Each year as the holiday season approaches, an individual will set aside a specific part of his or her consumption bundle to be used for the purchase of holiday gifts. This bundle will vary from year to year as the individual financial situation fluctuates, and may vary from person to person as each will derive a different and specific level of utility from the giving of gifts. The value of this Holiday Bundle is determined in advance, and as such a mandated change in the manner of gift giving will not have an effect on its size. Rather, such a change will serve only to alter the allocation of gifts given.
Suppose Santa has decided to allocate S dollars of his consumption bundle to giving gifts this Christmas. Let Y be equal to the number of individuals in the gift-giving circle, or economy. In a normal year, Santa will buy one gift for each of the Y – 1 individuals on his list; call this “State 1.” Under State 1, Santa will spend a total of S dollars buying gifts and each individual on his list will receive a gift of value S/Y-1. However, this year, The Grinch has decided that he would like to change the rules of the game by setting up a lottery type system whereby each participant draws the name of one person to be the recipient of a holiday gift from them; call this “State 2.” Under State 2, Santa will still spend S dollars on giving gifts, but instead of each recipient receiving a gift of value S/Y-1, one individual will receive a gift of value S.
Bob Cratchit, finding himself in a somewhat more difficult financial situation than Santa this year, has decided to allocate C dollars of his consumption bundle to giving gifts this Christmas, with C < S. As was the case with Santa, this Holiday Bundle is determined ahead of time and not influenced by the change from State 1 to State 2 brought about by The Grinch. Thus, the individual whose name Bob Cratchit draws will receive a gift of value C, instead of each individual receiving a gift of C/Y-1. Recall that C < S; the individual whose name is drawn by Cratchit will receive a gift of some value less than that of the individual drawn by Santa.
Suppose that the economy consists solely of Santa, Bob Cratchit, and The Grinch. Under State 1, Santa will receive a total haul of C/Y-1 + G/Y-1 = HS1, Bob Cratchit will receive S/Y-1 + G/Y-1 = HC1, and The Grinch will receive S/Y-1 + C/Y-1 = HG1. Suppose we move to a world under State 2, and that Santa has drawn The Grinch, The Grinch has drawn Bob Cratchit, and Bob Cratchit has drawn Santa. Under this scenario, the total hauls will be:
HS2 = C
HC2 = G
HG2 = S
In the case of The Grinch, simple arithmetic will yield (Y – 1)HG1 – C = HG2. Thus, The Grinch’s haul is twice as great in State 1, less the relatively small Holiday Bundle of Bob Cratchit. Because Cratchit’s bundle is small, The Grinch is relatively better off. If we look at Cratchit’s situation, note that we get (Y – 1)HC1 – S = HC2. Thus, Cratchit’s haul is twice as great as in State 1, less the relatively large haul of Santa. The Grinch and Cratchit have received very different levels of utility.
To push the example to the extreme, suppose that our economy includes a fourth individual, Jesus. Being the Almighty Himself and as such not saddled by mundane and worldly constraints such as budgets, Jesus has a Holiday Bundle of J = ∞. Thus, whoever has his name drawn by Jesus will be the recipient of a haul of HX2 = ∞, and those whose names are not drawn will have their utility reduced infinitely from the State 1 level. Although certainly hyperbolic, this example helps to illustrate what occurs to a lesser extent at the margin.
Similarly, suppose we were to include a fifth individual; let us call him Ebenezer Scrooge. Scrooge has allocated a Holiday Bundle of E = 0 because he does not approve of this whole Christmas thing and does not care if the person whose name he draws does not receive a gift. Under a State 1 system, Scrooge’s miserliness is equally spread among the Y – 1 individuals, and as such its effect is minimized. However, moving to a State 2 system, one unlucky individual will receive a total haul of 0, and an infinite decrease in utility.
One might argue that this finding may not be valid, as it requires us to assume that the utility levels under the State 1 scenario are equivalent, and that this would not be the case unless each individual gave himself a gift. However, we can relax that assumption if we instead assume the utility derived per dollar to be the same whether the gift is given or received, as is likely. By doing so we see that the situation is identical to that of a world where individuals give themselves gifts. Thus, the result is valid.
As we have shown, the State 2 system, although Pareto Optimal will result in gifts of different value being received by each individual. This will lead to Hard Feelings, which will invariably decrease the amount of Christmas Cheer. As shown below, Christmas Cheer is a product of a utility derived from giving gifts, X, and utility derived from receiving gifts, R, each raised to some constant, α and β, respectively.
Christmas Cheer = (Xα Rβ)/Hard Feelings
As clearly shown, Christmas Cheer and Hard Feelings share an inverse relationship, and, ceteris paribus, an increase in one leads to a decrease in the other.
One might argue that such a market can clear through external controls; namely, that by fixing the amount of money that each individual may spend on gifts to be equal or less than the group’s smallest Holiday Bundle, a steady-state will be achieved in which all hauls are equal. However, this does not take into account the fact that forcing individuals to change their Holiday Bundle cannot result in maximized utility because this decreases the utility they derive from giving gifts. Thus we see that, in the great Chicago School tradition, external controls lead to an inefficient market.
The most unsettling result is the potential for such a system to “ruin Christmas.” As tradition goes, should Hard Feelings ever rise to a level so as to be greater than or equal to the derived utility of giving and receiving gifts, Xα Rβ, Christmas Cheer will be less than 1 and Christmas will have been ruined for all. As we can see from Figure 1, there is a positive correlation between the magnitude of change introduced to the Christmas routine and Hard Feelings. Because the drawing of names represents a substantial change from State 1 operations, the amount of Hard Feelings thus imposed is likely to be significant. As such, this change is dangerously likely to ruin Christmas. Support for this claim can be found in Figure 2, which gives results from a survey detailing the predominant cause of Christmases that have been ruined in the past.


To sum up, the introduction of a system in which names are drawn for Christmas gift giving will invariably ruin Christmas by resulting in discrepancies in gift value, as this leads to Hard Feelings and results in fractional Christmas Cheer. Therefore, the clear choice for utility maximaztion is to remain under a State 1 system.
*This is something I wrote in response to my family, you guessed it, deciding to draw names for gifts last Christmas. Its just a joke but I had fun writing it and I wanted to save it somewhere, what better place than the internet! (Plus since the button says "publish post," and this is an "academic" paper, I am now going to tell everyone that I am published.