<p>If production quantity is a continuous variable, then for differentiable revenue and cost functions MR and MC are defined as the derivatives of these functions. In your example, however, production quantities come in discrete units.</p>
<p>For discrete units, one first has to specify the exact definition of MR (and MC). Some textbooks use the additional revenue from the <em>next</em> unit produced, some use the additional revenue from the <em>last</em> unit produced. Your argument indicates that you work with the latter definition, so I'll stick to that here and assume that MR is defined as <span class="math-container">$MR(Q)=R(Q)-R(Q-1)$</span> (and analogously for MC).</p>
<p>For discrete untis, MR and MC are typically never <em>exactly</em> equal. In general, profit is uniquely maximized at <span class="math-container">$Q$</span> if <span class="math-container">$MR(Q)&gt;MC(Q)$</span> and <span class="math-container">$MR(Q+1)&lt;MC(Q+1)$</span>.</p>
<p>If MR and MC happen to be exactly equal at <span class="math-container">$Q$</span>, however, then you will have <span class="math-container">$MR(Q-1)&gt;MC(Q-1)$</span>, <span class="math-container">$MR(Q)=MC(Q)$</span>, and <span class="math-container">$MR(Q+1)&lt;MC(Q+1)$</span>. Therefore, profit is indeed maximized at <span class="math-container">$Q-1$</span> <em>and</em> at <span class="math-container">$Q$</span>, as your example indicates. In this case the firm will simply be indifferent between producing <span class="math-container">$Q-1$</span> or <span class="math-container">$Q$</span> units. Note, however, that this is an exceptional case for discrete units.</p>

CC BY-SA 4.0
2024-12-04T09:43:10.000Z
2024-12-04T09:43:10.000Z
VARulle
<p>Profit maximises when MR= MC and MC is rising.</p>
<p>Suppose this happens when 10 units of output is sold. And suppose MR and MC at 10units is 12.
And suppose gross profit TR-TVC is 20.</p>
<p>But my question is profit is also maximised when MR is not equal to MC, when 9 units of output is sold.</p>
<p>As when Both MR and MC at 10th unit is equal,which we assume 12 in this case, and gross profit is 20, then even at the 9th unit gross profit (TR-TVC)remains same as equal amount of MR and MC is added for the 10th unit that balances each other and we don't see any change in gross profit.</p>
<p>So why not we say profit is maximised at the 9th unit and Stop producing there?</p>
<p>To better illustrate,</p>
<p>TR at 10th = TR at 9th + MR at 10th</p>
<p>TVC at 10th = TVC at 9th + MC at 10th</p>
<p>Gross profit at 10th =
TR at 10th — TVC at 10th =
(TR at 9th + MR at 10th) — (TVC at 9th + MC at 10th)</p>
<p>Since MR and MC are equal at 10th,</p>
<p>Gross profit at 10th = TR at 9th — TVC at 9th</p>
<p>That is,
Gross profit at 10th = Gross profit at 9th</p>

CC BY-SA 4.0
2024-12-02T16:55:59.567Z
can you please include exact equations for mc or cost function and firm specific demand function from which you derived the mr and mc?
1muflon1
CC BY-SA 4.0
2024-12-02T16:58:51.427Z
It seems you are working with discrete units. There the MR = MC formula doesn't always exactly apply. It's meant for the continuous quantities case.
VARulle
CC BY-SA 4.0
2024-12-02T20:16:33.797Z
@1muflon1 I am trying to study microeconomics on my own and in my book as an example a table is given in which Units of output produced with corresponding MR and MC. Btw I just added a little equation at the end in my question to Better describe it.
RADS
CC BY-SA 4.0
2024-12-03T00:39:36.017Z
@RADS as VAR rule said, it looks like you are working just with discrete units, and in that case MR=MC does not perfectly apply (e.g. it could be that MR=MC is somewhere between whole single unit). Also, your question is not clear, but if the question is about MR=MC at more than one unique quantity that is possible, there can be more than one level output at which MR=MC
1muflon1
<microeconomics><supply-and-demand><producer-theory>
Doubt in Producer's equilibrium when MR=MC, and MC is rising
RADS
# Doubt in Producer's equilibrium when MR=MC, and MC is rising

(Asked by: username_0 on 2024-12-02)

Profit maximises when MR= MC and MC is rising.

Suppose this happens when 10 units of output is sold. And suppose MR and MC at 10units is 12.
And suppose gross profit TR-TVC is 20.

But my question is profit is also maximised when MR is not equal to MC, when 9 units of output is sold.

As when Both MR and MC at 10th unit is equal,which we assume 12 in this case, and gross profit is 20, then even at the 9th unit gross profit (TR-TVC)remains same as equal amount of MR and MC is added for the 10th unit that balances each other and we don't see any change in gross profit.

So why not we say profit is maximised at the 9th unit and Stop producing there?

To better illustrate,

TR at 10th = TR at 9th + MR at 10th

TVC at 10th = TVC at 9th + MC at 10th

Gross profit at 10th =
TR at 10th — TVC at 10th =
(TR at 9th + MR at 10th) — (TVC at 9th + MC at 10th)

Since MR and MC are equal at 10th,

Gross profit at 10th = TR at 9th — TVC at 9th

That is,
Gross profit at 10th = Gross profit at 9th

**Tags:** microeconomics, supply-and-demand, producer-theory

> **Comments:**
> **username_1**: can you please include exact equations for mc or cost function and firm specific demand function from which you derived the mr and mc?  
> **username_2**: It seems you are working with discrete units. There the MR = MC formula doesn't always exactly apply. It's meant for the continuous quantities case.  
> **username_0**: @username_1 I am trying to study microeconomics on my own and in my book as an example a table is given in which Units of output produced with corresponding MR and MC. Btw I just added a little equation at the end in my question to Better describe it.  
> **username_1**: @username_0 as VAR rule said, it looks like you are working just with discrete units, and in that case MR=MC does not perfectly apply (e.g. it could be that MR=MC is somewhere between whole single unit). Also, your question is not clear, but if the question is about MR=MC at more than one unique quantity that is possible, there can be more than one level output at which MR=MC  

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## 1 answers

### Answer by username_2 on 2024-12-04. Score: 2

If production quantity is a continuous variable, then for differentiable revenue and cost functions MR and MC are defined as the derivatives of these functions. In your example, however, production quantities come in discrete units.

For discrete units, one first has to specify the exact definition of MR (and MC). Some textbooks use the additional revenue from the *next* unit produced, some use the additional revenue from the *last* unit produced. Your argument indicates that you work with the latter definition, so I'll stick to that here and assume that MR is defined as $MR(Q)=R(Q)-R(Q-1)$ (and analogously for MC).

For discrete untis, MR and MC are typically never *exactly* equal. In general, profit is uniquely maximized at $Q$ if $MR(Q)>MC(Q)$ and $MR(Q+1)<MC(Q+1)$.

If MR and MC happen to be exactly equal at $Q$, however, then you will have $MR(Q-1)>MC(Q-1)$, $MR(Q)=MC(Q)$, and $MR(Q+1)<MC(Q+1)$. Therefore, profit is indeed maximized at $Q-1$ *and* at $Q$, as your example indicates. In this case the firm will simply be indifferent between producing $Q-1$ or $Q$ units. Note, however, that this is an exceptional case for discrete units.


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