<p>Your formula is overly simplified.</p>

<p>The elasticity is supposed to be "<em>how much does supply change if the price changes</em>". Now, the natural way of looking at this is $S'(p)$, the derivative of $S$. However, the units of that are hard to make use of. Hence, we normalize $S'(p)$ by multiplying it with $P/S(p)$, hence getting the "<em>percentage response of $S$ to a percent change in $P$</em>".</p>

<p>Long story short, your $k$ should satisfy </p>

<p>$$ k = S'(p)$$</p>

<p>Note that this is the price elasticity of supply. For the price elasticity of demand, you would instead use $D'(p) P / D(p)$.</p>

CC BY-SA 3.0
2015-06-04T11:45:16.600Z
2015-06-04T11:45:16.600Z
FooBar
<p>The function of demand is:\begin{align*} D(p) = 66-3p-p^2 \\\end{align*}
The function of supply is: \begin{align*}S(p) = 4p^2+8p-114\\
\end{align*}
The task is to find price elasticity of demand in the point of economic equilibrium.</p>

<p>I have found out that the equilibrium price is 5 and equilibrium demand is 26.</p>

<p>I also have a formula that states that $E = k * P/Q$
, where $P$ - equilibrium price, $Q$ - equilibrium demand and $k$ - coefficient  of $S(p)$ slope</p>

<p>How to find $k$ or are there another methods to solve this task?</p>

<supply-and-demand><elasticity>
Price elasticity of demand in the point of economic equilibrium
uiuiui000
# Price elasticity of demand in the point of economic equilibrium

(Asked by: username_0 on 2015-06-04)

The function of demand is:\begin{align\*} D(p) = 66-3p-p^2 \\\end{align\*}
The function of supply is: \begin{align\*}S(p) = 4p^2+8p-114\\
\end{align\*}
The task is to find price elasticity of demand in the point of economic equilibrium.

I have found out that the equilibrium price is 5 and equilibrium demand is 26.

I also have a formula that states that $E = k \* P/Q$
, where $P$ - equilibrium price, $Q$ - equilibrium demand and $k$ - coefficient of $S(p)$ slope

How to find $k$ or are there another methods to solve this task?

**Tags:** supply-and-demand, elasticity

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## 1 answers

### Answer by username_1 on 2015-06-04. Score: 0 | Accepted answer

Your formula is overly simplified.

The elasticity is supposed to be "*how much does supply change if the price changes*". Now, the natural way of looking at this is $S'(p)$, the derivative of $S$. However, the units of that are hard to make use of. Hence, we normalize $S'(p)$ by multiplying it with $P/S(p)$, hence getting the "*percentage response of $S$ to a percent change in $P$*".

Long story short, your $k$ should satisfy

$$ k = S'(p)$$

Note that this is the price elasticity of supply. For the price elasticity of demand, you would instead use $D'(p) P / D(p)$.


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