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i just don't get it.

Peak-load pricing wiki page gives example:

in public goods such as public urban transportation, where day demand (peak period) is usually much higher than night demand (off-peak period)

Price discrimination wiki page gives example:

For example, schedule-sensitive business passengers who are willing to pay \$300 for a seat from city A to city B cannot purchase a \$150 ticket because the \$150 booking class contains a requirement for a Saturday night stay, or a 15-day advance purchase, or another fare rule that discourages, minimizes, or effectively prevents a sale to business passengers.

But I don't really see the difference.

In the example of urban transportation, people pay more to buy the convenience of "peak period usage"; while in the other example of air tickets, people pay more to buy the convenience of "returning without spending a Saturday night stay" (so that they could enjoy quality time with family) or "without 15-day advance purchase" (so that they need not spend time planning the detailed, maybe even trifle things that might happen in the future).

For example, a company might hire a secretary to book tickets in 15-days' advance, while need to pay the secretary; or, just buy air tickets when needed, while need to pay the premium of convenience.

that convenience is really a need, why shall government bother?

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That things are similar but addresses different range of customers and separation is needed because some ranges are bigger then is less possibility of price movement. For example Price-Load addresses wide range and not much price movement are possible here, in Price discrimination range are more narrow and more possibility in price movement are possible. When 2 models are independent are profitable then best work on both.

Example for price discrimination working w/out price load:

First company w/out possibility to plan trip ahead pay more and that is calculated into that company operating costs.

Second company who have possibility of planning trip ahead and planning more rips than first company will hire secretary to plan all trips inside company and take return from lowering trip costs when money saved on tickets will be greater than payoff for secretary.

This is obvious that first company should have pay more for tickets because they are don't have possibility to plan trip ahead like second company and for transportation company is better to have tickets sold faster than slower, because that raising possibilities to make promotions on tickets not sold or gives time to better manage inside assets for lowering operating costs like change some bigger bus to lower that also carry all passengers, but have lower usage costs.

That will be not logic when price for both companies will be equal because after that: -

  1. income from tickets will be lower (same tickets sold, for company A pays lower price)
  2. company 2 probably will be drop planning trips ahead and fire secretary
  3. transportation company has higher operating costs due to lower possibility of managing assets in way that makes most revenue
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The peak-load wiki page is pretty poor. Public transit may not be the best example, especially since at most times it's close to zero marginal cost but tends not to be free.

The bottom line up front difference is price discrimination is specifically intended to avoid charging an efficient price (in the basic microeconomic sense of market efficiency), whereas peak-load pricing is specifically intended to create an efficient price at all times.

Price discrimination explicitly segments customers by their personal demand curve, so that instead of offering the market price based upon aggregate supply and demand, thus admitting quite a bit of consumer surplus, a seller is able to offer exactly what each customer is individually willing to pay by charging a different price to each customer. Clearly, it's nearly impossible to do this in practice except by individual negotiation and secret prices, so you'll see segmentation into sub-markets rather than by individual customer, hence the airline example trying to use a fairly hacky means of capturing at least a little more producer surplus if not all of it. The point is to not charge a single market-clearing price, which inherently benefits customers who would be willing to pay more but don't have to. The producer itself is still willing to charge the lowest market-clearing price, but of course would prefer not to.

Peak-load pricing, on the other hand, has nothing to do with producers trying to optimize their own welfare surplus. A better example than public transit, sticking with public goods, is utilities pricing. A line can only sustain so much transmission bandwidth at a time and prices act as a rationing mechanism to induce usage to stay balanced over the course of an entire day so the line will always work. Charging more during the day is not intended to take advantage of customers who absolutely need the power at noon. It's intended to reduce peak usage so the line doesn't break.

Of course, it can work in the opposite way for goods that have short-term supply flexibility. Uber is the obvious private sector example. Peak-load pricing there is also not intended to gouge customers (in spite of the headlines). They do that so they can send bulk text messages to all their drivers who are not currently on the road telling them 'hey, sign on right now and you can earn ten times your normal fare.' It's intended to increase the system capacity to meet the level of current demand, while at the same time discouraging riders who are not willing to pay that much.

In both cases, the purpose of the price change is to always maintain a single price that actually clears the market. It's not that the producer is willing to accept a lower price but prefers not to in order to change the balance of producer's versus consumer's surplus. Instead, the price rises to prevent or remedy a supply shortage, and then drops again later to prevent or remedy a supply surplus.

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