<p>It depends on the assumptions you make.</p>

<p>If you assume that preferences are <a href="https://books.google.hu/books?id=8tW9KAnkx04C&amp;pg=PA256&amp;lpg=PA256&amp;dq=locally%20insatiable&amp;source=bl&amp;ots=zhsgeinWKc&amp;sig=W0NxaFP4Anin1vNpXIwSu2oslgI&amp;hl=en&amp;sa=X&amp;ved=0CDMQ6AEwA2oVChMIjJbuyfyOxgIV4RTbCh3WbQAS#v=onepage&amp;q=locally%20insatiable&amp;f=false" rel="nofollow">locally insatiable</a> then no.</p>

<p>Without this assumption, it is easy to construct counterexamples. <br> Consider an economy with two consumers ($A,B$) and two goods ($x,y$). Both consumers have preferences represented by their utility function
$$
U_i(x_i,y_i) = \min(x_i,1) + y_i.
$$ 
If the initial endowments are such that the total supply of $x$ is larger than 2 then the equilibrium price of $x$ is 0. (The numeraire is the good $y$.)</p>

CC BY-SA 3.0
2015-06-14T10:35:03.267Z
2015-06-14T10:35:03.267Z
Giskard
<p>I don't think they can be, but I'm not very sure. Are their special cases where the equilibrium is competitive even when prices are zero?</p>

<microeconomics><competitive-equilibrium>
In a competitive equilibrium, can price of a commodity ever be zero?
dexter
# In a competitive equilibrium, can price of a commodity ever be zero?

(Asked by: username_0 on 2015-06-14)

I don't think they can be, but I'm not very sure. Are their special cases where the equilibrium is competitive even when prices are zero?

**Tags:** microeconomics, competitive-equilibrium

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## 1 answers

### Answer by username_1 on 2015-06-14. Score: 3 | Accepted answer

It depends on the assumptions you make.

If you assume that preferences are [locally insatiable](https://books.google.hu/books?id=8tW9KAnkx04C&pg=PA256&lpg=PA256&dq=locally%20insatiable&source=bl&ots=zhsgeinWKc&sig=W0NxaFP4Anin1vNpXIwSu2oslgI&hl=en&sa=X&ved=0CDMQ6AEwA2oVChMIjJbuyfyOxgIV4RTbCh3WbQAS#v=onepage&q=locally%20insatiable&f=false) then no.

Without this assumption, it is easy to construct counterexamples.   
 Consider an economy with two consumers ($A,B$) and two goods ($x,y$). Both consumers have preferences represented by their utility function
$$
U\_i(x\_i,y\_i) = \min(x\_i,1) + y\_i.
$$
If the initial endowments are such that the total supply of $x$ is larger than 2 then the equilibrium price of $x$ is 0. (The numeraire is the good $y$.)


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