  A consumer who wants to consume a good in a particular period may
nevertheless attempt to buy it earlier if he is concerned that in delaying he
would find the good already sold. This paper considers a model in which the
good may be offered in two periods; the period in which all consumers most
value the good (period 2), and an earlier period (period 1). Examining the
profit-maximizing strategy of the firm under unbounded demand, we find that
even with no cost of making the product available early, the firm does not
profit, and usually loses, by making the product available early.
Interestingly, the price that maximizes profits induces all arrivals to occur
early, or all arrivals to occur late, depending on the parameters. The firm
would not set a price which induces consumers to arrive in both periods. In
particular, if the firm controls the penalty for arriving early, then it should
set a high penalty so that no one arrives early. The Nash equilibrium behavior
of consumers, when deciding if and when to arrive is more complicated than one
may suppose, and can generate some unexpected behavior. For example, when there
is unbounded demand, most potential consumers decide not to arrive at all.
Additionally, the arrival rate may decline with the surplus a person gets from
buying the good. Surprisingly, we find that an increase in the number of units
for sale increases the number of consumers who arrive early. Moreover, we find
that the profit-maximizing price increases with the number of units offered for
sale. This too is unexpected as an increase in supply often results in price
reduction. In our case, an increase in the number of units on sale also
increases demand, and the seller may profit by increasing the price. In the
single-unit case, we give closed solutions for the equilibrium customer
behavior and profit-maximizing firm strategy and conduct sensitivity analysis.
