Assume the consumer’s preference relation is a complete preorder.
A) Now, given this, define a “strictly monotonic” preference relation for a consumer?
B) What is the difference with a “monotonic” (but not “strictly monotonic” preference relation? Give an example of a monotone preference relation that is not strictly monotonic.
C) Say the consumer’s preference relation is defined on the consumption set C = R2+ by the utility function u(x1; x2) = x51 x52 Does this consumer have strictly monotonic preferences on all of R2+? If so, show it. If not, explain why not. Further, if not, can you provide a subset of R2+ such that the preference relation is strictly monotonic?
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