# Measure of New Firms Born in Each Period

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?

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.