Valentine’s day

14th February, 2004

Dear Economist,

I have a Valentine’s Day problem.

I will be taking my sweetheart out for a romantic dinner and I know how it will conclude: Juliet will refuse dessert, I’ll order a chocolate cake and she will proceed to eat most of it. I find it an infuriating habit. Can you offer me any advice?

Yours sincerely,

Romeo, Verona

Dear Romeo,

It is safe to say that you will never persuade Juliet to order her own dessert, and ordering two for yourself as a joke is likely to be lost on her. You must take the quantity of cake as fixed and your problem as simply one of division.

This problem is not insoluble if basic utility theory is inventively deployed. Normally, utility theory allows us to choose between spending income on different goods. Your problem is how to choose between two goods: cake for you and cake for Juliet (which will also make you happy, since you love her). Your calculations are complicated by the fact that while Juliet enjoys eating cake, she also enjoys watching you eat cake. Each of you would, given the choice, only eat part of the cake and donate the other part to your lover. But how much to donate?

Fortunately, the economist Ted Bergstrom tackled the necessary equations 15 years ago. All you need to do is work out how strong your love is for Juliet, compared with your love for cake – and perform the same calculation for her. Substituting the result into Bergstrom’s equations gives you the answer. If you both tend to prefer cake, you will have to split the difference and each concede some cake to the other. If you care little for cake but love to watch each other enjoying it, you will try to foist the cake on each other.

True selflessness comes when both agree, without haggling, what the ideal division of cake should be. Then, true love is in the air.

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