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Pricing on the Internet
In this exercise, you will be competing with a number of other sellers in trying to sell
product on the Internet. Like many e-retailers, you buy a product after you receive
purchase orders. Each product costs $1 to obtain from wholesalers. Others have fairly
identical cost structure. Apart from sunk marketing costs to attract loyal consumers, you
have no additional costs of production or sales.
The demand in this market comes from two segments of the consumers: shoppers and
loyals. Shoppers view products being sold by you and all competing firms as perfect
substitutes. They simply buy from the firm offering the lowest price provided that price is
below their willingness to pay, which is estimated to be $100. Loyals are consumers who,
by virtue of past promotion activity, view your firm and its products as being far superior
to any of your rivals. These consumers will buy from you regardless of what prices your
rivals set so long as your price does not exceed their maximum willingness to pay, which
is also estimated to be $100.
Because of the results of Amazon and others with experiments in price discrimination,
you believe that price discrimination is not feasible between these classes of customers;
thus, you must charge all your customers the same price.
In each period, there are 1600 customers interested in purchasing at most one unit of the
item you are selling. Half of these customers are shoppers, with the remainder divided
evenly as loyal customers of each firm. Your job is to set a price to sell the product in
each period. All firms do this simultaneously.
Please note that the game will proceed for an uncertain number of periods before demand
changes. At some randomly determined time, the product you are selling will become
more commoditized and 75% of consumers will become shoppers, with the remaining
loyals still being equally distributed among the competing firms.
Problem Set Questions
Suppose that the total number of competing firms is 8.
1. Demonstrate that the “law of one price”, i.e. all firms charging the same price, is
not an equilibrium in this setting.
2. Derive a symmetric mixed strategy equilibrium in this game when half the
consumers are shoppers.
3. Now do the same when 75% of consumers are shoppers. What happens to firm
profits in this setting?
4. Suppose that 50% of all consumers are shoppers but, because of technological
obsolescence of the good you are selling, their maximum willingness to pay falls
to $50. What happens to the equilibrium? To firm profits?