility at some value, e.g. 1.

** Part b (10 marks)

Graphically show that for this utility function, the tangency condition does not lead to the optimum given prices (?1,?2)=(2,1)(p1,p2)=(2,1) and ?=3m=3.

A student propose a utility function as follows: U(x1, x2) = x? + x3 ** Part a (10 marks) Graphically show that this proposed utility function violates average is better than extreme. Hint: draw an IC by fixing the utility at some value, e.g. 1. ** Part b (10 marks) Graphically show that for this utility function, the tangency condition does not lead to the optimum given prices (131,192) = (2, 1) and m = 3