Question

You are the manager of a local coffee shop. There are two types of customers in your market, coffee addicts, and casual drinkers. Because coffee addicts buy large amounts of coffee, they are more willing to shop around for low prices and so, if you charge more than $2 for a medium coffee, which is what your competitor charges, they will not come to you at all. If you charge less than your competitor, they will each buy 8 drinks per week. Each casual drinker’s demand is given by Qc = 9 - 2P Your marginal cost is constant at $0.50 a. Devise a pricing scheme that will allow you to sell to both addicts and casual drinkers and maximize your profits. Show that your pricing scheme is incentive compatible. b. Do you think that coffee shops do something along these lines?

Answer 1

Pricing Scheme:
We can price our coffee at $1.5 per drink for the first 8 cups and $1 for each that is more than 8 for a single customer in a week.
From the demand function of the casual drinker we get:
Q = 9 – 2P hence for coffee at $1.5 the casual drinker will buy Q = 9 – 2x1.5 = 6 drinks.
The addict will order 8 drinks at least and because there is incentive on buying more than 8 cups he will buy more per week.
At $1 also we have a margin of $0.50 and will maximize our profits.
Some coffee shops do follow this as they provide their loyal customers with discounts or special offers.