<p>In equilibrium, we have supply equal to demand. So $Q_{s} = Q_{d} \implies 50 = 2p$, so $p^{*} = 25$ is the equilibrium price. Consumer surplus is defined as:</p>

<p>$$\int_{p^{*}}^{p_{max}} Q_{d}(p) dp$$</p>

<p>Here, $p_{max} = 50$, as $Q_{s} = 0$ when $p = 50$. So evaluate the integral. </p>

<p>Producer surplus is similarly defined as:</p>

<p>$$\int_{0}^{p^{*}} Q_{s}(p) dp$$</p>

CC BY-SA 3.0
2016-07-13T03:25:24.963Z
2016-07-13T03:25:24.963Z
ml0105
<blockquote>
  <p>Calculate the consumer surplus, producer surplus and total surplus in the market equilibrium.</p>
</blockquote>

<p>Market for beef and home demand and home supply:</p>

<p>$$ Q_d(p) = 50 - p $$</p>

<p>and</p>

<p>$$ Q_s(p) = p $$</p>

<p>With $p$ representing the price of 1 kg of beef</p>

<p>I understand that consumer surplus is consumer's willingness amount to pay minus consumer actual paying price.</p>

<p>But how do I derive from only information from above?</p>

<microeconomics>
How do I calculate consumer surplus and producer surplus from this?
Ken
# How do I calculate consumer surplus and producer surplus from this?

(Asked by: username_0 on 2016-07-12)

> Calculate the consumer surplus, producer surplus and total surplus in the market equilibrium.

Market for beef and home demand and home supply:

$$ Q\_d(p) = 50 - p $$

and

$$ Q\_s(p) = p $$

With $p$ representing the price of 1 kg of beef

I understand that consumer surplus is consumer's willingness amount to pay minus consumer actual paying price.

But how do I derive from only information from above?

**Tags:** microeconomics

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## 1 answers

### Answer by username_1 on 2016-07-13. Score: 1 | Accepted answer

In equilibrium, we have supply equal to demand. So $Q\_{s} = Q\_{d} \implies 50 = 2p$, so $p^{\*} = 25$ is the equilibrium price. Consumer surplus is defined as:

$$\int\_{p^{\*}}^{p\_{max}} Q\_{d}(p) dp$$

Here, $p\_{max} = 50$, as $Q\_{s} = 0$ when $p = 50$. So evaluate the integral.

Producer surplus is similarly defined as:

$$\int\_{0}^{p^{\*}} Q\_{s}(p) dp$$


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