Suppose that in a two-commodity world, the consumer's utility function takes the form u(x)=(a1x_1^
ho + a2x_2^
ho )1/
ho. This utility function is known as the constant elasticity of substitution (or CES) utility function.
(a) Show that when
ho =1, indifference curves become linear.
(b) Show that as
ho ->0, this utility function comes to represent the same preferences as the (generalized) Cobb-Douglas utility function u(x)=(chi _1^alpha 1+ chi _2^alpha 2).
(c) Show that as
ho ->-infty, indifference curves become "right angles"; that is, this utility function has in the limit the indifference map of the Leontief utility function U(x1,x2)=Min{x1 , x2}