Diamond coconut model
The Diamond coconut model is an economic model constructed by the American economist and 2010 Nobel laureate Peter Diamond which analyzes how a search economy in which traders cannot find partners instantaneously operates.
The model was first presented in a 1982 paper published in the Journal of Political Economy.
The main implication of the model is that people's expectations as to the level of aggregate activity play a crucial role in actually determining this level of aggregate economic activity.
A frequent interpretation of its conclusion, as applied to the labor market, is that the so-called natural rate of unemployment may not be unique (in fact there may exist a continuum of "natural rates") and even if it is unique, it may not be efficient.
Diamond's model was of interest to New Keynesian economists who saw it as potential source of coordination failure, which could cause markets to fail to clear.
[1] The model takes its name from the abstract set up imagined by Diamond.
He envisioned an island (a closed economy) populated by individuals who only consume coconuts.
Coconuts are obtained by being picked (they are "produced") from palm trees at a cost.
The key point is that when an individual finds a palm tree, because climbing the tree is costly, they will only be willing to climb it to get a coconut if there are a sufficiently high number of other individuals who are willing to do likewise.
Hence, what individuals believe others will do plays a crucial role in determining the overall outcome.
As a result, people's (fully rational) expectations become a self-fulfilling prophecy and the economy can wind up with multiple equilibria, most if not all of them characterized by inefficiency.
The fact that the probability of finding a trading partner is increasing in the number of people who already have coconuts - mathematically
It involves an externality because each person who chooses to pick a coconut does so with only their own self-interest in mind, but the fact that they do so has an effect on the overall social outcome.
People who are currently looking for coconut palm trees find these at a random rate
This means that the finding of palm trees follows a Poisson process characterized by the parameter
The present discounted value of this asset depends on the benefit or cost incurred when a person finds a trading partner or a palm tree (this is like a one time dividend payment), and the capital gain (or loss) involved in switching states when a trade or coconut-picking occurs.
Additionally, out of steady state, the value of the asset may fluctuate over time.
Likewise, the present discounted value of searching for palm trees is given by where
is the expected cost (hence it enters with a minus sign) of climbing a palm tree when one is found.
In the general version of the model, the cost of climbing a palm tree is a random draw from some (publicly known) probability distribution with non-negative support, for example the uniform distribution on
This means that on the island "some trees are tall and some are short", and as a result picking coconuts from them can be hard or easy.
In the most simple version of Diamond's model, the probability of finding a trading partner—another person who's carrying a coconut—is exactly equal to the share of the population that is currently in possession of a coconut,
Additionally the cost of obtaining a coconut when one finds a palm tree is constant, at
The evolution of the proportion of people who are currently carrying coconuts and looking for trading partners is given by: In the first equation
is just the number of searchers who happen to find a palm tree at a particular time
is the number of previous coconut-carriers who managed to successfully find a trading partner and hence reverted to being searchers (the "outflow").
In the second equation, since nobody ever bothers to climb a tree and obtain coconuts, the number of coconut-carriers simply declines over time.
Hence there are two possible steady state in the simple version of the model.
The "bad" outcome where nobody who finds a palm tree picks a coconut so that
The bad results occurs if everyone who finds a palm tree believes that not enough other people will pick coconuts and as a result it is not worth it to pick the coconut themselves.
