<p>I think calling this 'trick' is a bit of a misnomer because there is nothing particularly tricky about it.</p>
<p>When you make any welfare analysis of some change (tax/quota etc.) you need to compare situation after change with situation before change. For that reason you calculate the deadweight loss (DWL) of policy as a difference between consumer surplus before policy and after policy.</p>
<p>In your case the problem (including new restricted supply <span class="math-container">$S_R$</span> - painted in red color) would look like in the following picture I made (I linearized the problem in order to make the picture easier to render).</p>
<p>In order to calculate deadweight loss here you would first calculate the area of big triangle bounded by the original supply and demand (in black) and then subtract the area of the trapezoid that is created by the new restricted supply (in red).</p>
<p>I am surprised they call it a trick in that textbook since this is how DWL from a policy is defined. Following Mankiw Principles of Microeconomics 8th ed. pp 157:</p>
<blockquote>
<p><strong>Deadweight Loss</strong>: the fall in total surplus that results from a market distortion, such as a tax</p>
</blockquote>
<p>To calculate what a fall in CS is you need to either <em>implicitly</em> or <em>explicitly</em> take into account what the original situation was. One way of how to calculate this explicitly is to see what the original supply and demand was and comparing it to the new situation.</p>
<p><a href="https://i.sstatic.net/OGHTi.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/OGHTi.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2020-12-04T01:10:00.563Z
Thanks! I agree it’s a poor word choice. What I meant by not understanding why we wouldn’t use the “new” supply curve is for calculating the after policy surplus to compare to the before policy surplus - and thus get our DWL. In a tax example it looks a little different because there is tax revenue, etc. 

But in the graph you drew, it makes sense. The problem with the Perloff text is that they do not specify how the supply shifts. I was imagining a parallel shift, which didn’t make sense to me. I appreciate your example.
K Carroll
CC BY-SA 4.0
2020-12-04T01:13:42.617Z
@KCarroll you would get parallel shift with tax. With supply restriction the supply just becomes completely inelastic (vertical) at the point of restriction - this should make intuitive sense to you because when supply is restricted that means that no matter what price is supply can be maximum just that restricted quantity. By the way, if you think this answered your question consider accepting it (and consider doing so also for some of your older questions where you got answers)
1muflon1
CC BY-SA 4.0
2020-12-04T01:25:12.757Z
Sure, thanks. I’m still new to the forum. But what if the quantity restriction doesn’t result in a perfectly inelastic portion supply curve? The examples given in the text are that there may be implicit restrictions if, for example, capital markets are not functioning properly so that it is more costly for new firms to raise capital. What would that graph look like? Thanks again.
K Carroll
CC BY-SA 4.0
2020-12-04T01:27:36.847Z
@KCarroll that depends on the nature of implicit restriction. It could be stepwise if the restriction depends on price but even purely implicit restriction if it is hard (that is for example firm cannot produce more than 20 units due to not being able to raise capital at capital markets for such quantity) then it will be vertical line again. The line tells you how supply depends on price. If supply cannot increase when price does it will become vertical.
1muflon1
CC BY-SA 4.0
2020-12-04T10:58:40.537Z
The text says "if the supply curve in Figure 9.3 shifts to the left". There's nothing indicating that it becomes vertical at $Q_2$. I guess the "trick" consists of ignoring the fact that parts of $B$ and $D$ also disappear. $C+E$ is actually the minimal welfare loss resulting from any such shift of the supply curve to the left.
VARulle
CC BY-SA 4.0
2020-12-04T11:03:48.653Z
@VARulle but the text says that this policy is not tax but restriction on supply. Normally hard restriction would lead to vertical supply at some point.
1muflon1
CC BY-SA 4.0
2020-12-04T11:12:10.020Z
@VARulle also if the supply did not become vertical because there was some 'uncommon' restriction that just shifted the supply at any price (although that would be very weird cap on a supply) then B and D should no longer be part of producer surplus (in their entirety). Of course, it is possible that the authors of a textbook made mistake when drawing the picture but I would be quite surprised if such big mistake would not be uncovered by peer review/editors/authors/lecturers using it. The picture from the textbook is certainly consistent with supply becoming vertical
1muflon1
CC BY-SA 4.0
2020-12-04T12:02:58.643Z
The picture, yes, but the text? I find it odd to describe a supply limitation as a "shift of the supply curve to the left". And also then there's no "trick" involved, as you noted. Anyhow, the explanation in the textbook is just not very good...
VARulle
CC BY-SA 4.0
2020-12-04T12:06:41.917Z
@VARulle agreed but I think they meant by the shift the ‘bent’. But totally agreed the explanation is not clear in that textbook - this being said I taught some micro undergraduate courses and we did discussed cases as pictured above, and I think if the supply would truly shift at any price the first sentence would be strange since they say they want to look at simpler case. I agree with you there is some ambiguity there but by Occam’s razor I would say they meant hard restriction on supply. In terms of modeling soft restriction on supply at any price would be above level of 101 micro
1muflon1
CC BY-SA 4.0
2020-12-04T15:14:54.953Z
@VARulle - I think you have clarified my confusion much better than I did. I have edited the original question to add in a graph that Perloff used in a previous version of the textbook which actually makes sense to me. I cannot figure out what he is assuming for the "trick" in the new version - unless he is assuming that B & D are all surplus. Thank you both for your input.
K Carroll
CC BY-SA 4.0
2020-12-04T15:44:00.440Z
@KCarroll I still think my answer would apply to the new picture. The old picture shows again a valid situation and the old picture in itself is not wrong but these two pictures simply cannot model the same situation otherwise the CS calculations in the new case would be plain wrong. As you see from the old picture the grey area will be the area that will be ‘cut off’ by the new supply curve so in the new picture the new supply curve should be vertical
1muflon1
CC BY-SA 4.0
2020-12-04T00:49:47.377Z
2020-12-04T00:57:04.803Z
2020-12-04T00:57:04.803Z
1muflon1
<p><a href="https://i.sstatic.net/GFCiE.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GFCiE.png" alt="enter image description here" /></a></p>
<p>In Perloff's intermediate microeconomics book, he explains that producer surplus will increase with policies that limit entry. I get this intuitively - if we limit competition, producers will earn rents in the long run - but I am not following the graphical explanation. The text reads as follows:</p>
<p>&quot;Although government policies may cause either the supply curve or the demand curve to shift, we concentrate on policies that limit supply because they are used frequently and have clear-cut effects. If a government policy causes the supply curve to shift to the left, consumers make fewer purchases at a higher price and welfare falls. For example, if the supply curve in Figure 9.3 shifts to the left so that it hits the demand curve at e2, then output falls from Q1 to Q2,
the price rises from p1 to p2, and the drop in welfare is −C − E. The only “trick” in this analysis is that we use the original supply curve to evaluate the effects on producer surplus and welfare.&quot;</p>
<p>Can someone explain to me the intuition behind this &quot;trick&quot;? There is nothing provided in the text. I don't understand why we wouldn't use the &quot;new&quot; supply curve to calculate welfare.</p>
<p>To add in for reference, in a previous version of the textbook Perloff uses the following graph as an example. This graph makes sense to me. The new one does not given what is written unless it assumes a vertical supply curve.</p>
<p><a href="https://i.sstatic.net/VfvUJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VfvUJ.png" alt="enter image description here" /></a></p>

