John\'s preferences over bundles of (apple, banana) are complete, transitive and

Question

John's preferences over bundles of (apple, banana) are complete, transitive and have the more is better' property. John likes ( 3 apples, 7 bananas) more than ( 6 apples, 3 bananas); he likes ( 5 apples, 4 bananas) more than ( 2 apples, 7 bananas); and he likes ( 6 apples, 3 bananas) more than ( 5 apples, 5 bananas).
(a) Can you conclude anything about whether John likes ( 3 apples, 7 bananas) more than, less than, or just as much as (5 apples, 4 bananas) Is every one of the preferences' properties necessary to generate your answer? Explain
(b) Can you tell whether John's preferences exhibit diminishing marginal rate of substitution?

Explanation / Answer

John prefers 3A, 7B to 6A, 3B and 6A,3B to 5A,5B. Therefore by transitivity he must prefer 3A,7B to 5A,5B. By more is better he must prefer 5A, 5B to 5A,4B. Therefore once again by transitivity he must prefer 3A, 7B to 5A, 4B. Since you're only supposed to ask one question at a time, I'll leave the second for another post.

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