Upward Sloping Demand Curves? The Case of the NY Metropolitan Museum of Art

When can a demand curve slope up?  Gary Becker has an under cited JPE that offers a theory.  In his "snob good model",  my pleasure from consuming a good decreases if more people consume it.  For example, if a Mercedes is a Veblen "conspicuous consumption good', then if its price increases I may value driving one even more because I know that you can't afford it!. Thus,  I will be willing to pay more to have this "snob good" (so this is a relative status good that Richard Frank and others like to talk about).

This logic flashed through my head today because of this NY Times story about introducing a $20 price to enter the NYC Metropolitan Museum of Art.

Ayad Akhtar

Playwright, “Disgraced” (Pulitzer Prize, 2013)

I remember when MoMA raised the ticket price to $20. And I heard that oddly enough, counterintuitively, admissions went up — but I wasn’t making enough money to justify spending $20 a ticket. Because of that, I ended up going to the Met more.

IN This case, I don't think the Becker model explains Ayad's upward sloping demand curve.   Museums (as I learned at Versaiilles, France recently) suffers from congestion problems.   This congestion is especially bad if the price of entrance is $0.  At a $20 charge , fewer people will show up and more sophisticated art lovers will show up. Thus, charging a price changes the attributes of the differentiated product and makes the quality of the visit more enjoyable, this will increase the demand for the product and create the possibility of an upward sloping demand curve.    BLP should reunite to write a structural IO paper on museum demand and the resulting consumer surplus with  endogenous product attributes!  When economists talk about demand curves, we mean --- holding all else constant, how is demand affected if the price declines but if the price decline lowers the product's quality (through introducing congestion effects) then two things change at once as you drop the price and this isn't the "demand curve experiment".  

They would face a challenge here in modelling the supply side. Given that museums are not profit maximizers, how do they set prices? What is their objective?  Is it the quantity of museum guests or the quantity*quality of the experience? What is the tradeoff they perceive as the museum sets prices?