<p>The key to this is in the hint. It lets you know supply and demand are both linear, so you need to figure out what the functions of those two curves are. In this case, you have</p>
<p><span class="math-container">$$ Q_D = 18 - 1.5P $$</span>
<span class="math-container">$$ Q_S = 3P $$</span></p>
<p>Plot these on a supply/demand graph (P on the vertical axis, Q on the horizontal), and the consumer surplus is the shaded area (note, it stops at Q=6 because only 6 units were traded in the question):</p>
<p><a href="https://i.sstatic.net/qFHo4.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/qFHo4.png" alt="Supply/Demand Graph" /></a></p>
<p>Using the formula for the area of a trapezoid, we have:</p>
<p><span class="math-container">$$ CS = \frac{1}{2} [(12-4)+(8-4)]*6 = 36 $$</span></p>

CC BY-SA 4.0
2020-12-11T23:17:30.927Z
The supply curve in the image is a little off! it should start at the origin as it does, but then cross demand at (Q = 12, P = 4), sorry about that!
Amaan M
CC BY-SA 4.0
2020-12-12T01:11:52.967Z
Great, that makes alot of sense now. Thank you so much!
Komi Alasse
CC BY-SA 4.0
2020-12-11T23:03:57.327Z
2020-12-11T23:16:18.270Z
2020-12-11T23:16:18.270Z
Amaan M
<p>Can someone help me? The answer is supposed to be 36 but I have no idea how they got that answer. Can someone explain why consumer surplus is 36 in this instance? Thanks!</p>
<p>Refer to Table below. If the price is four dollars but only six units are exchanged in the market, <strong>consumer surplus will be?</strong>
[Hint: Both the supply curve and the demand curve are linear]</p>
<p>Edit: Shouldn't the equation be (1/2)* 8 * 6 = $24?</p>
<p><a href="https://i.sstatic.net/o3qmm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/o3qmm.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2022-03-25T20:00:31.543Z
Given the demand and supply schedules, equilibrium in a free market is to exchange 12 units at price 4.  If only 6 units are exchanged, then presumably the market is not entirely free, but we are not told what is preventing exchange of 12 units..  Suppose that demand is the sum of the individual demands of several people, and that only 6 units are exchanged because some of those people are not allowed to buy the good.  To find the consumer surplus we would need to know the demand schedule for those who are allowed to buy it, and the answer could easily be less than 36.
Adam Bailey
<microeconomics><supply-and-demand><consumer-surplus><producer-surplus>
Calculating Consumer Surplus Given Table
Komi Alasse
# Calculating Consumer Surplus Given Table

(Asked by: username_0 on 2020-12-11)

Can someone help me? The answer is supposed to be 36 but I have no idea how they got that answer. Can someone explain why consumer surplus is 36 in this instance? Thanks!

Refer to Table below. If the price is four dollars but only six units are exchanged in the market, **consumer surplus will be?**
[Hint: Both the supply curve and the demand curve are linear]

Edit: Shouldn't the equation be (1/2)\* 8 \* 6 = $24?

[![enter image description here](https://i.sstatic.net/o3qmm.png)](https://i.sstatic.net/o3qmm.png)

**Tags:** microeconomics, supply-and-demand, consumer-surplus, producer-surplus

> **Comments:**
> **username_1**: Given the demand and supply schedules, equilibrium in a free market is to exchange 12 units at price 4.  If only 6 units are exchanged, then presumably the market is not entirely free, but we are not told what is preventing exchange of 12 units..  Suppose that demand is the sum of the individual demands of several people, and that only 6 units are exchanged because some of those people are not allowed to buy the good.  To find the consumer surplus we would need to know the demand schedule for those who are allowed to buy it, and the answer could easily be less than 36.  

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## 1 answers

### Answer by username_2 on 2020-12-11. Score: 2

The key to this is in the hint. It lets you know supply and demand are both linear, so you need to figure out what the functions of those two curves are. In this case, you have

$$ Q\_D = 18 - 1.5P $$
$$ Q\_S = 3P $$

Plot these on a supply/demand graph (P on the vertical axis, Q on the horizontal), and the consumer surplus is the shaded area (note, it stops at Q=6 because only 6 units were traded in the question):

[![Supply/Demand Graph](https://i.sstatic.net/qFHo4.png)](https://i.sstatic.net/qFHo4.png)

Using the formula for the area of a trapezoid, we have:

$$ CS = \frac{1}{2} [(12-4)+(8-4)]\*6 = 36 $$

> **Comments:**
> **username_2**: The supply curve in the image is a little off! it should start at the origin as it does, but then cross demand at (Q = 12, P = 4), sorry about that!  
> **username_0**: Great, that makes alot of sense now. Thank you so much!  

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