Samspends her entire monthly income of $600 on champagne (C) and
perfume (F). The price of a bottle of champagne is $30 and the price of an ounce
of perfume is $10. If she consumes 12 bottles of champagne and 24 ounces of
perfume, her MRS is -1. Is her choice optimal?
What does it mean by optimal?
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Verified answer
Optimal choice means that her utiltiy on the last dollar spent on champagne is exactly the same as her utility on the last dollar spent on perfume. At any other substitution rate, she could improve her total utility by changing her purchasing choices.
According to my textbook, MRS is based on units, not dollars. If the MRS is -1, it means that at the level of 12 bottles of champagne and 24 ounces of perfume, she is equally willing to give up one bottle of champagne for one ounce of perfume, or vice versa; she is therefore indifferent as to the last purchase. The only way I see that she could be indifferent on the last purchase is if she had already maxed out her utility. So I would say yes, her choice is optimal. Although I believe this is the first time I have seen the question asked in a way that doesn't include calculating the utiltiy per dollar of each item (which has to be equal).