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Classical supply and demand examples use linear functions for both supply and demand.

From a mathematical standpoint, this guarantees that there is at most one intersection, which corresponds to the equilibrium price.

However, nothing says that those curves have to be linear. For example, this blog post describes a nonlinear demand curve, and I expect the same can be true for supply curves as well.

And nonlinear functions can have more than one intersection. For example, an upward facing parabola and a downward facing parabola can have two intersections.

Does this (nonlinear S&D curves and multiple equilibria) make sense from an economic standpoint?

And what are the implications in price taking? If there are two or more equilibrium points, which price will be "chosen"?

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Nonlinearity per se is not an issue. As long as demand is decreasing and supply is increasing in price, there will be at most one equilibrium point. However, if e.g. supply is "backwards bending", then there might be multiple equilibrium points. The static model is silent on which of those would "realize", but under a meaningful price adjustment dynamics you might (but need not) have a unique stable equilibrium. See this question and answer for details.

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  • $\begingroup$ It's not just "backwards bending" the issue, right? If either supply or demand (or both) are not monotonic, you could have two intersections if I'm not mistaken. $\endgroup$
    – A. Darwin
    Commented Jun 12 at 11:22
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    $\begingroup$ @A.Darwin Yes, any kind of non-monotonicity would do. But non-monotonicity is hard to justify, except in some special cases, and a backwards bending (labor) supply is just the most common such case. $\endgroup$
    – VARulle
    Commented Jun 12 at 13:02
  • $\begingroup$ I accepted your contribution because it already answers my questions, but if you could point me in the right direction on "non-monotonicity is hard to justify, except in some special cases" it would be great. Do you have any sources? As you probably know, standard introductory textbooks don't really delve that deep. $\endgroup$
    – A. Darwin
    Commented Jun 12 at 13:15
  • $\begingroup$ @A.Darwin These monotonicity properties are known as en.wikipedia.org/wiki/Law_of_demand and en.wikipedia.org/wiki/Law_of_supply. As any economic "law", there are some exceptions, also listed in these articles. Hope that helps. $\endgroup$
    – VARulle
    Commented Jun 12 at 14:03

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