#### Optimal Pricing in a Hazard Rate Model of Demand

**Abstract: **Optimal control theory is employed to
derive explicitly the optimal (profit-maximizing) price of a durable new product
over time. The sales rate dynamics depends on the product price and
on the unsold portion of the market. Specifically, the hazard rate (i.e. the
probability of a purchase by a new customer) increases as the price decreases in
a linear fashion. It is shown
that both the price and sales rate decline over time for finite horizon problems
with or without discounting. In the infinite horizon case, the price remains
constant over time. When there is no discounting in the infinite
horizon case, there does not exist an optimal solution. However, it is possible
to attain a profit level which is arbitrarily close to the theoretical,
albeit unattainable, maximum level profit. Economic interpretations are provided
for the various quantities that arise in the course of solving the optimal
pricing problem.