<p><strong>TL;DR version:</strong> "the tunnel" and D+A+B have exactly the same area.</p>

<hr>

<p>You are right to say that post-subsidy producer surplus is equal to the blue area in the following figure:</p>

<p><a href="https://i.sstatic.net/FPa6u.png" rel="noreferrer"><img src="https://i.sstatic.net/FPa6u.png" alt="enter image description here"></a></p>

<p><strong>However</strong>, it turns out that <em>The Tunnel</em> (i.e. the dark blue area) is exactly equal in size to D+A+B.</p>

<p>Intuitively, there are two ways to think of a unit subsidy:</p>

<ol>
<li>Paying the seller a subsidy of $S=p^s-p^d$ per unit sold has an effect equivalent to reducing his marginal cost by $S$. The seller's marginal cost curve shifts down in the same way as the supply curve in your figure. From the seller's point of view, its as if he is paid price $p^d$ for each unit he sells but had a low marginal cost. When we calculate producer surplus (by looking at the area between the marginal cost curve and the price) this creates some new producer surplus equal to 'the tunnel' (which represents the seller's lower perceived cost). This way of thinking about things gives us the blue area above.</li>
<li>The subsidy does not reduce the seller's cost [so the seller's perceived marginal cost curve coincides with S(pre-subsidy)], but the subsidy is paid to 'top-up' the price received by the seller from $p^d$ to $p^s$. So from the seller's point of view it is as if he is being paid price $p^s$ with a high marginal cost. When we calculate producer surplus we look at the green area in the following figure: </li>
</ol>

<p>Since these are two ways of thinking about the same subsidy, they must yield the same value for producer surplus. But you should be able to see by comparing the blue and green areas that this necessarily implies that the tunnel has the same area as D+A+B.</p>

<p><a href="https://i.sstatic.net/Uyftr.png" rel="noreferrer"><img src="https://i.sstatic.net/Uyftr.png" alt="enter image description here"></a></p>

<hr>

<p>You can check this is true in an example by drawing the curves $Q_S=0.5+p$ and $Q_D=2-p$ and then applying a subsidy of $0.5$ to produce a new supply curve $Q_S'=p$. It looks like this:</p>

<p><a href="https://i.sstatic.net/9rwtV.png" rel="noreferrer"><img src="https://i.sstatic.net/9rwtV.png" alt="enter image description here"></a></p>

<p>Geometrically calculating the areas, you should find that 'the tunnel' and A+D+B both have area 3/8.</p>

CC BY-SA 4.0
2020-05-28T19:31:01.977Z
That is A LOT of work put into a SE answer
brunosalcedo
CC BY-SA 4.0
2022-10-02T14:01:48.747Z
First time I've ever seen it explained that way. Nicely done.
Studi
CC BY-SA 3.0
2016-07-14T14:25:52.227Z
2016-07-14T14:39:59.297Z
2016-07-14T14:39:59.297Z
Ubiquitous
<p>Producer surplus is calculated using the S(pre-subsidy) and the demand curve. </p>

<p>You're probably confused because you think the surplus should be calculated using the new supply curve. However, the producer is actually still producing on the original supply curve.</p>

CC BY-SA 3.0
2016-07-14T15:31:16.510Z
But he gets a subsidy while doing so, raising his surplus.
Giskard
CC BY-SA 3.0
2016-07-14T15:50:37.653Z
Yes. You can include that in the producer surplus as well (some people do, some do not). That would be equal to the quantity * surplus amount (ps - pd)
Kontorus
CC BY-SA 3.0
2016-07-14T13:58:40.633Z
2016-07-14T13:58:40.633Z
Kontorus
<p><a href="https://i.sstatic.net/G5Vvc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/G5Vvc.png" alt="enter image description here"></a></p>

<p>So, I am trying to evaluate the consumer and producer surplus. In my notes it is written that the new consumer surplus (defined by the change of the graph from pre-subsidy to post-subsidy) is G + A + D + E - which I do understand. But now, the new producer surplus is defined as the area H + D + A + B. This, one the other hand, doesn't maky any sense to me. Shouldn't the producer surplus be the area H + the "tunnel" that is not marked below H? </p>

<consumer-surplus><producer-surplus>
consumer and producer surplus
Julian
# consumer and producer surplus

(Asked by: username_0 on 2016-07-14)

[![enter image description here](https://i.sstatic.net/G5Vvc.png)](https://i.sstatic.net/G5Vvc.png)

So, I am trying to evaluate the consumer and producer surplus. In my notes it is written that the new consumer surplus (defined by the change of the graph from pre-subsidy to post-subsidy) is G + A + D + E - which I do understand. But now, the new producer surplus is defined as the area H + D + A + B. This, one the other hand, doesn't maky any sense to me. Shouldn't the producer surplus be the area H + the "tunnel" that is not marked below H?

**Tags:** consumer-surplus, producer-surplus


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## 2 answers

### Answer by username_1 on 2016-07-14. Score: 6

**TL;DR version:** "the tunnel" and D+A+B have exactly the same area.

---

You are right to say that post-subsidy producer surplus is equal to the blue area in the following figure:

[![enter image description here](https://i.sstatic.net/FPa6u.png)](https://i.sstatic.net/FPa6u.png)

**However**, it turns out that *The Tunnel* (i.e. the dark blue area) is exactly equal in size to D+A+B.

Intuitively, there are two ways to think of a unit subsidy:

1. Paying the seller a subsidy of $S=p^s-p^d$ per unit sold has an effect equivalent to reducing his marginal cost by $S$. The seller's marginal cost curve shifts down in the same way as the supply curve in your figure. From the seller's point of view, its as if he is paid price $p^d$ for each unit he sells but had a low marginal cost. When we calculate producer surplus (by looking at the area between the marginal cost curve and the price) this creates some new producer surplus equal to 'the tunnel' (which represents the seller's lower perceived cost). This way of thinking about things gives us the blue area above.
2. The subsidy does not reduce the seller's cost [so the seller's perceived marginal cost curve coincides with S(pre-subsidy)], but the subsidy is paid to 'top-up' the price received by the seller from $p^d$ to $p^s$. So from the seller's point of view it is as if he is being paid price $p^s$ with a high marginal cost. When we calculate producer surplus we look at the green area in the following figure:

Since these are two ways of thinking about the same subsidy, they must yield the same value for producer surplus. But you should be able to see by comparing the blue and green areas that this necessarily implies that the tunnel has the same area as D+A+B.

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

---

You can check this is true in an example by drawing the curves $Q\_S=0.5+p$ and $Q\_D=2-p$ and then applying a subsidy of $0.5$ to produce a new supply curve $Q\_S'=p$. It looks like this:

[![enter image description here](https://i.sstatic.net/9rwtV.png)](https://i.sstatic.net/9rwtV.png)

Geometrically calculating the areas, you should find that 'the tunnel' and A+D+B both have area 3/8.

> **Comments:**
> **username_2**: That is A LOT of work put into a SE answer  
> **username_3**: First time I've ever seen it explained that way. Nicely done.  

---

### Answer by username_4 on 2016-07-14. Score: 0

Producer surplus is calculated using the S(pre-subsidy) and the demand curve.

You're probably confused because you think the surplus should be calculated using the new supply curve. However, the producer is actually still producing on the original supply curve.

> **Comments:**
> **username_5**: But he gets a subsidy while doing so, raising his surplus.  
> **username_4**: Yes. You can include that in the producer surplus as well (some people do, some do not). That would be equal to the quantity * surplus amount (ps - pd)  

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