The Power of Purple Pricing

Any business trying to sell its products profitably must have some idea of what sales and hence revenue would be at different prices. Suppose we double our prices. Sales will fall, but will margins go up so much that it is worth it? Suppose we halve our prices. Margins will fall, but will sales go up so much that it is worth it?

In making these judgments, a business might use historical data or simply guess by adding a mark-up over costs. But there is a better way to learn the structure of demand, one that uses real time information and discovers the revenue-maximizing price at the same time. It is a variant on the so-called Dutch auction that has been used for over a hundred years in the Netherlands to sell flowers.

In a Dutch auction, the price starts off high and is lowered until someone buys. Dutch auctions are fast: only one person has to say they want the object for sale and the auction is over.

We used a variant of the Dutch auction to set prices for basketball games at Northwestern University where we work at the Kellogg School of Management and the Department of Economics. We call it Purple Pricing. Our Dutch auction has one vital and important twist: the Purple Pledge guarantees that, wherever the final price ended up, if someone buys a ticket at a higher price, they get a refund for the difference between the price they paid and the final price. The Purple Pledge is the key feature that allows us to learn demand and set the optimal price at the same time.

Let's say you are a huge Wildcats fan and are willing to pay $100 to see them play the Ohio State Buckeyes. The current price for the game stands at $99, so if you think the price is going to stay there, you would buy straight away to get the best seats possible. But in a traditional Dutch auction, since the price might go down, you might wait to get a better deal. The Purple Pledge solves your dilemma because if the price does go down you get a refund anyway. So, in fact you should buy as soon as the price falls just below your maximum willingness to pay as the Purple Pledge fully insures you against price cuts. This means that Purple Pricing with the Purple Pledge allows us to determine what sales would be at different prices — say a price of $70 — by looking at sales that occurred at that price or above. We learn the "demand curve."

We can also set prices on the fly. Let's say current sales are 6,000 at a price of $70. If we cut the price by a dollar we have to give $6,000 back to people who already bought tickets. But the last price cut from $71 to $70, only increased sales by 50. So, most likely we would only gain 50 times $69 by cutting the price, a gain of $3,450. If our objective is pure revenue maximization, then it is not worth cutting the price. If our objective is to increase attendance for the game, then we know how much revenue we are giving up to get extra attendance. Whichever way we decide to go, we can make the decision based on real-time data.

This is the kind of thing we did for tickets for Wildcats Games against Ohio State and Penn State. We ended up charging $38 for some seats in the OSU game; NU Sports had planned to sell tickets for $35 before we got involved. We ended up charging $20 for tickets to the PSU game; NU Sports had planned on charging $28 for this game before we got involved. After the games, someone gave us data from the secondary market StubHub. If we had known the data in advance we would have set the same prices we ended up setting on the fly. In other words, we did not need the benefit of hindsight to set prices. Purple Pricing discovered the "right'' prices anyway.

Purple Pricing was a big hit. But we repeatedly get the same questions: Why use a descending price Dutch auction and not the usual ascending price auction? Why would anyone want to give refund and not just keep the money?

The problem with an ascending price auction is that it is does not do a good job at capturing value. If you begin at $50 then someone whose maximum willingness to pay is $100 just buys straight away, and you lose revenue. A Dutch auction with decreasing prices has a similar problem: if you begin the auction at $99 but cut the prices, the person who values the ticket at $100 will just wait to buy. You still do not capture their value. The Purple Pledge resolves this issue: you get a refund if the price goes down and the earlier you buy the better the seat selection. And, since you have to pass on refunds, you might end up settling at price of $70 not $50. You would have given a bigger "refund" in the ascending price auction by starting the auction at $50.

As a pricing mechanism, Purple Pricing allows a seller to learn buyers' maximum willingness to pay so they get an excellent picture of demand. And, at the same time, the seller makes money despite giving refunds. Buyers, in the meantime, are comfortable buying early, getting the best seat they can, confident that they won't pay more than anyone else.

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