Would Scrooge Play Secret Santa?

Nathan Waller (1st year Economics)

“As hard and sharp as flint”:​ Charles Dickens’ character Ebeneezer Scrooge is the archetypal greedy, clever businessman. For this reason, he is of interest as a personification of ‘rational economic man’. Extending this idea, Scrooge’s priority is to maximise the amount of money, goods or services that he has access to. Dickens’ novella introduces Scrooge to us at Christmas and explores how he interacts with key features of the festive season: family, charity, society and the question of the hereafter. However, some intriguing economics can be investigated in this context. 

In the modern day, Secret Santa is a staple of Christmas time. It is even the subject of a poem by a prize-winning US writer​. It is also a fascinating game from an economic perspective, not least because it could easily suffer from a free-rider problem where participants would not buy presents for others but would still want to receive them. It is most likely the participants’ concern about what others think of them that avoids this outcome. The game relies on players being different to Scrooge or it just wouldn’t work.

So, would Scrooge play Secret Santa? If he did, how would he play it and why? 

Given his rationality and greed, Scrooge would weigh up the benefits of joining in. Assuming that everyone spends £5 and that he will like what he is bought 50% of the time, then he can expect to receive £2.50 on average (also assuming he can’t resell his present). In terms of giving a present, he would have three options. He could spend the full five pounds, resulting in a net loss of £2.50. He could also spend something less than £5, leaving him with a net gain of somewhere between plus and minus £2.50. The low cost of his present can be assumed to cause annoyance to the other players so that they prohibit his participation the following years. This would also happen if he spent nothing but this third path would lead to a net gain of £2.50 because Scrooge would still receive a present even though he didn’t buy one. Of the three options: lose £2.50, gain some amount between -£2.50 and £2.50 or gain exactly £2.50, Scrooge would choose the latter; he would play once and buy nothing.

Yet, this might be a premature conclusion. A Christmas Carol was written in 1843 and Secret Santa only began its genesis in 1979​. Assuming Scrooge knew about the game, he would instead face a choice between not playing or introducing it to society. 

If he does the former, he gains nothing and loses nothing. The impact of starting a game is more difficult to calculate. The first step is to ask how he would organise it. He can either set up and take part in lots of smaller games or create one large game. If Scrooge is starting this game, he does not want to cause annoyance. So, by the logic above, he makes a loss on every game he plays. This means that he wants to be in as few games as possible. 

The next step is to estimate the gains Scrooge could reap from starting Secret Santa. So far, we have seen him as only being connected to the game through giving and receiving gifts but Scrooge was also a money lender. To calculate the gains through this channel, we assume that the market for Christmas gifts is a perfectly competitive constant-cost market where firms can buy and sell equipment quickly at a constant price and can easily adjust the amount of labour they employ. Firms will take out a loan from Scrooge to cover these extra costs from expanding production. These expenses – equipment, labour and loans – will define their average cost, which will be constant and equal to £5, the price that they sell for. If 4​ Scrooge lends at 3%​ to each of these firms, as the interest rate in 1843 was probably somewhere between 1 and 5% (and this maximises profits as we also assume the market for capital is perfectly competitive), then he will make £0.15 from each person who plays. 

If he plays, he spends £5, £2.50 of which he recoups through the present he is bought and another £0.15 of which he recoups through interest repayment, leaving him with loss of £2.35 at this point. If n is the number of other people he can get to play, he will set up the game if 0.15n > 2.35 (where 0.15 is the interest he gains from each gift and 2.35 is his current net loss). Solving this inequality, Scrooge would profit if n was 16 or higher. If his involvement was necessary to keep the game going in subsequent years then he would continue to participate but if this wasn’t necessary, he would stop. 

In conclusion, if Secret Santa existed and Scrooge’s participation had no impact on manufacturers, he would play once and not buy a gift. However, it has been demonstrated that he would start Secret Santa if he could get at least 16 other people to play in one large game. Whilst there is some uncertainty about this, it seems likely that he would continue playing in subsequent years as a social necessity to keep the game going. Scrooge might spread some Christmas cheer after all. 

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