econometrics, price-adjustmentThis is a little strange question i suppose, but i can’t find any simpler solution to my problem. Anyway this is the question. A friends of mine has a bar and asked me: If i raise the price of a coffee i know that fewer people will come to me to buy a coffee. If i lower the price of a coffee much more people come to me to buy a coffee but i will gain lesser. So the question is: how can i know the right price of a coffee in order maximize the gain?
After a little of thinking my answer was:
if we let C the cost (to seller) of one coffee, P the price of one coffee and N(P) the people the on average will buy a coffee at price P, then the cost of coffee will be
P=max{(P-C)N(P)} at the variation of P
…after a further thinking i found another solution:
I define Ge the gain expected, Gr the real Gain an P the price of a coffee. Now if i rise the price the real gain Gr will be different form gain expected Ge and i can adjust the P price as
Pn=P+k(Gr-Ge)
where Pn is the new price. if the real gain Gr is greater then the expected Ge i can rise even further the price, if it is lesser i have to lowering the price.
Now the questions are:
-How can i measure the distribution of N(P) or the factor K?
I used to ask my students, "When is a cup of coffee not a cup of coffee?"
Answer: When it's a cup of coffee with a biscuit.
More than a single specific and "correct" price, you're looking to provide Price Discrimination and permit your customers to find their own price level. You need your customers to reveal their preferences by picking a price-point they're comfortable with.
From Wikipedia: "The effects of price discrimination on social efficiency are unclear; typically such behavior leads to lower prices for some consumers and higher prices for others."
Such revealed preferences are also indicative of your various customer's level of price elasticity. Many chain coffee stores use such discrimination by keeping entry-level coffees at static levels while bringing much greater elasticity to their "premium" coffees.
Tim Harford has a lovely chapter on coffee and disriminatory pricing in his book, The Undercover Economist, which is well worth a read.
This is, ultimately, a strategic decision about the type of retail environment you wish to create. Discrimination allows you to select your customers out of the wider consumer market.
You might want to take a look at the markup rule, which gives you the profit maximizing price as a function of elasticity (how price sensitive consumers are) and your marginal cost. If you want to use this formula, then you will need an estimate of the elasticity. Here are some lecture notes about how you might go about doing that. Another good source that gets into the nitty-gritty of pricing theory is Oz Shy's How To Price, which includes a nice discussion of price discrimination, which is really important for coffee, but probably less relevant if you're a bar, rather than a coffee shop.
All content is licensed under CC BY-SA 3.0.