# Consumer Theory - Relationship between compensating variation (CV) and the equivalent variation (EV)

John consumes two products – X and Y and his preferences are represented by an unknown utility function – u(x,y) (we may assume his indifference curves are well-behaved). His income is m, while the product prices are Px and Py. John was made an offer to sign up for a rewards card. This card would allow him to purchase x at a 10% discount. He would, however, have to pay A dollars to sign up for this card. John is indifferent between accepting and declining the offer. John’s mother has offered to pay the signup price. Alternatively, she’s willing to give John B dollars instead (in which case, John would be prohibited from signing up for the card). John is indifferent between the two options. What can one say about A and B?

1. A > B
2. A = B
3. A < B
4. We can’t know the relation between A and B, however if X were known to be a normal good, we could.
5. The above answers are incorrect.

I'd appreciate it if someone could direct me to info about the relationship between the compensating variation (CV) and the equivalent variation (EV) and their sizes, dependent on income elasticity (classification of the good as normal\neutral\inferior.

• The incredibly specific form of this question (e.g. the discount is 10%, not 9% or 11%, and the offer comes from John's mother, not his second cousin) makes it a) pretty obvious that this is homework and b) not at all (in my opinion) suitable for this site, whether it's homework or not. – Steven Landsburg Feb 4 '15 at 6:39
• Your latent assumption is that laziness is involved. This is not homework at all, rather an old test question that I have been unable to answer, in preparation for my exam, despite spending hours in an attempt to gain some sort of intuition on the matter. Would stating the question in general terms meet your suitability requirements? What is the CV-EV relationship for a price reduction and the effect of the good being normal\inferior. I'd appreciate it if someone could direct me to some place where I could read about comparisons between CV and EV and why one would be larger than the other. – yonatan Feb 5 '15 at 9:58
• @StevenLandsburg – yonatan Feb 5 '15 at 10:05
• I don't think the assumption of laziness needs to be involved. We try not to answer questions like this because it isn't beneficial to the community to post a question that looks like this (and it encourages other people to be lazy whether you are or not). That being said, I had to look up what C.V. and E.V. are --apparently my intro micro course skipped that. Maybe to show the understanding you have, you could explain what you think is happening (and define C.V. and E.V.) – cc7768 Feb 5 '15 at 15:20
• @yonatan: The reformulation in your comment would have been a much better question, but I would still have voted to close, since you can find the answer in any of a hundred good textbooks. – Steven Landsburg Feb 5 '15 at 15:24