<p>Total revenue in economics is defined as <span class="math-container">$TR=PQ$</span> (if competition is not perfect <span class="math-container">$P=P(Q)$</span>). You can see this definition of total revenue in basically any economic textbook. For example, have a look at Mankiw Principles of Economics pp 267.</p>
<p>In a static model there is no time dimension, total revenue is function that tells you at a point in time what revenue is given <span class="math-container">$P$</span> and <span class="math-container">$Q$</span>.</p>

CC BY-SA 4.0
2022-04-15T08:57:52.880Z
2022-04-15T08:57:52.880Z
1muflon1
<p>Yes, marginal revenue refers to marginal revenue per time unit.</p>
<p>These basic models are static, i.e. variables such as quantity, revenue, profit, demand, supply, etc., are measured per time unit. Therefore, your claim that <em>total revenue is an accumulation over time of the daily marginal revenue</em> does not hold for these models. The total revenue function TR is defined over quantities, <span class="math-container">$TR=TR(Q)=P(Q)Q$</span>, not over time.</p>

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2022-04-16T11:11:38.407Z
2022-04-16T11:11:38.407Z
VARulle
<p>Note that marginal revenue is a simplifying theoretical construct.</p>
<p>The way you describe it above, it is essential that the inverse demand function defines the same price for all units sold. This usually means that marginal revenue is calculated for a single time period in a single market.</p>

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2022-04-15T18:29:29.190Z
If price is constant during this time period, would marginal revenue not be equal to the inverse demand function? Or do we assume the price change is very small?
Joe Z
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2022-04-15T20:17:55.087Z
I don't understand why that would be the case. As to your second question: yes, marginal revenue is a marginal measure.
Giskard
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2022-04-15T20:33:13.427Z
Ok, thanks. For my first question: since P is constant, dP/dQ = 0, and dR/dQ = P, which is also the inverse demand. But I think one can assume P to be constant while dP/dQ is nonzero, as long as dP is small.
Joe Z
CC BY-SA 4.0
2022-04-16T05:54:32.850Z
I didn't write that "$P$ is constant", because it is not constant w.r.t. $Q$. Perhaps you mean that the price is same for all the buyers? This is true, unless there is price discrimination. In the case of [first degree price discrimination](https://en.wikipedia.org/wiki/Price_discrimination#First_degree) marginal revenue is equal to the inverse demand. (Again, this is for a single time period in a single market.)
Giskard
CC BY-SA 4.0
2022-04-16T16:15:36.830Z
My main confusion is that when the price P is decreased to (P-dP) to allow for a higher quantity (Q+dQ) sold, it is not as if the seller started afresh and sold Q+dQ units; the seller only sold an additional dQ units. However, the formula above calculates marginal revenue as [(P-dP)(Q+dQ) - PQ] / dQ = P + P dQ/dP. This formula implies that the seller actually sold another Q+dQ units at a later time, then calculated the difference in revenue over dQ.
Joe Z
CC BY-SA 4.0
2022-04-16T19:25:55.823Z
"*it is not as if the seller started afresh*" In this theoretical model it is indeed the case that the seller starts afresh. The argument usually made is that this model is for non-durable goods, thus demand starts afresh in each time period. There are similar models for durable goods and firms pricing in multiple time periods.
Giskard
CC BY-SA 4.0
2022-04-15T08:58:52.257Z
2022-04-15T08:58:52.257Z
Giskard
<p>When I was learning about why marginal revenue is lower than demand, I referred to this derivation:</p>
<p><span class="math-container">$$\frac{d(TR)}{dQ} = \frac{d(PQ)}{dQ} = \frac{PdQ + QdP}{dQ} = P + Q\frac{dP}{dQ}$$</span></p>
<p>Wikipedia explains that marginal revenue is the &quot;change in revenue for some change in quantity sold, to that change in quantity sold&quot; (<a href="https://en.wikipedia.org/wiki/Marginal_revenue" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Marginal_revenue</a>) and uses TR in the derivation, as in total revenue.</p>
<p>However, this is confusing for me, because the function that describes the total revenue over the history of the firm is not equal to the function used above, PQ. Is marginal revenue instead the change in daily revenue for its corresponding change in daily quantity sold? (Or maybe hourly, or weekly, depending on the rate at which that good is actually sold?)</p>
<p>This makes more sense to me, since total revenue is an accumulation over time of the daily marginal revenue.</p>

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2022-04-16T11:03:34.053Z
Marginal revenue (MR) is not "lower than demand", it is lower than inverse demand. (MR is measured in monetary units, demand in quantity units.)
VARulle
<microeconomics><monopoly><marginal>
Does marginal revenue actually refer to marginal revenue per time unit?
Joe Z
# Does marginal revenue actually refer to marginal revenue per time unit?

