All About the Two-Part Tariff

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What Is a Two-Part Tariff?

A two-part tariff is a pricing scheme where a producer charges a flat fee for the right to purchase units of a good or service and then charges an additional per-unit price for the good or service itself.  Common examples of two-part tariffs include cover charges and per-drink prices at bars, entry fees and per-ride fees at amusement parks, wholesale club memberships, and so on.

Technically speaking, "two-part tariff" is somewhat of a misnomer, since tariffs are taxes on imported goods.  for most purposes, you can just think of "two-part tariff" as a synonym for "two-part pricing," which makes sense since the fixed fee and the per-unit price do in fact constitute tow parts. 

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Necessary Conditions for a Two-Part Tariff

In order for a two-part tariff to be logistically feasible in a market, a few conditions have to be satisfied.  Most importantly, a producer looking to implement a two-part tariff must control access to the product- in other words, the product must not be available to purchase without paying the entry fee.  This makes sense, since without access control a single consumer could go buy a bunch of units of the product and then put them up for sale to customers who didn't pay the original entry fee.  Therefore, a closely-related necessary condition is that resale markets for the product do not exist.

The second condition that needs to be satisfied for a two-part tariff to be sustainable is that the producer looking to implement such a policy have market power.  It's pretty clear that a two-part tariff would be infeasible in a competitive market, since producers in such markets are price takers and therefore don't have flexibility to innovate with respect to their pricing policies.  On the other end of the spectrum, it's also easy to see that a monopolist should be able to implement a two-part tariff (assuming access control of course), since it would be the only seller of the product.  That said, it could be possible to maintain a two-art tariff in imperfectly competitive markets, especially if competitors are utilizing similar pricing policies.

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Producer Incentives for a Two-Part Tariff

When producers have the ability to control their pricing structures, they are going to implement a two-part tariff when it is profitable for them to do so.  More specifically, two-part tariffs will most likely be implemented when they are more profitable than other pricing schemes- charging all customers the same per-unit price, price discrimination, and so on.  In most cases, a two-part tariff will be more profitable than regular monopoly pricing since it enables producers to sell a larger quantity and also capture more consumer surplus (or, more accurately, producer surplus that would otherwise be consumer surplus) than it could have under regular monopoly pricing.  It is less clear whether a two-part tariff would be more profitable than price discrimination (especially first-degree price discrimination, which maximizes producer surplus), but it may be easier to implement when consumer heterogeneity and/or imperfect information about consumers' willingness to pay is present.

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Comparing Monopoly Pricing to a Two-Part Tariff

In general, the per-unit price for a good will be lower under a two-part tariff than it would be under traditional monopoly pricing.  This encourages consumers to consume more units under the two-part tariff than they would under monopoly pricing.  The profit from the per-unit price, however, will be lower than it would have been under monopoly pricing, since otherwise the producer would have offered a lower price under regular monopoly pricing.  The flat fee is set high enough to at least make up for the difference but low enough that consumers are still willing to participate in the market.

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A Basic Two-Part Tariff Model

One common model for a two-part tariff is to set the per-unit price equal to marginal cost (or the price at which marginal cost meets the consumers' willingness to pay) and then set the entry fee equal to the amount of consumer surplus that consuming at the per-unit price generates.  (Note that this entry fee is the maximum amount that could be charged before the consumer walks away from the market entirely).  The difficulty with this model is that it implicitly assumes that all consumers are the same in terms of willingness to pay, but it still works as a helpful starting point.

Such a model is depicted above.  On the left is the monopoly outcome for comparison- quantity is set where marginal revenue is equal to marginal cost (Qm), and price is set by the demand curve at that quantity (Pm).  Consumer and producer surplus (common measures of well being or value for consumers and producers) are then determined by the rules for finding consumer and producer surplus graphically, as shown by the shaded regions.

On the right is the two-part tariff outcome as described above.  The producer will set price equal to Pc (named as such for a reason that will become clear) and the consumer will buy Qc units.  The producer will capture the producer surplus labeled as PS in dark grey from the unit sales, and the producer will capture the producer surplus labeled as PS in light grey from the fixed up-front fee.

