<p>Let $v_i$ be the valuation that the $i$-th consumer has for the product, and $v^*$ the common valuation of the product, where the $v$'s are measured in monetary units, and are assumed continuous.  Consumers are here assumed binary -they either purchase $0$ or $1$ (i.e. the product is indivisible). We assume that if the valuation is equal to the price, they do want to purchase the product.</p>

<p>Write the indicator function $I\{v_i\geq p\}$, that takes the value $1$ if the valuation is greater or equal than the price (and so the consumer will want to buy the one unit of product. Let there be $N$ consumers. Then, demand can be expressed as</p>

<p>$$Q^{d} = \sum_{i=1}^NI\{v_i\geq p\}$$</p>

<p>and since the valuation is assumed common to all,</p>

<p>$$Q^{d} = N\cdot I\{v^*\geq p\}$$</p>

<p>We see that  if $p\leq v^*$, quantity demanded will be equal to $N$, while if $p&gt; v^*$ quantity demanded will be equal to $0$.</p>

<p>Diagrammatically, this gives</p>

<p><img src="https://i.sstatic.net/Ezq1y.png" alt="enter image description here"></p>

CC BY-SA 3.0
2015-05-14T13:27:30.233Z
2015-05-14T13:27:30.233Z
Alecos Papadopoulos
<p>A horizontal demand curve could be assembled if you had an sufficiently large number of customers who will buy of the price is $p*$ or less.  When $p \leq p*$ then they purchase all units available until they reach the limiting factor of the quantity supplied.  At any point, they purchase $Q_s$ units at a price of $p*$. The good would then be perfectly inelastic, a flat demand curve.</p>

<p>As for why this behavior would exist, I imagine perhaps the good is a necessary input into a widely available machine. This machine produces another good worth only $p*$ plus the cost of other inputs. There are probably better examples for perfectly inelastic goods, but at the moment I'm drawing a relative blank.</p>

CC BY-SA 3.0
2015-05-18T05:38:01.023Z
2015-05-18T05:38:01.023Z
RegressForward
<p>If it is assumed that every consumer within a particular region has the same 'valuation' for a certain product, and consumers will purchase no more than one unit of the product, is the market demand curve perfectly elastic (horizontal)?</p>

<p>Any insight would be appreciated.</p>

CC BY-SA 3.0
2015-05-14T06:20:38.637Z
*no more than one unit EACH
James
<supply-and-demand><elasticity>
Horizontal demand curve
James
# Horizontal demand curve

(Asked by: username_0 on 2015-05-14)

If it is assumed that every consumer within a particular region has the same 'valuation' for a certain product, and consumers will purchase no more than one unit of the product, is the market demand curve perfectly elastic (horizontal)?

Any insight would be appreciated.

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

> **Comments:**
> **username_0**: *no more than one unit EACH  

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## 2 answers

### Answer by username_1 on 2015-05-14. Score: 5

Let $v\_i$ be the valuation that the $i$-th consumer has for the product, and $v^\*$ the common valuation of the product, where the $v$'s are measured in monetary units, and are assumed continuous. Consumers are here assumed binary -they either purchase $0$ or $1$ (i.e. the product is indivisible). We assume that if the valuation is equal to the price, they do want to purchase the product.

Write the indicator function $I\{v\_i\geq p\}$, that takes the value $1$ if the valuation is greater or equal than the price (and so the consumer will want to buy the one unit of product. Let there be $N$ consumers. Then, demand can be expressed as

$$Q^{d} = \sum\_{i=1}^NI\{v\_i\geq p\}$$

and since the valuation is assumed common to all,

$$Q^{d} = N\cdot I\{v^\*\geq p\}$$

We see that if $p\leq v^\*$, quantity demanded will be equal to $N$, while if $p> v^\*$ quantity demanded will be equal to $0$.

Diagrammatically, this gives

![enter image description here](https://i.sstatic.net/Ezq1y.png)


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### Answer by username_2 on 2015-05-18. Score: 1

A horizontal demand curve could be assembled if you had an sufficiently large number of customers who will buy of the price is $p\*$ or less. When $p \leq p\*$ then they purchase all units available until they reach the limiting factor of the quantity supplied. At any point, they purchase $Q\_s$ units at a price of $p\*$. The good would then be perfectly inelastic, a flat demand curve.

As for why this behavior would exist, I imagine perhaps the good is a necessary input into a widely available machine. This machine produces another good worth only $p\*$ plus the cost of other inputs. There are probably better examples for perfectly inelastic goods, but at the moment I'm drawing a relative blank.


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