<p>First of all, this is not something special to "the basic New Keynesian Model". It is a commonly used technique when modeling an economy with competitive environment.</p>

<p>In your case, the author wrote that there is a continuum of differentiated goods represented by the interval [0,1] and each firm is producing one of the goods. You can imagine that there are uncountably many different kinds of good in the market. As a result, the size of each firm is negligible (just a point on the [0,1] interval) compared to the entire economy. Each firm indexed by $i$ solves its individual profit maximization problem to obtain its labor demand $N(i)$. Then, the aggregate labor demand is simply the "sum". In this case, the sum is replaced by the integral because the variety of different firms is the whole unit interval.</p>

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2018-01-13T18:10:48.343Z
2018-01-13T18:10:48.343Z
Norman
<p>In the basic New Keynesian Model most variables are described as an integral equation. Lets for Instance look at labour demand which is defined as:
$$N_t=\int_{0}^{1}N_t(i)di$$</p>

<p>What is the intuition behind that. How does the $N_t(x)$ function look like and why do we integrate it interval $[0,1]$?</p>

<p>I am reading Gali's book.</p>

<macroeconomics><new-keynesian-economics>
Basic New Keynesian Model: Why variables are defined by integral equations
Sanjay
# Basic New Keynesian Model: Why variables are defined by integral equations

(Asked by: username_0 on 2018-01-12)

In the basic New Keynesian Model most variables are described as an integral equation. Lets for Instance look at labour demand which is defined as:
$$N\_t=\int\_{0}^{1}N\_t(i)di$$

What is the intuition behind that. How does the $N\_t(x)$ function look like and why do we integrate it interval $[0,1]$?

I am reading Gali's book.

**Tags:** macroeconomics, new-keynesian-economics

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## 1 answers

### Answer by username_1 on 2018-01-13. Score: 6 | Accepted answer

First of all, this is not something special to "the basic New Keynesian Model". It is a commonly used technique when modeling an economy with competitive environment.

In your case, the author wrote that there is a continuum of differentiated goods represented by the interval [0,1] and each firm is producing one of the goods. You can imagine that there are uncountably many different kinds of good in the market. As a result, the size of each firm is negligible (just a point on the [0,1] interval) compared to the entire economy. Each firm indexed by $i$ solves its individual profit maximization problem to obtain its labor demand $N(i)$. Then, the aggregate labor demand is simply the "sum". In this case, the sum is replaced by the integral because the variety of different firms is the whole unit interval.


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