Tim has rational preferences %A, and Jim has rational preferences %B. However, Jim is a bit insecure, so when asked to report preferences between two alternatives, he first asks Tim which option he prefers. If Tim strictly prefers one over the other, then Jim reports Tim’s preference as his own. If Tim is indifferent between the two alternatives, then Jim reports his own true preference. In this way, we get a third preference ordering, Jim’s reported preference %R. Is %R complete? Transitive? Explain.
Completeness of a preference: Preferences of a consumer is considered to be complete when the consumer is able to rank his preferences of all the goods available to him in a proper order.
Transitivity in preferences : The consumer's preferences are said to be transitive when the consumer's relative preference between two or three goods is clearly stated. Suppose if the consumer is faced with three goods, A B and C. If the consumer prefers A over B and B over C, then the consumer will always prefer A over C. This fact will always hold.
In the above situation, we are left with two cases,
case 1: When Jim's strictly states his preferences: In this case, whatever Jim will choose, Tim will choose that combination as well.If Jim prefers combination A, Tim will also prefer combination A but if Jim prefers combination B, Tim will also prefer combination B. There is an inconsistency in decision and choice of selection between A and B. So we see that, Tim's preference in this case is neither complete nor transitive.
Case 2: When Jim is indifferent between the combinations: In this case, since Jim is indifferent between both the combinations, Tim strictly states his preference which is R. Now this R preference is clearly stated by Tim and is ranked higher than other combinations in terms of preference. Also, since this combination will always be preferred by Tim over the other combinations, this implies that Tim's preference with respect to R is transitive. So individually if we consider case 2, then R can be said to be transitive and complete
But when the entire situation is taken into consideration, either of the case can happen. This makes Tim's preferences lack clarity and consistency as we see that Tim's preference is hugely dependent upon Jim's preferences.
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