The problem of pricing wine

Photo by steven­de­polo via Flickr.

Imagine you’re a wine pro­ducer and you’re changing your prices. Your cus­tomers have an infi­nite range of pref­er­ences — some of them require very high quality wines while others are happy with the two buck chuck. You obvi­ously can’t make a sep­a­rate bottle for every cus­tomer, each with a dif­ferent cost suited for their indi­vidual budget. Instead you need to figure out some way to pro­vide a finite range of qual­i­ties — a gold, a silver and a bronze label, say — and stamp each with an optimal price tag.

But how do you do that? How do you iden­tify optimal pricing when your mil­lion or so cus­tomers all have dif­ferent needs? The stan­dard eco­nomics method is to do some kind of qual­i­ta­tive market research study. “There was no sys­tem­atic way of arriving at the optimal wine qual­i­ties that one should make,” said Elec­trical and Com­puter Engi­neering pro­fessor Edmund Yeh.

In June, Yeh pre­sented a paper at the Elec­tronic Com­merce meeting of the Asso­ci­a­tion for Com­puting Machinery that adds an entirely new method to the field of eco­nomics. “We can use infor­ma­tion tech­niques to ana­lyze eco­nomics prob­lems,” said Yeh.  The paper uses a method called quan­ti­za­tion to iden­tify your optimal wine (or any other product) prices.

Typ­i­cally, quan­ti­za­tion is a data com­pres­sion tech­nique that turns things like analog audio sound into a dig­ital file for your iPod. “It’s a pow­erful tool that econ­o­mists had not used before,” said Yeh, who was appar­ently approached by many inter­ested econ­o­mists after the paper’s presentation.

The method has the poten­tial to reach a range of eco­nomics prob­lems that require solu­tions based on lim­ited infor­ma­tion, Yeh said. He is already in dis­cus­sions with sev­eral local econ­o­mists who wish to imple­ment the method in their own research programs.

In the case of a dig­ital audio file, the infor­ma­tion (an infi­nite col­lec­tion of sound waves) needs to be turned into a finite number of bits (or regions). You cannot rep­re­sent every pos­sible sound, but rather need to deliver a rep­re­sen­ta­tive col­lec­tion of sounds.

In the case of product pricing, you have an infi­nite number of pref­er­ences but only three or four price regions. “The trick is how to choose those regions,” said Yeh. You need to choose three or four types of wine whose qual­i­ties “max­i­mize either the aggre­gate social wel­fare or the seller’s rev­enue,” he explained.

It is quite serendip­i­tous how a stan­dard problem in eco­nomics becomes a problem in infor­ma­tion pro­cessing,” said Yeh.  He and his col­leagues mapped the vari­ables in an eco­nomic pricing problem to the vari­ables in a data quan­ti­za­tion problem. The product’s quality becomes the rep­re­sen­ta­tion point while the pref­er­ence para­meter becomes the signal to be quantized.

The work is a col­lab­o­ra­tion between Yeh, his grad­uate stu­dent Yun Xu, Pro­fessor Dirk Berge­mann from the Yale Eco­nomics Depart­ment and Ji Shen, a grad­uate stu­dent at the London School of Economics.