by Rebecca Wilder
Here’s a nice little model I discussed in 2007: The Economics of Christmas! Hope that you enjoy; I do. (This commentary was written in my more ‘academic days’ when I was inundated with models of theoretical macro. As you have no doubt noticed, I’ve gone the applied financial route since then.)
The economic model of Santa delivering presents and spreading the Christmas joy – Santa is a social planner!
In advanced economic theory, there are two types of models: the social planner model (very much like its political connotation) and the competitive equilibrium model (again, very much like its market connotation). The social planner seeks to maximize the welfare (happiness) of all agents in the economy. The competitive equilibrium model allows for markets (households + firms + government) to determine the allocation of goods and resources. In theory, and if certain conditions hold, both models yield the highest and same amount of welfare.
From a theoretical point of view, the economic representation of Santa Claus delivering gifts at Christmas is that of a social planner problem. See, Santa Claus is in charge of gift giving and not the markets. He allocates goods (presents and coal) according to who has been good and who has been bad in order to maximize the welfare of all children jointly. Those who have been good are blessed with many presents, while those who have been bad are given coal. The economy of Christmas is full of many individual economic agents (the children). Each child writes Santa Claus a note indicating the presents that he/she desires; the presents that give each child joy. This represents a utility function in economics, where utility (joy) is dependent on the consumption of goods and services (each child’s choice of presents). Finally, the total welfare of Christmas is the spread of Christmas joy.
Santa’s economic problem below the fold:
Santa is a social planner that chooses the allocation of presents and coal in order to maximize the joint Christmas joy of all the children, given several constraints.
- Constraint 1: There is a goodness level for each child that is dependent on the child’s behavior over the past year; this level may be positive or negative.
- Constraint 2: Each child specifies only those presents that give him/her joy.
- Constraint 3: The total amount of presents demanded by the children cannot exceed the supply of presents that Santa Claus carries on his sleigh.
- Constraint 4: Santa’s workshop is subject to an availability of resources: elves (labor), toy-building machines (capital), blueprints for toys, coal, etc.
- Constraint 5: Santa’s workshop is subject to the available technology (they cannot make hover-craft skateboards yet) and the type of toy production in the workshop (perhaps the elves work in an assembly line).
- Constraint 6: The toy-building machines may be used this year or next year and are subject to a rate of depreciation (older machines are slower and less-efficient at toy production).
- Constraint 7: Santa only has one night to deliver all gifts on his magic sleigh. Solution to the problem: The optimal allocation of presents and coal is delivered across the world in one quick night.
The globe is spread with the highest amount of Christmas joy. What will be your allocation? I’ve been good this year – I think that I’ll be rewarded with a very nice present. Merry Christmas and Happy Holidays!
originally published at The Wilder View…Economonitors