<p>I don't know your model. Just some general input:</p>

<p>It seems that you have a model with a continuum of firms. That is, there are many firms and each one is strategically small. In mathematics, a measure of a set is a way to express the size of this set. Hence, the measure of firms alive represents "how many firms are active". The authors normalize this measure to 1. If it helps, think of 1 million individual small firms and think of "measure 1" as a normalization of this million.</p>

<p>In your model, each period a only a fraction <span class="math-container">$(1- \rho)$</span> of this measure 1 survives and additional measure <span class="math-container">$\rho$</span> of firms are "born". Thus, the total measure of firms remains 1.
Again, it may help to think of it as a normalization of a large finite number. For example, if <span class="math-container">$\rho=0.5$</span>, only 500 000 out of 1 000 000 firms from last period survive and 500 000 additional firms are created such that there are still 1 000 000 firms.</p>

CC BY-SA 4.0
2019-06-08T01:12:39.250Z
Thanks for the response. Yes, it is a model with a continuum of firms. Could think of as uniform distribution, but the author of the paper does not specify this.
Frank Swanton
CC BY-SA 4.0
2019-06-07T09:53:15.323Z
2019-06-07T09:53:15.323Z
Bayesian
<p>In an economy with stochastic overlapping generations of firms, how do we easily understand the measure of new firms born?</p>

<p>The set-up states:</p>

<p>"In each period, measure <span class="math-container">$\rho\in(0,1)$</span> of new firms are born and are endowed with net worth <span class="math-container">$w_0&gt;0$</span>. Firms survive to the next period with probability <span class="math-container">$(1-\rho)$</span> and hence the measure of firms alive in every period is 1."</p>

<p><span class="math-container">$\textbf{My Question:}$</span></p>

<ol>
<li>What is the measure of firms?</li>
<li>How does the measure of firms relate to the firm's survival probability onto the next period?</li>
</ol>

<p>I think I am not understanding clearly when the author uses these related but distinct terms. Can someone explain easily?</p>

<macroeconomics><firm>
Measure of New Firms Born in Each Period
Frank Swanton
# Measure of New Firms Born in Each Period

(Asked by: username_0 on 2019-06-07)

In an economy with stochastic overlapping generations of firms, how do we easily understand the measure of new firms born?

The set-up states:

"In each period, measure $\rho\in(0,1)$ of new firms are born and are endowed with net worth $w\_0>0$. Firms survive to the next period with probability $(1-\rho)$ and hence the measure of firms alive in every period is 1."

$\textbf{My Question:}$

1. What is the measure of firms?
2. How does the measure of firms relate to the firm's survival probability onto the next period?

I think I am not understanding clearly when the author uses these related but distinct terms. Can someone explain easily?

**Tags:** macroeconomics, firm

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## 1 answers

### Answer by username_1 on 2019-06-07. Score: 2 | Accepted answer

I don't know your model. Just some general input:

It seems that you have a model with a continuum of firms. That is, there are many firms and each one is strategically small. In mathematics, a measure of a set is a way to express the size of this set. Hence, the measure of firms alive represents "how many firms are active". The authors normalize this measure to 1. If it helps, think of 1 million individual small firms and think of "measure 1" as a normalization of this million.

In your model, each period a only a fraction $(1- \rho)$ of this measure 1 survives and additional measure $\rho$ of firms are "born". Thus, the total measure of firms remains 1.
Again, it may help to think of it as a normalization of a large finite number. For example, if $\rho=0.5$, only 500 000 out of 1 000 000 firms from last period survive and 500 000 additional firms are created such that there are still 1 000 000 firms.

> **Comments:**
> **username_0**: Thanks for the response. Yes, it is a model with a continuum of firms. Could think of as uniform distribution, but the author of the paper does not specify this.  

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