December 25th is always Christmas and kids always receive gifts from others. The gift recipient did not choose the gift. For example, when I was a kid my grandma would buy me a sweater (perhaps for $50) and while I loved my grandma I did not love the gifts she bought me and I wouldn’t wear it.
Suppose that a researcher observes the purchase price of every Christmas gift and she observes whether the person who received the gift returned it to the store or not. What can we learn about the gift recipient’s willingness to pay for the product that she received?
Answer
Let’s solve this problem twice. In case #1, let’s assume that it is costless to return a gift and that people feel no guilt from cashing out a gift they receive from someone else.
Define the dollar price of the gift as $p. Define the gift recipient’s willingness to pay for the good she received as a gift as $X. So, to be clear. If the gift is a pair of socks then X represents her willingness to pay for a new pair of socks.
The rational individual will return the socks if X < p. For example, if the socks cost $12 but she only values them at $8, then she would want to return the socks and collect the $12.
So, the researcher who observes the price of purchasing the gift and observes that they are returned recovers an upper bound on the willingness to pay for the gift. If the researcher observes the price of gift and the gift is not returned, then the researcher recovers a lower bound on the willingness to pay for the gift. To be clear, suppose the socks cost my grandma $12 to buy and I don’t return them. This means that a lower bound on my willingness to pay for socks is $12.
Now let’s make the problem much harder. Suppose that you cannot costlessly return the gift. After all, you don’t have the receipt and you don’t know where your grandma bought it. You may also feel guilt about returning such a gift. Define the first transaction cost as F (measured in dollars) and the guilt cost as G (also measured in dollars).
In this economy, you return the gift if
X < p - F - G.
For example if the price of the socks is $12 (p=12) and it will cost you $5 in time and hassle to return them (F=5) and $9 in guilt (G=9), you will never return the socks even if you value them at only a penny. Why?
.01 > 12 - 5 - 9 , .01 > -2 . Since you valuation of goods cannot be negative, in this setting you won’t return the good even though you only value the socks at a penny!
The key point that I want to teach you is in the presence of transaction costs and guilt costs, the bounds we recover on preferences are very loose. This is the reason that Joel Waldfogel conducted his famous survey of his Yale students where he directly asked them to report their valuations of their Christmas gifts because it is very difficult to use revealed preference techniques to study how gift recipients value their gifts.
The Deadweight Loss of Christmas = p - X .