<p>Let us assume that the current price <span class="math-container">$P$</span> is lower than the 'equilibrium price' <span class="math-container">$P^\star$</span> so that <span class="math-container">$Q$</span> is lower than <span class="math-container">$Q^\star$</span>. If we move from this combination towards the equilibrium one, it may be the case that the producer surplus decreases. I understand that the total surplus (consumers+producers) increases, but it is not clear to me why producers should be willing to reduce their surplus. So it looks like to me that there is not pareto improvement in moving from <span class="math-container">$(P,Q)$</span> to (<span class="math-container">$P^\star$</span>,<span class="math-container">$Q^\star$</span>), in that consumers are better off but producers may be worse off.
What is wrong with my reasoning? Could you help me with this, please?</p>

CC BY-SA 4.0
2019-09-26T13:02:02.553Z
As pointed out in Kenny LJ's answer, you are using the wrong definition of Pareto efficiency (which requires there to be no universal improvment over $(P^*,Q^*)$, not that there is no other such $(P,Q)$. But, putting that aside, your example also isn't very well thought-through. Indeed, it is perfectly possible for there the be a Pareto improvement in moving from $(P,Q)$ to $(P^*,Q^*)$. For example, if $P=0$ and $Q=0$ then both producer surplus and consumer surplus are zero and almost anything would be a Pareto improvement!
Ubiquitous
CC BY-SA 4.0
2019-09-26T13:40:11.930Z
That is why I wrote: 'it MAY be the case'
Alchemy
CC BY-SA 4.0
2019-09-26T13:43:11.437Z
According to the definition you gave it may be the case that $(P,Q)$ is still Pareto efficient
Alchemy
<pareto-efficiency><competitive-equilibrium>
Why is market equilibrium pareto efficient?
Alchemy
# Why is market equilibrium pareto efficient?

(Asked by: username_0 on 2019-09-26)

Let us assume that the current price $P$ is lower than the 'equilibrium price' $P^\star$ so that $Q$ is lower than $Q^\star$. If we move from this combination towards the equilibrium one, it may be the case that the producer surplus decreases. I understand that the total surplus (consumers+producers) increases, but it is not clear to me why producers should be willing to reduce their surplus. So it looks like to me that there is not pareto improvement in moving from $(P,Q)$ to ($P^\star$,$Q^\star$), in that consumers are better off but producers may be worse off.
What is wrong with my reasoning? Could you help me with this, please?

**Tags:** pareto-efficiency, competitive-equilibrium
> **Comments:**
> **username_1**: As pointed out in Kenny LJ's answer, you are using the wrong definition of Pareto efficiency (which requires there to be no universal improvment over $(P^*,Q^*)$, not that there is no other such $(P,Q)$. But, putting that aside, your example also isn't very well thought-through. Indeed, it is perfectly possible for there the be a Pareto improvement in moving from $(P,Q)$ to $(P^*,Q^*)$. For example, if $P=0$ and $Q=0$ then both producer surplus and consumer surplus are zero and almost anything would be a Pareto improvement!  
> **username_0**: That is why I wrote: 'it MAY be the case'  
> **username_0**: According to the definition you gave it may be the case that $(P,Q)$ is still Pareto efficient  

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