<p><span class="math-container">$MC/AC$</span> is not a quantity, it is a function. More precisely it would be written as <span class="math-container">$MC(y)/AC(y)$</span>.</p>

<p>It is true that in a competitive setting in the long-run equilibrium <span class="math-container">$MC(y^*) = AC(y^*)$</span>.</p>

<p>However, this can also be true in a monopoly setting. For example in the special case when <span class="math-container">$C(y) = c y$</span> where <span class="math-container">$c \in \mathbb{R}_+$</span>, you have
<span class="math-container">$$
\forall y: \ MC(y) = c = AC(y).
$$</span>
Also the monopolist's profit-maximizing <span class="math-container">$y^*$</span> is independent of any fixed costs <span class="math-container">$F$</span>, but <span class="math-container">$AC(y^*)$</span> is not. For example if the inverse demand function is <span class="math-container">$p(y) = 1 - y$</span> and the cost function is <span class="math-container">$C(y) = y^2 + F$</span> then
<span class="math-container">\begin{align*}
y^* &amp; = \arg\max_y (1 - y)y - y^2 - F = 1/4 \\
MC(y^*) &amp; = 2y^* = 1/2 \\
AC(y^*) &amp; = y^* + F/y^* = 1/4 + 4F. 
\end{align*}</span>
In this case
<span class="math-container">$$
\begin{array}{lcl}
MC(y^*)/AC(y^*) &lt; 1 &amp; \mbox{ if } &amp; F &gt; 1/8 \\
MC(y^*)/AC(y^*) = 1 &amp; \mbox{ if } &amp; F = 1/8 \\
MC(y^*)/AC(y^*) &gt; 1 &amp; \mbox{ if } &amp; F &lt; 1/8.
\end{array}
$$</span>
Yet there is exactly one firm in the market, so there is no competition in the classical sense. Nor is it the case that the firm is a natural monopoly at <span class="math-container">$F = 1/8$</span>. This could mean that this is the 'efficient level of competition', but it is not the case, because when  <span class="math-container">$F = 1/8$</span> we have
<span class="math-container">\begin{align*}
y^* &amp; = 1/4 \\
p(y^*) &amp; = 3/4 \\
AC(y^*) &amp; = 1/2 \\
\text{Profits} &amp; = 1/16 &gt; 0. 
\end{align*}</span></p>

CC BY-SA 4.0
2019-01-01T13:17:43.187Z
2019-01-01T13:23:47.610Z
2019-01-01T13:23:47.610Z
Giskard
<p>Marginal cost and average cost are both a u-curve. They cross in the competitive equilibrium. If we divide one by the other, is the ratio the degree of competition?   Ratio is 1 in perfect competition. What is the name of this quantity, MC/AC?</p>

CC BY-SA 4.0
2019-01-01T12:41:02.857Z
I think it's related to the markup. MC=P and AC is the average cost. So markup is defined as price over cost. Markup is an indicator of market competition.
chatGPT
<microeconomics>
what is the marginal cost divided by the average cost
HazellFR
# what is the marginal cost divided by the average cost

(Asked by: username_0 on 2018-12-28)

Marginal cost and average cost are both a u-curve. They cross in the competitive equilibrium. If we divide one by the other, is the ratio the degree of competition? Ratio is 1 in perfect competition. What is the name of this quantity, MC/AC?

**Tags:** microeconomics

> **Comments:**
> **username_1**: I think it's related to the markup. MC=P and AC is the average cost. So markup is defined as price over cost. Markup is an indicator of market competition.  

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## 1 answers

### Answer by username_2 on 2019-01-01. Score: 1

$MC/AC$ is not a quantity, it is a function. More precisely it would be written as $MC(y)/AC(y)$.

It is true that in a competitive setting in the long-run equilibrium $MC(y^\*) = AC(y^\*)$.

However, this can also be true in a monopoly setting. For example in the special case when $C(y) = c y$ where $c \in \mathbb{R}\_+$, you have
$$
\forall y: \ MC(y) = c = AC(y).
$$
Also the monopolist's profit-maximizing $y^\*$ is independent of any fixed costs $F$, but $AC(y^\*)$ is not. For example if the inverse demand function is $p(y) = 1 - y$ and the cost function is $C(y) = y^2 + F$ then
\begin{align\*}
y^\* & = \arg\max\_y (1 - y)y - y^2 - F = 1/4 \\
MC(y^\*) & = 2y^\* = 1/2 \\
AC(y^\*) & = y^\* + F/y^\* = 1/4 + 4F.
\end{align\*}
In this case
$$
\begin{array}{lcl}
MC(y^\*)/AC(y^\*) < 1 & \mbox{ if } & F > 1/8 \\
MC(y^\*)/AC(y^\*) = 1 & \mbox{ if } & F = 1/8 \\
MC(y^\*)/AC(y^\*) > 1 & \mbox{ if } & F < 1/8.
\end{array}
$$
Yet there is exactly one firm in the market, so there is no competition in the classical sense. Nor is it the case that the firm is a natural monopoly at $F = 1/8$. This could mean that this is the 'efficient level of competition', but it is not the case, because when $F = 1/8$ we have
\begin{align\*}
y^\* & = 1/4 \\
p(y^\*) & = 3/4 \\
AC(y^\*) & = 1/2 \\
\text{Profits} & = 1/16 > 0.
\end{align\*}


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