 

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A Two-Part Tariff Illustration

It's also helpful to think through the logic of how a two-part tariff impacts consumers and producers, so let's work through a simple example with only one consumer and one producer in the market.  If we consider the willingness to pay and marginal cost numbers in the figure above, we will see that regular monopoly pricing would result in 4 units being sold at a price of $8.  (Remember that a producer will only produce as long as marginal revenue is at least as large as marginal cost, and the demand curve represents willingness to pay.)  This gives consumer surplus of $3+$2+$1+$0=$6 of consumer surplus and $7+$6+$5+$4=$22 of producer surplus.

 Alternatively, the producer could charge the price where the consumer's willingness to pay equals marginal cost, or $6. In this case, the consumer would purchase 6 units and gain consumer surplus of $5+$4+$3+$2+$1+$0=$15.  The producer would gain $5+$4+$3+$2+$1+$0=$15 in producer surplus from per-unit sales.  The producer could then implement a two-part tariff by charging a $15 up-front fee.  The consumer would look at the situation and decide that it's at least as good to pay the fee and consume 6 units of the good than it would be to avoid the market, leaving the consumer with $0 of consumer surplus and the producer with $30 of producer surplus overall.  (Technically, the consumer would be indifferent between participating and not participating, but this uncertainty could be resolved with no significant change to the outcome by making the flat fee $14.99 rather than $15.)

One thing that is interesting about this model is that it requires the consumer to be aware of how her incentives will change as a result of a lower price- if she didn't anticipate purchasing more as a result of the lower per-unit price, she would not be willing to pay the fixed fee.  This consideration becomes particularly relevant when consumers have a choice between traditional pricing and a two-part tariff, since consumers' estimates of purchasing behavior have direct effects on their willingness to pay the up-front fee.

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The Efficiency of a Two-Part Tariff

One thing to note about a two-part tariff is that, like some forms of price discrimination, it is economically efficient (despite fitting many people's definitions of unfair, of course).  You may have noticed earlier that the quantity sold and per-unit price in the two-part tariff diagram were labeled as Qc and Pc, respectively- this is not random, it is instead meant to highlight that these values are the same as what would exist in a competitive market.  As the above diagram shows, total surplus (i.e. the sum of consumer surplus and producer surplus) is the same in our basic two-part tariff model as it is under perfect competition, it is only the distribution of surplus that is different.  This is possible because the two-part tariff gives the producer a way to recoup (via the fixed fee) the surplus that would be lost by lowering the per-unit price below the regular monopoly price.

Because total surplus is generally greater with a two-part tariff than with regular monopoly pricing, it is possible to design a two-part tariff such that both consumers and producers are better off than they would be under monopoly pricing.  This concept is particularly relevant in situations where, for various reasons, it is prudent or necessary to offer consumers the choice of regular pricing or a two-part tariff.

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More Sophisticated Two-Part Tariff Models

It if, of course, possible to develop more sophisticated two-part tariff models to determine what the optimal fixed fee and per-unit price are in a world with different consumers or consumer groups.  In these cases, there are two main options for the producer to pursue.  First, the producer may choose to sell only to the highest willingness-to-pay customer segments and set the fixed fee at the level of consumer surplus that this group receives (effectively shutting other consumers out of the market) but setting the per-unit price at marginal cost.  Alternatively, the producer may find it more profitable to set the fixed fee at the level of consumer surplus for the lowest willingness-to-pay customer group (therefore keeping all consumer groups in the market) and then setting a price above marginal cost.

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Beggs, Jodi. "All About the Two-Part Tariff." ThoughtCo, Jun. 1, 2016, thoughtco.com/overview-of-the-two-part-tariff-4050243. Beggs, Jodi. (2016, June 1). All About the Two-Part Tariff. Retrieved from https://www.thoughtco.com/overview-of-the-two-part-tariff-4050243 Beggs, Jodi. "All About the Two-Part Tariff." ThoughtCo. https://www.thoughtco.com/overview-of-the-two-part-tariff-4050243 (accessed January 17, 2018).