# Shopping example in Kőszegi / Rabin (2006)

In "Section IV Shopping" of Kőszegi / Rabin (A model of reference-dependent preferences, QJE 2006), the example of consumer buying a pair of shoes is given.

They claim that "her disutility from spending on the shoes is between $(1+\eta)p$ and $(1+ \eta \lambda)p$" (p. 1146).

How do they get this result?

I can see where the second term comes from, namely buying at $p$ when expectations were to buy at 0, which generates money-related utility of

$$-p - \eta \lambda p = - (1+\eta \lambda) p$$

But the first term is beyond me: If she buys at $p$, but expected to buy at some $p' > p$, I would obtain

$$- p + \eta(p' - p) = -(1+\eta)p + \eta p'$$

which is not the same as the $(1+\eta)p$ stated in the paper.

What am I missing here? Thank you.

Suppose for instance that she expects to buy the shoes at price $p$. Her "money" utility of buying the shoes equals \begin{equation*} U(\text{Buying}) = -p \end{equation*} since there is no gain-loss utility in that case, and $-p$ is her final wealth (normalizing initial wealth to zero).
However, if she finally decides not to buy the shoes, her money utility equals \begin{equation*} U(\text{Not Buying}) = \eta p \end{equation*} since her final wealth equals $0$, and in addition she experiences a gain-utility of $p$ with respect to the reference point (spending $p$).
• Makes sense! When you say after buying the final wealth is $1-p$, you seem to assume the initial wealth is 1, which I think isn't stated anywhere. I doesn't matter since it cancels out anyway, but I would say it's just $-p$ instead of $1-p$. – bonifaz May 15 '15 at 9:23