page_title: Diamond coconut model
section_title: Simple mathematical version of the model
hierarchical_section_title: Diamond coconut model / Simple mathematical version of the model
caption_attribution_description: English: A diagram of the Diamond coconut model showing two adjustment paths to steady state under different expectations. Based on David Romer "Advanced Macroeconomics", 2000
context_page_description: 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 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.
  The model takes its name from the abstract set up imagined by Diamond. He envisioned an island populated by individuals who only consume coconuts. Coconuts are obtained by being picked from palm trees at a cost.
context_section_description: 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  (this is the "all trees are of the same height" assumption).
  The evolution of the proportion of people who are currently carrying coconuts and looking for trading partners is given by:
   if every searcher who finds a palm tree chooses to climb it and obtain a coconut, and
   if every searcher who finds a palm tree chooses not to obtain a coconut when coming upon the opportunity of doing so.
  In the first equation  is just the number of searchers who happen to find a palm tree at a particular time  (the "inflow" of coconut carriers), while  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. The two potential adjustment paths are illustrated in the figure below.
caption: Basic diagram of the Diamond model showing two possible adjustment paths.
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