The following summarizes Thaler, R. H. (1999), “Mental Accounting Matters,” Journal of Behavioral Decision Making, 12(3), 183–206. It is recommended that you read the original article besides the summary here.
“A former colleague of mine, a professor of finance, prides himself on being a thoroughly rational man. Long ago he adopted a clever strategy to deal with life’s misfortunes. At the beginning of each year he establishes a target donation to the local United Way charity. Then, if anything untoward happens to him during the year, for example an undeserved speeding ticket, he simply deducts this loss from the United Way account. He thinks of it as an insurance policy against small annoyances.”
Thaler (1999), p. 183
“A few years ago I gave a talk to a group of executives in Switzerland. After the conference my wife and I spent a week visiting the area. At that time the Swiss franc was at an all-time high relative to the US dollar, so the usual high prices in Switzerland were astronomical. My wife and I comforted ourselves that I had received a fee for the talk that would easily cover the outrageous prices for hotels and meals. Had I received the same fee a week earlier for a talk in New York though, the vacation would have been much less enjoyable.”
Thaler (1999), pp. 183–184
“A friend of mine was once shopping for a quilted bedspread. She went to a department store and was pleased to find a model she liked on sale. The spreads came in three sizes: double, queen and king. The usual prices for these quilts were $\$200$, $\$250$ and $\$300$ respectively, but during the sale they were all priced at only $\$150$. My friend bought the king-size quilt and was quite pleased with her purchase, though the quilt did hang a bit over the sides of her double bed.”
Thaler (1999), p. 184
The respective accounts in action:
A hot day at the beach. A cold beer is worth $\$5$ to you and costs $\$4$. A friend will buy it either at a fancy resort hotel, where you expect a beer to cost $\$5$, or at a run-down grocery store, where you expect it to cost $\$3$.
${u(x)=\sqrt{x}}$ for $x\ge 0$, ${u(x)=-2\sqrt{-x}}$ for $x\lt 0$.
Price felt as a loss, segregated: ${u(5)+u(-4)}={\sqrt{5}-4}\approx-1.76$. No beer.
Price netted against the beer, integrated: ${u(5-4)}=1$. This is acquisition utility.
Add transaction utility, ${u(p^*-4)}$, with $p^*$ the price you expect:
Resort, $p^*=5$: ${1+u(1)}=2$. Buy.
Grocery store, $p^*=3$: ${1+u(-1)}=-1$. Don’t buy.
You bought two stocks for $\$100$ each. Stock A is now worth $\$125$, stock B $\$84$. You need cash and must sell one of them. A gain or loss stays on paper until the stock is sold; selling closes its account.
${u(x)=\sqrt{x}}$ for $x\ge 0$, ${u(x)=-2\sqrt{-x}}$ for $x\lt 0$.
An open account stays out of $u$; only a closed one is felt.
Sell A: $u(25)=5$.
Sell B: $u(-16)=-8$.
You sell the winner, even though taxes favor selling the loser. If B must go, sell it the same day as A: ${u(25-16)}=3\gt{u(25)+u(-16)}=-3$.
Dinner costs $\$100$. You pay cash at the table, or you put it on the credit card and see it weeks later on a $\$676$ monthly bill, next to $\$576$ of other charges.
${u(x)=\sqrt{x}}$ for $x\ge 0$, ${u(x)=-2\sqrt{-x}}$ for $x\lt 0$.
Cash: the payment is felt on its own, $u(-100)=-20$.
Card: the payment is folded into the bill, ${u(-676)-u(-576)}={-52+48}=-4$.
The same $\$100$ hurts a fifth as much on the card.
A lecture in Switzerland pays a $\$2{,}500$ fee, and the week of vacation after it costs $\$900$. Either the fee and the vacation share a “Swiss lecture” account, or the fee came a week earlier, for a lecture in New York, and sits in another account.
${u(x)=\sqrt{x}}$ for $x\ge 0$, ${u(x)=-2\sqrt{-x}}$ for $x\lt 0$.
One account, integrated: ${u(2500-900)}={u(1600)}=40$.
Two accounts, segregated: ${u(2500)+u(-900)}={50-60}=-10$.
Same fee, same prices: the Swiss lecture account takes the sting out of the vacation.
Samuelson offers a colleague a coin flip: win $\$200$ or lose $\$100$. The colleague turns down one flip but would take a hundred of them.
${u(x)=\sqrt{x}}$ for $x\ge 0$, ${u(x)=-2\sqrt{-x}}$ for $x\lt 0$.
One flip: ${\tfrac12u(200)+\tfrac12u(-100)}\approx{7.07-10}=-2.93$. Reject.
Two flips, each judged alone: ${2\times(-2.93)}=-5.86$.
Two flips judged together: win $\$400$ or $\$100$, or lose $\$200$, with probabilities $\tfrac14$, $\tfrac12$, $\tfrac14$: ${\tfrac14u(400)+\tfrac12u(100)+\tfrac14u(-200)}\approx{5+5-7.07}=2.93$. Accept.