What is non-optimal about current sorting?

In club theory, clubs have congestion costs and charge fees, in part to reflect those costs.  If there are enough clubs, or non-convexities are not too severe, the voluntary outcome is roughly optimal.

So why then are guidelines for social distancing needed?  Why can’t we just let consumers decide to stay away from stores or other venues that might be too dangerous?

The problem with pandemics is that congestion costs are endogenous, and not fixed as in the simple club models.  If you get infected, congestion costs rise, and entry fees rise, increasing both congestion and exclusion (shut stores as one symptom of exclusion), both reducing the welfare of others.  Individuals do not take those costs into account when deciding their risk of exposure.

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