Imagine that there are 1,000 consumers. For each consumer, the willingness to pay for a widget is distributed uniformly over the interval [0,1] depending on the style of the widget. A retailer with a particular study of the good knows this distribution. Its costs are zero. Consumers do not know the style that the retailer has stocked and each incur a transport or search cost of T= 0.125. Once this cost is incurred it is sunk. At that point, a consumer in the retailer’s store will purchase the product so long as the consumer’s valuation is greater than or equal to the price charged by the retailer.
A) Show that facing a random selection of customers, the retailer’s profit maximizing price is p= 0.5.
B) Show that with T= 0.125, all consumers will come to shop expecting a price of 0.5. What would happen if T= 0.15?