<p>I am reading an economics <a href="https://web.williams.edu/Economics/wp/ChenPhelan_DynamicConsequences.pdf" rel="nofollow noreferrer">paper</a> which contains a model with households and banks. In the model, banks are owned by households. The authors make this assumption when they discuss households (section 2.2, page 8):</p>

<blockquote>
  <p>There is a continuum of risk-neutral households denoted by <span class="math-container">$h \in [0,1]$</span> ...</p>
</blockquote>

<p>When they move to discussing banks, they make a similar assumption (section 2.3, page 9):</p>

<blockquote>
  <p>There is a continuum of banks denoted by <span class="math-container">$b \in [0,1]$</span> ...</p>
</blockquote>

<p>I have seen countless papers in economics with such assumptions regarding continuum of agents. Most of the time, I just gloss over this but I don't really understand what these assumptions mean, what they are useful for and why there are there in the first place. It seems like it's something basic and nobody discusses it but I really want to grasp the meaning and purpose of this assumption. </p>

<macroeconomics><mathematical-economics>
Meaning of assumptions regarding continuum of agents in economics models
V Kahn
# Meaning of assumptions regarding continuum of agents in economics models

(Asked by: username_0 on 2019-07-21)

I am reading an economics [paper](https://web.williams.edu/Economics/wp/ChenPhelan_DynamicConsequences.pdf) which contains a model with households and banks. In the model, banks are owned by households. The authors make this assumption when they discuss households (section 2.2, page 8):

> There is a continuum of risk-neutral households denoted by $h \in [0,1]$ ...

When they move to discussing banks, they make a similar assumption (section 2.3, page 9):

> There is a continuum of banks denoted by $b \in [0,1]$ ...

I have seen countless papers in economics with such assumptions regarding continuum of agents. Most of the time, I just gloss over this but I don't really understand what these assumptions mean, what they are useful for and why there are there in the first place. It seems like it's something basic and nobody discusses it but I really want to grasp the meaning and purpose of this assumption.

**Tags:** macroeconomics, mathematical-economics


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## 0 answers

