<p>You are told that in a given week <code>4</code> of a given good are sold at a price of <code>100</code> and <code>6</code> of the same good are sold at a price of <code>80</code>. You need to summarize your sales and price for the week. You ought to report your quantity sold as <code>10 [= 4 + 6]</code>. What price level is best to associate with this quantity sold?</p>
<p>One way to approach this is to take the weighted average a contribution to sales:</p>
<p><code>80 * 6/10 + 100 * 4/10 = 88 =</code> summary price</p>
<p>Another way is to take the weighted average as a contribution to revenue:</p>
<p><code>80*6 = 480</code> ; <code>100*4 = 400</code>; <code>480 + 400 = 880 =</code> net revenue</p>
<p><code>80 * 480/880 + 100 * 400/880 = 89.09 =</code> summary price</p>
<p>I am feeding this data to an AI model which is predicting quantity sold in a given week. My data is provided in days.</p>
<p>It is worth mentioning that if I were to compute the demand line between points <code>(4,100)</code> and <code>(10,80)</code> (where <code>10 = 4 + 6 </code>) I would get <code>y = -20x/6 + 113.3</code>. Neither point <code>(10,88)</code> nor <code>(10, 89.09)</code> are on this line.</p>

CC BY-SA 4.0
2022-10-19T02:39:22.603Z
Instead of using only two points, you should use the whole sample (10 data points) to estimate the linear demand. The data points are $(1,100), (2,100),\dots,(4,100), (5,80), (6,80),\dots,(10,80)$.
Herr K.
CC BY-SA 4.0
2022-10-31T14:50:20.970Z
I decided to just think of the price values as a distribution and take a weighted (by quantity) mean.
oolveea
CC BY-SA 4.0
2022-12-15T17:24:48.940Z
Why are we using monospace code format for equations?
ahorn
CC BY-SA 4.0
2022-12-16T18:25:41.023Z
What does monospace code format mean in this context?
oolveea
<econometrics><applied-econometrics><price-discrimination>
Statistic to best summarize changing price level over an interval?
oolveea
# Statistic to best summarize changing price level over an interval?

(Asked by: username_0 on 2022-10-13)

You are told that in a given week `4` of a given good are sold at a price of `100` and `6` of the same good are sold at a price of `80`. You need to summarize your sales and price for the week. You ought to report your quantity sold as `10 [= 4 + 6]`. What price level is best to associate with this quantity sold?

One way to approach this is to take the weighted average a contribution to sales:

`80 * 6/10 + 100 * 4/10 = 88 =` summary price

Another way is to take the weighted average as a contribution to revenue:

`80*6 = 480` ; `100*4 = 400`; `480 + 400 = 880 =` net revenue

`80 * 480/880 + 100 * 400/880 = 89.09 =` summary price

I am feeding this data to an AI model which is predicting quantity sold in a given week. My data is provided in days.

It is worth mentioning that if I were to compute the demand line between points `(4,100)` and `(10,80)` (where `10 = 4 + 6` ) I would get `y = -20x/6 + 113.3`. Neither point `(10,88)` nor `(10, 89.09)` are on this line.

**Tags:** econometrics, applied-econometrics, price-discrimination

> **Comments:**
> **username_1**: Instead of using only two points, you should use the whole sample (10 data points) to estimate the linear demand. The data points are $(1,100), (2,100),\dots,(4,100), (5,80), (6,80),\dots,(10,80)$.  
> **username_0**: I decided to just think of the price values as a distribution and take a weighted (by quantity) mean.  
> **username_2**: Why are we using monospace code format for equations?  
> **username_0**: What does monospace code format mean in this context?  

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## 0 answers