<microeconomics><welfare-economics><producer-surplus>
How do you show welfare changes with limited entry versus perfect competition?
K Carroll
# How do you show welfare changes with limited entry versus perfect competition?

(Asked by: username_0 on 2020-12-04)

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

In Perloff's intermediate microeconomics book, he explains that producer surplus will increase with policies that limit entry. I get this intuitively - if we limit competition, producers will earn rents in the long run - but I am not following the graphical explanation. The text reads as follows:

"Although government policies may cause either the supply curve or the demand curve to shift, we concentrate on policies that limit supply because they are used frequently and have clear-cut effects. If a government policy causes the supply curve to shift to the left, consumers make fewer purchases at a higher price and welfare falls. For example, if the supply curve in Figure 9.3 shifts to the left so that it hits the demand curve at e2, then output falls from Q1 to Q2,
the price rises from p1 to p2, and the drop in welfare is −C − E. The only “trick” in this analysis is that we use the original supply curve to evaluate the effects on producer surplus and welfare."

Can someone explain to me the intuition behind this "trick"? There is nothing provided in the text. I don't understand why we wouldn't use the "new" supply curve to calculate welfare.

To add in for reference, in a previous version of the textbook Perloff uses the following graph as an example. This graph makes sense to me. The new one does not given what is written unless it assumes a vertical supply curve.

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

**Tags:** microeconomics, welfare-economics, producer-surplus


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## 1 answers

### Answer by username_1 on 2020-12-04. Score: 1 | Accepted answer

I think calling this 'trick' is a bit of a misnomer because there is nothing particularly tricky about it.

When you make any welfare analysis of some change (tax/quota etc.) you need to compare situation after change with situation before change. For that reason you calculate the deadweight loss (DWL) of policy as a difference between consumer surplus before policy and after policy.

