Is there a name for this type of problem? I am having trouble formulating the concept I am thinking about. It has to do with looking at observed behavior of the sales of a particular product during each hour of the day, and trying to adjust prices accordingly.

If you have a time series of 24 pairs of values, $(x_1,y_1), (x_2,y_2), \ldots, (x_{24},y_{24})$, where $(x_t,y_t)$ represents the data at time $t$ o'clock: $x_t$ is the number of sales and $y_t$ is the average price paid (both at time $t$).

Given this information, is there anything that can be deduced about how the product should be priced? What about by the hour?

My background is not in economics, so I don't know if there is a framework for this type of problem.
I take from your comments that you are interested in airline seating prices.

The subject of airline pricing is very complex: 


There are different seating classes at different sizes, where the offered quantities vary over time
There is overbooking, because more expensive tariffs allow "last second changing" into and out of a specific flight, and companies try to accommodate for that
Demand for the same flights vary with season and even day of the week. Typical example: There is higher demand on short distance flights for Thursday Evening/Friday Afternoon and Sunday night / Monday morning flights
Elasticities vary with the distance: The more short term flights are being booked, the "more desperate" customers are, and the higher the faires are that companies can charge them. However, at the "last minute", the companies potentially become "desperate" to fill seatings themselves, and offer low prices themselves


I remember sitting into one, two lectures on this when a professor of Business Administration was treating the subject. The elasticities part of could equally well be treated by Economists, but most who look at the subject are BAs involved with logistics and similar - I would refer you to look for their literature (I have none at hand) for more detailed information.