<p>That follows from profit maximization of a competitive firm. Profits <span class="math-container">$\Pi$</span> are given by revenue <span class="math-container">$P\times Y$</span> minus costs <span class="math-container">$W\times N$</span>. Using the production function <span class="math-container">$Y=N$</span> we can write this as</p>
<p><span class="math-container">$$\Pi=PY-WN=PN-WN.$$</span></p>
<p>Maximizing profits by choosing the optimal input amount <span class="math-container">$N$</span> yields the standard condition that the price needs to be equal to marginal costs:
<span class="math-container">$$P-W=0\Leftrightarrow W=P.$$</span></p>
<p>Hence, <span class="math-container">$W$</span> is the marginal cost of production. Intuitively, it costs <span class="math-container">$W$</span> to produce an additional unit of output. If the price of a unit <span class="math-container">$P$</span> were lower than that, the firm would make losses on the last unit. If it were higher, you could still make additional profits by increasing production by an additional unit.</p>

CC BY-SA 4.0
2024-10-08T15:39:37.557Z
2024-10-08T15:39:37.557Z
jpfeifer
<p>In blanchard's macroeconomics, in analysing the labor market and solving for the natural rate of unemployment, he explains a model where the real wage workers are willing to accept, W/P = F(u,z), where u is unemployment and z captures all other factors that strengthen the bargaining power for workers.</p>
<p>He then sets up an equation for the wage that firms are willing to offer, for the case of a simplified production function Y = N, where N is the number of workers, given a price level P and markup m, and calls this the price determination equation: P = (1+m), or W/P = 1/(1+m)</p>
<p>And the solves for equilibrium.</p>
<p>What is confusing to me, however, is, for the price determination equation, P seems to represent the aggregate or average price level, with m being the aggregate markup and W being the aggregate or average wage. But he emphasizes W being the <em>marginal cost</em> of labor. To quote the text:</p>
<blockquote>
<p>The production function Y = N implies that the cost of producing one more unit
of output is the cost of employing one more worker, at wage W. Using the terminology
introduced in your microeconomics course: The marginal cost of production—the cost
of producing one more unit of output—is equal to W.</p>
<p>If there was perfect competition in the goods market, the price of a
unit of output would be equal to marginal cost: P would be equal to W.
But many goods markets are not competitive, and firms charge a price
higher than their marginal cost. A simple way of capturing this fact
is to assume that firms set their price according to P = (1 + m) W</p>
</blockquote>
<p>I don't understand why the marginal wage is what is relevant in this case?</p>

<macroeconomics><labor-economics>
Why are marginal wages used when solving for the natural rate of unemployment?
User2956
# Why are marginal wages used when solving for the natural rate of unemployment?

(Asked by: username_0 on 2024-10-08)

In blanchard's macroeconomics, in analysing the labor market and solving for the natural rate of unemployment, he explains a model where the real wage workers are willing to accept, W/P = F(u,z), where u is unemployment and z captures all other factors that strengthen the bargaining power for workers.

He then sets up an equation for the wage that firms are willing to offer, for the case of a simplified production function Y = N, where N is the number of workers, given a price level P and markup m, and calls this the price determination equation: P = (1+m), or W/P = 1/(1+m)

And the solves for equilibrium.

What is confusing to me, however, is, for the price determination equation, P seems to represent the aggregate or average price level, with m being the aggregate markup and W being the aggregate or average wage. But he emphasizes W being the *marginal cost* of labor. To quote the text:

> The production function Y = N implies that the cost of producing one more unit
> of output is the cost of employing one more worker, at wage W. Using the terminology
> introduced in your microeconomics course: The marginal cost of production—the cost
> of producing one more unit of output—is equal to W.
>
> If there was perfect competition in the goods market, the price of a
> unit of output would be equal to marginal cost: P would be equal to W.
> But many goods markets are not competitive, and firms charge a price
> higher than their marginal cost. A simple way of capturing this fact
> is to assume that firms set their price according to P = (1 + m) W

I don't understand why the marginal wage is what is relevant in this case?

**Tags:** macroeconomics, labor-economics

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## 1 answers

### Answer by username_1 on 2024-10-08. Score: 0

That follows from profit maximization of a competitive firm. Profits $\Pi$ are given by revenue $P\times Y$ minus costs $W\times N$. Using the production function $Y=N$ we can write this as

$$\Pi=PY-WN=PN-WN.$$

Maximizing profits by choosing the optimal input amount $N$ yields the standard condition that the price needs to be equal to marginal costs:
$$P-W=0\Leftrightarrow W=P.$$

Hence, $W$ is the marginal cost of production. Intuitively, it costs $W$ to produce an additional unit of output. If the price of a unit $P$ were lower than that, the firm would make losses on the last unit. If it were higher, you could still make additional profits by increasing production by an additional unit.


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