An Example of Price Discrimination and Its Consequences

Imagine a company, ACME CROSS-THREADED WIDGETS (AC-TW), which has two geographical markets for its products, the island of Manhattan in New York City and the region surrounding Jackson, Mississippi.

The company has estimated that, if the two markets can be kept effectively isolated, it will maximize its overall profits (or minimize its losses) as well as the profits in each market separately by setting a unit price of $10 in NYC and a unit price of $6 in Jackson. In order to attempt to keep the two markets effectively isolated, the company writes restrictions into its sales and distribution contracts that limit both quantities of units sold and re-distribution.

To the extent that the two markets are substantially statistically different in both willingness and ability to pay, mandating a single price across both markets by prohibiting price discrimination is likely to result in a single unit price that is not much below $10 as the incremental loss of profits from the NYC market as the price is lowered below $10 is not compensated for by an increase in profits from the Jackson market.

Under this condition, we can summarize the consequences as follows :

1. As stated above, the company is best off maximizing profits in each of the two separate markets, and will lose almost all of the Jackson profits if price discrimination is prohibited.

2. The Manhattan consumers will benefit only slightly, if at all, if price discrimination is prohibited.

3. The Jackson consumers will be injured severely by a prohibition of price discrimination, as they will see their price increased from $6 to $10 and they may even have to travel to NYC to get that price.

Instead of price discrimination being prohibited, we can look at the consequences of the Mississippi state government setting a price ceiling on sales to Mississippi residents.

1. If the state sets a price ceiling at the profit-maximizing price of $6 or above, there are no immediate consequences for anyone.

2. If the price ceiling is set below $6, the Jackson consumers will benefit to the extent that the company loses, but only the Jackson market will be affected.

For all of the conditions described above, the results are independent of the relative sizes of the two markets. The NYC market could be 100 times larger in revenue than the Jackson market, or the Jackson market could be 10 times larger than the NYC market, without effect in either case.

However, it only takes a small change in conditions to invalidate this.

If the Mississippi price setting procedure involves percentage discounts to the NYC price instead of absolute prices AND the result is a Jackson price less than the $6 profit-maximizing price, then the prices in both markets are no longer independent and will tend to move together with the result very much depending on the relative sizes of the two markets.

To illustrate this,consider the following :

The profit-maximizing prices of $10 and $6 in the two markets are also consistent with a 40% or smaller discount. When the discount increases beyond 40%, say to 50%, one or both of the two markets must be priced at a non-profit-maximizing price. But the larger market of the two will predominate in determining the prices. For a 50% discount, the pair of prices must range between $10/$5 and $12/$6. This is because as soon as both prices are on the same side of their profit-maximizing levels, further price movements reduce profits no matter what the size of the markets are. If Jackson has only a single consumer, then the Jackson price is of little importance to the company and the resulting price pair will be $10/$5. Similarly, a small NYC market relative to Jackson would result in a $12/$6 price pair.

We can note in passing that a prohibition of price discrimination is a special case of a percentage discount mandate, namely 0%.

Subject to correction, all of the above is general. It doesn't depend on monopoly, patents, development costs, marginal costs, advertising, etc. The only qualification that I can see is that it doesn't account for competitive responses to price changes, which simply means that profit-maximizing prices are often not stationary.

There seem to be important implications of all this to be explored later.

Share this

Consider a real company in a

Consider a real company in a real economy. What's that you say? Economists don't do real? Pfeh!

Consider a real company in a

Consider a real company in a real economy. What's that you say? Economists don't do real? Pfeh!

Maybe you don't think so, but this has a lot of relevance to the issue of drug reimportation. If you have anything constructive to offer, please do so, instead of throwing barbs. Otherwise, feel free to ignore this thread.

Jonathan, I don't think that

Jonathan,

I don't think that was a barb, just a satiric comment on the usual disconnect between economics and reality.

Regards, Don

Don, How important do you

Don,

How important do you think the cost of contract enforcement is to the actual efficiency of price discrimination? For example, hardcover books are released a few months before they come out in softcover. They cost a bit more, but those who are willing to pay a premium get to enjoy the book in advance. The publisher is able to reap the benefits of price discrimination without having to worry much about discouraging arbitrage.

Even if a company writes restrictions into its sales contracts, it is still costly to enforce these contracts. If the cost is high enough, this may cancel out any benefits the company may have enjoyed as a result of discrimination.

