<p>The answer by Herr K is correct so far as it goes and is probably what your teacher is looking for, but it's worth adding the following.</p>
<p>Walt and Jessie place their orders before looking at the price.  Nevertheless, they probably have a fairly good idea what the price will be - say within 5% of some price \$P per gallon.  Suppose Walt really had <em>no idea</em> what the price would be, eg he regarded \$1 or \$10 or \$100 or \$1,000 per gallon as equally probable.  In that case, would he really order 10 gallons without looking at the price?  Almost certainly he would not, because at some sufficiently high price, the cost of 10 gallons would amount to a higher proportion of his income than he could reasonably afford given his demand for other items (housing, food, etc).  So at such a high price his demand for gas would not be price-inelastic.</p>
<p>What this illustrates is that price-elasticity of demand for a good can and usually does vary with price. So a more precise statement about the drivers' price elasticity of demand would be that Walt's demand for gas is inelastic within the range of his expectations of the price of gas at the station, and Jessie's demand has unit elasticity within the range of his/her expectations.</p>

CC BY-SA 4.0
2022-02-26T12:07:57.893Z
2022-02-26T12:07:57.893Z
Adam Bailey
<p>Since Jessie's expenditure on gas is fixed at <span class="math-container">$\\\$10$</span>, it follows that a <span class="math-container">$1\%$</span> increase in price must lead to a <span class="math-container">$1\%$</span> decrease in quantity demanded, which in other words means Jessie has unit-elastic demand.</p>
<p>Mathematically, let <span class="math-container">$q(p)$</span> denote Jessie's quantity demanded as a function of the price <span class="math-container">$p$</span>. The fixed expenditure condition can be written as
<span class="math-container">\begin{equation}
p\cdot q(p)=10.
\end{equation}</span>
Differentiating with respect to <span class="math-container">$p$</span> on both sides:
<span class="math-container">\begin{align}
\frac{\mathrm d}{\mathrm dp}[p\cdot q(p)]&amp;=\frac{\mathrm d}{\mathrm dp}[10]\\
q(p)+p\cdot q'(p) &amp;=0 \\
-p\cdot q'(p) &amp;=q(p) \\
-q'(p)\frac{p}{q(p)} &amp;=\frac{q(p)}{q(p)} \\
\text{price elasticity of demand}&amp;=1
\end{align}</span></p>

CC BY-SA 4.0
2022-02-26T01:37:46.403Z
2022-02-26T01:37:46.403Z
Herr K.
<p>Two drivers--Walt and Jessie--each drive up to a gas station. Before looking at the price, each places an order. Walt says, 'I'd like 10 gallons of gas.' Jessie says, 'I'd like $10 worth of gas.' What is each driver's price elasticity of demand?</p>
<p>Walt’s demand is inelastic he buys the same quantity regardless of the price;
But, Jessie as per my teacher has unit elastic demand. But, I don’t know how. It doesn’t make sense for me.</p>

<microeconomics><consumer-theory><elasticity>
Microeconomics question on elasticity
Vinay Sharma
# Microeconomics question on elasticity

(Asked by: username_0 on 2022-02-26)

Two drivers--Walt and Jessie--each drive up to a gas station. Before looking at the price, each places an order. Walt says, 'I'd like 10 gallons of gas.' Jessie says, 'I'd like $10 worth of gas.' What is each driver's price elasticity of demand?

Walt’s demand is inelastic he buys the same quantity regardless of the price;
But, Jessie as per my teacher has unit elastic demand. But, I don’t know how. It doesn’t make sense for me.

**Tags:** microeconomics, consumer-theory, elasticity

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## 2 answers

### Answer by username_1 on 2022-02-26. Score: 6

The answer by Herr K is correct so far as it goes and is probably what your teacher is looking for, but it's worth adding the following.

Walt and Jessie place their orders before looking at the price. Nevertheless, they probably have a fairly good idea what the price will be - say within 5% of some price \$P per gallon. Suppose Walt really had *no idea* what the price would be, eg he regarded \$1 or \$10 or \$100 or \$1,000 per gallon as equally probable. In that case, would he really order 10 gallons without looking at the price? Almost certainly he would not, because at some sufficiently high price, the cost of 10 gallons would amount to a higher proportion of his income than he could reasonably afford given his demand for other items (housing, food, etc). So at such a high price his demand for gas would not be price-inelastic.

What this illustrates is that price-elasticity of demand for a good can and usually does vary with price. So a more precise statement about the drivers' price elasticity of demand would be that Walt's demand for gas is inelastic within the range of his expectations of the price of gas at the station, and Jessie's demand has unit elasticity within the range of his/her expectations.


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### Answer by username_2 on 2022-02-26. Score: 5

Since Jessie's expenditure on gas is fixed at $\\\$10$, it follows that a $1\%$ increase in price must lead to a $1\%$ decrease in quantity demanded, which in other words means Jessie has unit-elastic demand.

Mathematically, let $q(p)$ denote Jessie's quantity demanded as a function of the price $p$. The fixed expenditure condition can be written as
\begin{equation}
p\cdot q(p)=10.
\end{equation}
Differentiating with respect to $p$ on both sides:
\begin{align}
\frac{\mathrm d}{\mathrm dp}[p\cdot q(p)]&=\frac{\mathrm d}{\mathrm dp}[10]\\
q(p)+p\cdot q'(p) &=0 \\
-p\cdot q'(p) &=q(p) \\
-q'(p)\frac{p}{q(p)} &=\frac{q(p)}{q(p)} \\
\text{price elasticity of demand}&=1
\end{align}


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