<p>The condition <span class="math-container">$MC=MR$</span> comes from studying the case where you can produce any quantity, for example, <span class="math-container">$4.0, 4.1, 4.41, 4.987$</span> or any fraction of production. In that case (under some general conditions), <span class="math-container">$MC=MR$</span> will give you the unique quantity that maximizes profits. </p>

<p>In contrast, in your table, you can only produce whole units, for example, <span class="math-container">$3, 4, 5$</span>, etc. In that case, <span class="math-container">$MC=MR$</span> is an approximate condition to find the optimal profits and usually, it gives you the unique solution. Your example is special in the sense that there are 2 optimal quantities and the <span class="math-container">$MC=MR$</span> condition only gives you one such solution, but you can actually choose either. </p>

CC BY-SA 4.0
2019-05-16T20:08:25.443Z
2019-05-16T20:08:25.443Z
Regio
<p>Literally from the definition of Marginal Cost; it is the cost of producing one additional unit. </p>

<p>As your marginal revenue remains constant, pretty clear that you are going to make the maximum profits as the curves intersect at MC = MR. In the specific case that you consider, YES, you can choose either of 4 units or 5 units to be produced but, as Maarten said, your profits will definitely rise if you consider Optimal Production -2 units VS -1 unit in a general scenario. </p>

<p>This is the simple the reason why we say that MC = MR equilibrium is the optimal point to maximize profits. Doesn't mean you can't reach a similar state of profits before it can happen, just that MC = MR will for sure give you a maximal profit.</p>

<p>Also, emphasis on the point Discrete Quantities. Under a continuous distribution, your profits will keep increasing as long as the next extra unit produced will sell for more than it's production cost; i.e. till MC tends to the value of MR.</p>

CC BY-SA 4.0
2019-05-16T16:40:20.233Z
2019-05-16T16:40:20.233Z
Rohan Teja
<pre><code>Price  Quantity   TR      TC   Profit   MR    MC
6         0       0       3     -3     -     -
6         1       6       5      1     6     2
6         2       12      8      4     6     3
6         3       18      12     6     6     4
6         4       24      17     7     6     5
6         5       30      23     7     6     6
</code></pre>

<p>Consider table above. If my understanding is correct, optimal quantity equals 5, because at this point MR = MC. 
But after producing 5th widget, profit does not increase.
Then why is producing 5 widgets considered to be profit maximizing quantity, but not 4?</p>

CC BY-SA 4.0
2019-05-16T13:41:23.153Z
Both quantities yield the same profit. Therefore if q=5 maximizes profit so does q=4.
Bayesian
CC BY-SA 4.0
2019-05-16T15:07:05.900Z
That's the point. Both quantities yield the same profit, yet q=5 is considered to be optimal (MR=MC). Why?
Stokolos Ilya
CC BY-SA 4.0
2019-05-16T15:57:01.040Z
The reason is that you are working with discrete quantities. Therefore your MR and MC are approximations. If you use continuous functions profit is maximized at the point where MR=MC. (In this case you'd get an even higher profit if you'd produce 4.5 units.)
Maarten Punt
CC BY-SA 4.0
2019-05-16T18:06:40.070Z
My point was that q=4 is optimal as well and no one would argue with this. If your profit is differentiable then by definition "profit = revenue - cost" is maximized at some quantity with "marginal revenue -  marginal cost =0". This is where the equality comes from. You only provided a table - we don't even know how costs look like for, e.g., q=4.5.
Bayesian
<microeconomics>
Why marginal revenue must equal marginal cost?
Stokolos Ilya
# Why marginal revenue must equal marginal cost?

(Asked by: username_0 on 2019-05-16)

Price  Quantity   TR      TC   Profit   MR    MC
6         0       0       3     -3     -     -
6         1       6       5      1     6     2
6         2       12      8      4     6     3
6         3       18      12     6     6     4
6         4       24      17     7     6     5
6         5       30      23     7     6     6

Consider table above. If my understanding is correct, optimal quantity equals 5, because at this point MR = MC. 
But after producing 5th widget, profit does not increase.
Then why is producing 5 widgets considered to be profit maximizing quantity, but not 4?

**Tags:** microeconomics
> **Comments:**
> **username_1**: Both quantities yield the same profit. Therefore if q=5 maximizes profit so does q=4.  
> **username_0**: That's the point. Both quantities yield the same profit, yet q=5 is considered to be optimal (MR=MC). Why?  
> **username_2**: The reason is that you are working with discrete quantities. Therefore your MR and MC are approximations. If you use continuous functions profit is maximized at the point where MR=MC. (In this case you'd get an even higher profit if you'd produce 4.5 units.)  
> **username_1**: My point was that q=4 is optimal as well and no one would argue with this. If your profit is differentiable then by definition "profit = revenue - cost" is maximized at some quantity with "marginal revenue -  marginal cost =0". This is where the equality comes from. You only provided a table - we don't even know how costs look like for, e.g., q=4.5.  

---

## 2 answers

### Answer by username_3 on 2019-05-16. Score: 0 | Accepted answer

The condition $MC=MR$ comes from studying the case where you can produce any quantity, for example, $4.0, 4.1, 4.41, 4.987$ or any fraction of production. In that case (under some general conditions), $MC=MR$ will give you the unique quantity that maximizes profits.

In contrast, in your table, you can only produce whole units, for example, $3, 4, 5$, etc. In that case, $MC=MR$ is an approximate condition to find the optimal profits and usually, it gives you the unique solution. Your example is special in the sense that there are 2 optimal quantities and the $MC=MR$ condition only gives you one such solution, but you can actually choose either.


---

### Answer by username_4 on 2019-05-16. Score: 0

Literally from the definition of Marginal Cost; it is the cost of producing one additional unit.

As your marginal revenue remains constant, pretty clear that you are going to make the maximum profits as the curves intersect at MC = MR. In the specific case that you consider, YES, you can choose either of 4 units or 5 units to be produced but, as Maarten said, your profits will definitely rise if you consider Optimal Production -2 units VS -1 unit in a general scenario.

This is the simple the reason why we say that MC = MR equilibrium is the optimal point to maximize profits. Doesn't mean you can't reach a similar state of profits before it can happen, just that MC = MR will for sure give you a maximal profit.

Also, emphasis on the point Discrete Quantities. Under a continuous distribution, your profits will keep increasing as long as the next extra unit produced will sell for more than it's production cost; i.e. till MC tends to the value of MR.


---

