<p>The DWL triangle has (horizontally) height <span class="math-container">$20-100/7$</span> and (vertically) base <span class="math-container">$40$</span> (the marginal external benefit). So we have</p>
<p><span class="math-container">$$DWL=\frac{1}{2}\left(20-\frac{100}{7}\right)(40)=\frac{1}{2}\frac{40}{7}(40)=\frac{80}{7}\approx 11.43$$</span></p>
<hr />
<p>In your calculation, you found the base of the triangle by finding:</p>
<ol>
<li><span class="math-container">$MSB$</span> at <span class="math-container">$q=20$</span>: <span class="math-container">$140-4(20)$</span></li>
<li><span class="math-container">$MPB$</span> at <span class="math-container">$q=100/7\approx 14.29$</span>: <span class="math-container">$100-4(14.29)$</span></li>
</ol>
<p>and then subtracting  2 from 1. You should have found the base of the triangle by finding:</p>
<ol>
<li><span class="math-container">$MSB$</span> at <span class="math-container">$q=100/7$</span>: <span class="math-container">$140-4(100/7)$</span></li>
<li><span class="math-container">$MPB$</span> at <span class="math-container">$q=100/7$</span>: <span class="math-container">$100-4(100/7)$</span></li>
</ol>
<p>and then subtracting 2 from 1. This just gives <span class="math-container">$40$</span>, the marginal external benefit of consumption.</p>

CC BY-SA 4.0
2023-11-02T09:18:41.967Z
2023-11-02T09:18:41.967Z
smcc
<p>here's the problem and my solution so far:</p>
<blockquote>
<p>In this case, the Marginal Private Benefit (MPB) is given by the
equation MPB = 100 - 4q and the Marginal Social Cost (MSC) is given by
the equation MSC = 3q.</p>
<p>The market equilibrium occurs where MPB equals MSC, so we can set the
two equations equal to each other and solve for q:</p>
<p>100 - 4q = 3q
=&gt; 7q = 100
=&gt; q = 100 / 7 ≈ 14.29</p>
<p>However, there is a positive consumption externality of $40 per unit
consumed. This means that the Marginal Social Benefit (MSB) is
actually MPB + Externality = (100 - 4q) + 40 = 140 - 4q.</p>
<p>The socially optimal quantity occurs where MSB equals MSC, so we can
set these two equations equal to each other and solve for q:</p>
<p>140 - 4q = 3q
=&gt; 7q = 140
=&gt; q = 140 / 7 = 20</p>
<p>The Deadweight Loss (DWL) is the area of the triangle formed by the
quantity difference (20 - 14.29) and the price difference ((140 -
4<em>20) - (100 - 4</em>14.29)). So,</p>
<p>DWL = 0.5 * (20 - 14.29) * ((140 - 4<em>20) - (100 - 4</em>14.29))
=&gt; DWL ≈ \$19.60</p>
<p>So, the deadweight loss that results in the market equilibrium is
approximately \$19.60.
'</p>
</blockquote>
<p>I'm not too sure why this is incorrect. Can anyone give me a hand. Any help will be greatly appreciated.</p>

<microeconomics>
Deadweight loss and consumption externalities
Kedagi 16
# Deadweight loss and consumption externalities

(Asked by: username_0 on 2023-11-02)

here's the problem and my solution so far:

> In this case, the Marginal Private Benefit (MPB) is given by the
> equation MPB = 100 - 4q and the Marginal Social Cost (MSC) is given by
> the equation MSC = 3q.
>
> The market equilibrium occurs where MPB equals MSC, so we can set the
> two equations equal to each other and solve for q:
>
> 100 - 4q = 3q
> => 7q = 100
> => q = 100 / 7 ≈ 14.29
>
> However, there is a positive consumption externality of $40 per unit
> consumed. This means that the Marginal Social Benefit (MSB) is
> actually MPB + Externality = (100 - 4q) + 40 = 140 - 4q.
>
> The socially optimal quantity occurs where MSB equals MSC, so we can
> set these two equations equal to each other and solve for q:
>
> 140 - 4q = 3q
> => 7q = 140
> => q = 140 / 7 = 20
>
> The Deadweight Loss (DWL) is the area of the triangle formed by the
> quantity difference (20 - 14.29) and the price difference ((140 -
> 4*20) - (100 - 4*14.29)). So,
>
> DWL = 0.5 \* (20 - 14.29) \* ((140 - 4*20) - (100 - 4*14.29))
> => DWL ≈ \$19.60
>
> So, the deadweight loss that results in the market equilibrium is
> approximately \$19.60.
> '

I'm not too sure why this is incorrect. Can anyone give me a hand. Any help will be greatly appreciated.

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2023-11-02. Score: 1

The DWL triangle has (horizontally) height $20-100/7$ and (vertically) base $40$ (the marginal external benefit). So we have

$$DWL=\frac{1}{2}\left(20-\frac{100}{7}\right)(40)=\frac{1}{2}\frac{40}{7}(40)=\frac{80}{7}\approx 11.43$$

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In your calculation, you found the base of the triangle by finding:

1. $MSB$ at $q=20$: $140-4(20)$
2. $MPB$ at $q=100/7\approx 14.29$: $100-4(14.29)$

and then subtracting 2 from 1. You should have found the base of the triangle by finding:

1. $MSB$ at $q=100/7$: $140-4(100/7)$
2. $MPB$ at $q=100/7$: $100-4(100/7)$

and then subtracting 2 from 1. This just gives $40$, the marginal external benefit of consumption.


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