In your case the problem (including new restricted supply $S\_R$ - painted in red color) would look like in the following picture I made (I linearized the problem in order to make the picture easier to render).

In order to calculate deadweight loss here you would first calculate the area of big triangle bounded by the original supply and demand (in black) and then subtract the area of the trapezoid that is created by the new restricted supply (in red).

I am surprised they call it a trick in that textbook since this is how DWL from a policy is defined. Following Mankiw Principles of Microeconomics 8th ed. pp 157:

> **Deadweight Loss**: the fall in total surplus that results from a market distortion, such as a tax

To calculate what a fall in CS is you need to either *implicitly* or *explicitly* take into account what the original situation was. One way of how to calculate this explicitly is to see what the original supply and demand was and comparing it to the new situation.

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

> **Comments:**
> **username_0**: Thanks! I agree it’s a poor word choice. What I meant by not understanding why we wouldn’t use the “new” supply curve is for calculating the after policy surplus to compare to the before policy surplus - and thus get our DWL. In a tax example it looks a little different because there is tax revenue, etc.   But in the graph you drew, it makes sense. The problem with the Perloff text is that they do not specify how the supply shifts. I was imagining a parallel shift, which didn’t make sense to me. I appreciate your example.  
> **username_1**: @username_0 you would get parallel shift with tax. With supply restriction the supply just becomes completely inelastic (vertical) at the point of restriction - this should make intuitive sense to you because when supply is restricted that means that no matter what price is supply can be maximum just that restricted quantity. By the way, if you think this answered your question consider accepting it (and consider doing so also for some of your older questions where you got answers)  
> **username_0**: Sure, thanks. I’m still new to the forum. But what if the quantity restriction doesn’t result in a perfectly inelastic portion supply curve? The examples given in the text are that there may be implicit restrictions if, for example, capital markets are not functioning properly so that it is more costly for new firms to raise capital. What would that graph look like? Thanks again.  
> **username_1**: @username_0 that depends on the nature of implicit restriction. It could be stepwise if the restriction depends on price but even purely implicit restriction if it is hard (that is for example firm cannot produce more than 20 units due to not being able to raise capital at capital markets for such quantity) then it will be vertical line again. The line tells you how supply depends on price. If supply cannot increase when price does it will become vertical.  
> **username_2**: The text says "if the supply curve in Figure 9.3 shifts to the left". There's nothing indicating that it becomes vertical at $Q_2$. I guess the "trick" consists of ignoring the fact that parts of $B$ and $D$ also disappear. $C+E$ is actually the minimal welfare loss resulting from any such shift of the supply curve to the left.  
> **username_1**: @username_2 but the text says that this policy is not tax but restriction on supply. Normally hard restriction would lead to vertical supply at some point.  
> **username_1**: @username_2 also if the supply did not become vertical because there was some 'uncommon' restriction that just shifted the supply at any price (although that would be very weird cap on a supply) then B and D should no longer be part of producer surplus (in their entirety). Of course, it is possible that the authors of a textbook made mistake when drawing the picture but I would be quite surprised if such big mistake would not be uncovered by peer review/editors/authors/lecturers using it. The picture from the textbook is certainly consistent with supply becoming vertical  
> **username_2**: The picture, yes, but the text? I find it odd to describe a supply limitation as a "shift of the supply curve to the left". And also then there's no "trick" involved, as you noted. Anyhow, the explanation in the textbook is just not very good...  
> **username_1**: @username_2 agreed but I think they meant by the shift the ‘bent’. But totally agreed the explanation is not clear in that textbook - this being said I taught some micro undergraduate courses and we did discussed cases as pictured above, and I think if the supply would truly shift at any price the first sentence would be strange since they say they want to look at simpler case. I agree with you there is some ambiguity there but by Occam’s razor I would say they meant hard restriction on supply. In terms of modeling soft restriction on supply at any price would be above level of 101 micro  
> **username_0**: @username_2 - I think you have clarified my confusion much better than I did. I have edited the original question to add in a graph that Perloff used in a previous version of the textbook which actually makes sense to me. I cannot figure out what he is assuming for the "trick" in the new version - unless he is assuming that B & D are all surplus. Thank you both for your input.  
> **username_1**: @username_0 I still think my answer would apply to the new picture. The old picture shows again a valid situation and the old picture in itself is not wrong but these two pictures simply cannot model the same situation otherwise the CS calculations in the new case would be plain wrong. As you see from the old picture the grey area will be the area that will be ‘cut off’ by the new supply curve so in the new picture the new supply curve should be vertical  

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