(Asked by: username_0 on 2022-04-15)

When I was learning about why marginal revenue is lower than demand, I referred to this derivation:

$$\frac{d(TR)}{dQ} = \frac{d(PQ)}{dQ} = \frac{PdQ + QdP}{dQ} = P + Q\frac{dP}{dQ}$$

Wikipedia explains that marginal revenue is the "change in revenue for some change in quantity sold, to that change in quantity sold" (<https://en.wikipedia.org/wiki/Marginal_revenue>) and uses TR in the derivation, as in total revenue.

However, this is confusing for me, because the function that describes the total revenue over the history of the firm is not equal to the function used above, PQ. Is marginal revenue instead the change in daily revenue for its corresponding change in daily quantity sold? (Or maybe hourly, or weekly, depending on the rate at which that good is actually sold?)

This makes more sense to me, since total revenue is an accumulation over time of the daily marginal revenue.

**Tags:** microeconomics, monopoly, marginal
> **Comments:**
> **username_1**: Marginal revenue (MR) is not "lower than demand", it is lower than inverse demand. (MR is measured in monetary units, demand in quantity units.)  

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## 3 answers

### Answer by username_2 on 2022-04-15. Score: 1

Total revenue in economics is defined as $TR=PQ$ (if competition is not perfect $P=P(Q)$). You can see this definition of total revenue in basically any economic textbook. For example, have a look at Mankiw Principles of Economics pp 267.

In a static model there is no time dimension, total revenue is function that tells you at a point in time what revenue is given $P$ and $Q$.


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### Answer by username_1 on 2022-04-16. Score: 1

Yes, marginal revenue refers to marginal revenue per time unit.

These basic models are static, i.e. variables such as quantity, revenue, profit, demand, supply, etc., are measured per time unit. Therefore, your claim that *total revenue is an accumulation over time of the daily marginal revenue* does not hold for these models. The total revenue function TR is defined over quantities, $TR=TR(Q)=P(Q)Q$, not over time.


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### Answer by username_3 on 2022-04-15. Score: 1

Note that marginal revenue is a simplifying theoretical construct.

The way you describe it above, it is essential that the inverse demand function defines the same price for all units sold. This usually means that marginal revenue is calculated for a single time period in a single market.

> **Comments:**
> **username_0**: If price is constant during this time period, would marginal revenue not be equal to the inverse demand function? Or do we assume the price change is very small?  
> **username_3**: I don't understand why that would be the case. As to your second question: yes, marginal revenue is a marginal measure.  
> **username_0**: Ok, thanks. For my first question: since P is constant, dP/dQ = 0, and dR/dQ = P, which is also the inverse demand. But I think one can assume P to be constant while dP/dQ is nonzero, as long as dP is small.  
> **username_3**: I didn't write that "$P$ is constant", because it is not constant w.r.t. $Q$. Perhaps you mean that the price is same for all the buyers? This is true, unless there is price discrimination. In the case of [first degree price discrimination](https://en.wikipedia.org/wiki/Price_discrimination#First_degree) marginal revenue is equal to the inverse demand. (Again, this is for a single time period in a single market.)  
> **username_0**: My main confusion is that when the price P is decreased to (P-dP) to allow for a higher quantity (Q+dQ) sold, it is not as if the seller started afresh and sold Q+dQ units; the seller only sold an additional dQ units. However, the formula above calculates marginal revenue as [(P-dP)(Q+dQ) - PQ] / dQ = P + P dQ/dP. This formula implies that the seller actually sold another Q+dQ units at a later time, then calculated the difference in revenue over dQ.  
> **username_3**: "*it is not as if the seller started afresh*" In this theoretical model it is indeed the case that the seller starts afresh. The argument usually made is that this model is for non-durable goods, thus demand starts afresh in each time period. There are similar models for durable goods and firms pricing in multiple time periods.  

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