Under our current system, contract enforcment is heavily subsidized by the government. Were this not the case, we might see a decline in price discrimination overall.

Don, ...mandating a single

Don,

...mandating a single price across both markets by prohibiting price discrimination is likely to result in a single unit price that is not much below $10 as the incremental loss of profits from the NYC market as the price is lowered below $10 is not compensated for by an increase in profits from the Jackson market.

I'm having trouble understanding the state of the combined market when price discrimination is not possible.

I realize that the price/revenues curves for each market likely drop off steeply in either direction - for Jackson, above $6 and for NYC, below $10.

The final price will be somewhere in between. You arrive at the conclusion that it will be closer to $10 and this is independent of the sizes of the two markets. How and why?

Micha, "...Even if a company

Micha,

"...Even if a company writes restrictions into its sales contracts, it is still costly to enforce these contracts. If the cost is high enough, this may cancel out any benefits the company may have enjoyed as a result of discrimination.

Under our current system, contract enforcment is heavily subsidized by the government. Were this not the case, we might see a decline in price discrimination overall...."

What you say is true, but to my mind, not the overwhelming consideration.

If the government didn't subsidize contract enforcement, by which I believe you mean the provision of the civil courts, there is no real reason that the free market would be unable to provide private services at an efficient scale. A company would pay an annual retainer to keep both investigative and enforcement services available.

The real effectiveness would not likely be in the actual enforcement of the contracts, but rather in the real threat of the cut-off of supply and blacklisting that could be applied.

I have seen price discrimination described in positive terms by both Milton Friedman and Brad DeLong recently, so it's likely that its bad taste comes from general ignorance and ideological opponents of capitalism.

Regards, Don

Jonathan, "...The final

Jonathan,

"...The final price will be somewhere in between. You arrive at the conclusion that it will be closer to $10 and this is independent of the sizes of the two markets. How and why?"

You are correct to question this. It IS possible that the unit demand in Jackson is so overwhelming that even though every unit sold in Jackson has a far lower profit than units sold in NYC at $10, the unified market could yield a profit-maximizing price close to $6. It remains true that the company will benefit from two isolated markets.

Thanks, Don

Don, You are correct to

Don,

You are correct to question this. It IS possible that the unit demand in Jackson is so overwhelming that even though every unit sold in Jackson has a far lower profit than units sold in NYC at $10, the unified market could yield a profit-maximizing price close to $6.

My intuition is that the final price will be determined, at least in part, by the sizes of the two markets.

"2. If the price ceiling is

"2. If the price ceiling is set below $6, the Jackson consumers will benefit to the extent that the company loses, but only the Jackson market will be affected."

Are you assuming for some reason that a shortage will not emerge, or disregarding its consequences?

Noah, That's a fair

Noah,

That's a fair question.

The unstated assumption would be that the State would not set the price so low that the company would abandon the market. This would mean that the company would supply the Jackson market if and only if it made sense to do so. It IS possible that the Jackson demand at a lowered, mandated price, would require additional capacity to completely meet, so whether this capacity would be brought on line or not depends on the cost/benefit of doing so.

Thanks, Don

Price discrimination is all

Price discrimination is all you had up until about a few hundred years ago!

In ancient markets, there were no fixed prices. Everything was "haggled," which is simply a seller determining his best-case price discrimination point for the particular buyer.

Auctions are another form of price discrimination.

Price discrimination appears to be easier in goods where there is more monopoly power. Patented drugs and copyrighted media come to mind. In these areas, sellers have a wide selection of pricing because of low cost of marginal production, although they may need to recover a large orginal sunk cost of research, development, or authoring.

Price discrimination by area shows up in branded gasoline wholesaling. Areas that are richer pay more for gas, areas that are poorer pay less. This can be done because customers can't really FedEx 20 gallons of gas from Amazon.Com.

Auto sales, of course, are haggled to achieve price discrimination.

The benefits of fixed pricing is mainly in the ability to easilly sell large amounts of things to large amounts of people without having to haggle for every item. It is a time and effort efficiency issue.

But speaking of Amazon.Com, the power of computers gives the ability of online shops to try to price discriminate using artificial intelligence. Also EBay has made auctioning anything much easier than dragging your wares to the auction house. Computers and the Web are making price discrimination being to make inroads into fixed pricing.