<p>Apart from the elasticity between the first two points (0.79), your elasticities are incorrect. Try calculating the elasticities again using the midpoint method. You should find that, except for the elasticity between the first two points, the elasticities are all above 1. This is consistent with what happens with revenue.</p>
<p>It must always be consistent because the midpoint elasticity is</p>
<p><span class="math-container">$$
\varepsilon=\frac{-(q_2-q_1)(p_1+p_2)}{(q_1+q_2)(p_2-p_1)}$$</span></p>
<p>Now if <span class="math-container">$p_2&gt;p_1$</span> and <span class="math-container">$q_2&lt;q_1$</span> (demand is downward sloping) then the numerator and denominator are positive, and it follows that</p>
<p><span class="math-container">$$\varepsilon&lt;1 \iff -(q_2-q_1)(p_1+p_2)&lt;(q_1+q_2)(p_2-p_1) \iff p_2q_2&gt;p_1q_1 $$</span></p>
<p>I.e. if and only if revenue rises with the increase in price from <span class="math-container">$p_1$</span> to <span class="math-container">$p_2$</span>.</p>

CC BY-SA 4.0
2023-07-10T14:34:28.463Z
2023-08-10T12:54:01.740Z
2023-08-10T12:54:01.740Z
smcc
<p>I would have appreciated some help in this issue. I have a demand schedule that looks like this</p>
<pre><code>P --&gt; Q --&gt; Revenue

5000 --&gt; 10000 --&gt; 50,000,000
6500 --&gt; 8127 --&gt; 52,825,500
8000 --&gt; 6218 --&gt; 49,744,000
9500 --&gt; 4808 --&gt; 45.676,000
11,000 --&gt; 2832 --&gt; 31,141,000
</code></pre>
<p>Now the price elasticities at the first 4 prices calculated as (% change in Q/% change in price) each ratio calculated over the mid-points of the arc as denominators turn out to be (abs value) -0.79, 0.32, 0.37, 0.88. Each of these is less than 1, so revenue should increase with an increase in price? But the revenue increases between 5000 and 6500 and falls thereafter? Also, the percentage fall in revenue is highest for the price increase between 9500 and 11000 whereas here the elasticity is the highest. I do not have much of an issue is I just use the straightforward % change formula without using the denominator as the halfway point of the segments. Why do we use the formula with the halfway point as the denominator? For example for a price change from P1 to P2, we use ((P2-P1)/ ((P1+P2)/2)))?e</p>

CC BY-SA 4.0
2023-07-06T08:51:25.603Z
If you use the starting point for the percentage change rather than the midpoint then you hit the problem that going from $100$ to $80$ is a $20\%$ fall but going from $80$ to $100$ is a $25\%$ increase.  Better still would be to use logarithms rather than percentages  for elasticity calculations
Henry
<microeconomics><elasticity>
Elasticity computations and revenue
Yozi
# Elasticity computations and revenue

(Asked by: username_0 on 2023-07-05)

I would have appreciated some help in this issue. I have a demand schedule that looks like this
P --> Q --> Revenue

5000 --> 10000 --> 50,000,000
6500 --> 8127 --> 52,825,500
8000 --> 6218 --> 49,744,000
9500 --> 4808 --> 45.676,000
11,000 --> 2832 --> 31,141,000

Now the price elasticities at the first 4 prices calculated as (% change in Q/% change in price) each ratio calculated over the mid-points of the arc as denominators turn out to be (abs value) -0.79, 0.32, 0.37, 0.88. Each of these is less than 1, so revenue should increase with an increase in price? But the revenue increases between 5000 and 6500 and falls thereafter? Also, the percentage fall in revenue is highest for the price increase between 9500 and 11000 whereas here the elasticity is the highest. I do not have much of an issue is I just use the straightforward % change formula without using the denominator as the halfway point of the segments. Why do we use the formula with the halfway point as the denominator? For example for a price change from P1 to P2, we use ((P2-P1)/ ((P1+P2)/2)))?e

**Tags:** microeconomics, elasticity
> **Comments:**
> **username_1**: If you use the starting point for the percentage change rather than the midpoint then you hit the problem that going from $100$ to $80$ is a $20\%$ fall but going from $80$ to $100$ is a $25\%$ increase.  Better still would be to use logarithms rather than percentages  for elasticity calculations  

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## 1 answers

### Answer by username_2 on 2023-07-10. Score: 0

Apart from the elasticity between the first two points (0.79), your elasticities are incorrect. Try calculating the elasticities again using the midpoint method. You should find that, except for the elasticity between the first two points, the elasticities are all above 1. This is consistent with what happens with revenue.

It must always be consistent because the midpoint elasticity is

$$
\varepsilon=\frac{-(q\_2-q\_1)(p\_1+p\_2)}{(q\_1+q\_2)(p\_2-p\_1)}$$

Now if $p\_2>p\_1$ and $q\_2 (demand is downward sloping) then the numerator and denominator are positive, and it follows that

$$\varepsilon<1 \iff -(q\_2-q\_1)(p\_1+p\_2)<(q\_1+q\_2)(p\_2-p\_1) \iff p\_2q\_2>p\_1q\_1 $$

I.e. if and only if revenue rises with the increase in price from $p\_1$ to $p\_2$.


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