8.3: Second-Degree Price Discrimination
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Second-degree price discrimination can occur when there are different segments of consumers, for example, high demand customers and low demand customers. However, the firm is unable to accurately assign a customer to a segment prior to the sale. In this case, the seller provides volume discounts, essentially bundle pricing, but offers different amounts in the bundles at different prices. The separate bundles are carefully calibrated to extract the most surplus possible from each market segment. Schemes aimed at second-degree price discrimination are encountered every day (e.g., family-sized packaging).
The problem facing the seller is that he or she cannot assign consumers to one segment or another. Thus, the seller needs to set the bundles so that members of each segment self select into a particular bundle. To successfully implement second-degree price discrimination, the bundles must be designed so that the small bundle is most attractive to the low-demand customers and the large bundle is most attractive to the high-demand customers.
The firm must be careful when setting the volume discount. In fact, for second-degree price discrimination to work, the volume discount must satisfy the following conditions:
- The small bundle must be attractive to the low-demand segment (non-negative surplus).
- The large bundle must be attractive to the high-demand segment (non-negative surplus).
- The small bundle must provide a value to the low-demand segment that is at least as good as the large bundle.
- The large bundle must provide a value to the high-demand segment that is at least as good as the small bundle.
The first two conditions are called participation constraints. They will be satisfied provided the prices charged for the small and large bundles do not exceed the total willingness to pay of low-demand and high-demand customers, respectively. The last two conditions are called self-selection constraints and must be satisfied in order for the low-demand customers to voluntarily choose the small bundle and the high-demand customers to voluntarily choose the large bundle.
To meet these constraints, the firm should choose the size of the small bundle and set its price in order to extract the entire willingness to pay from the low-demand segment. By doing so, the firm gets as much as it can while still satisfying the participation constraint (specifically, the condition 1 above). Consumer surplus for low-demand customers will be zero.
The firm will then choose the size of the large bundle and set its price in order to capture as much of the high-demand customers’ willingness to pay as possible. However, unlike the low-demand segment, the firm will be unable to extract the entire magnitude of willingness to pay from the high-demand customers. Consequently, high-demand customers will have positive consumer surplus. To see why, note that the high-demand segment will derive a strictly positive net benefit from purchasing the small bundle. Consequently, if the firm were to set the large bundle and its price in a fashion that took all of the consumer surplus from high-demand customers, the high-demand customers would simply choose small bundles instead. In other words, the self-selection constraint (condition 4) would not hold. Thus, the firm must design and price the large bundle so that it provides at least as much surplus to high-demand customers as does the small bundle.
An example of a pricing scheme that meets all four conditions is presented in Figure \(\PageIndex{1}\). Panel A shows demand for a low-demand consumer. Panel B shows the demand for a high-demand consumer. The small bundle offered to the low-demand consumer consists of a two units. The low-demand consumer is charged his or her full willingness to pay (the area under the demand curve from 0 to 2 units) of $12. The size and price of the small bundle are determined in exactly the same way as described above under the bundle-pricing scheme.
The important thing is that a high-demand consumer gets positive surplus if they buy this small bundle. In this case, the high-demand consumer gets surplus of $4 from the small bundle. For this reason, the firm cannot charge the high-demand consumer his or her full willingness to pay for the large bundle. If it did, the high-demand consumer would simply buy small bundles in order to get positive surplus. Thus, the firm must set the price of the large bundle so that it provides at least $4 in surplus. The large bundle is set at three units. The large bundle price is set at no more than $17, which induces the high-demand consumer to purchase the large bundle. The per-unit price of the large bundle is $0.33 lower than the per unit price of the small bundle. Thus, the firm is giving the high-demand consumer a volume discount.
This volume discount is not offered because the firm is trying to be nice to its high-demand consumers. The volume discount allows it to make more money. It makes $4 by selling the small bundle. It makes $5 when it sells the large bundle. Thus, the ability to sell extra to the high-demand customers via the large bundle allows the firm to be more profitable. The volume discount described above is discriminatory because it allows the firm to price in a way that exploits differences in demand between the high- and low-demand segments. That said, not all volume discounts are discriminatory. For example, if it is less costly to package an deliver larger lots, volume discounts could represent differences in cost of providing the good in larger lots, not differences in willingness to pay.
Let us take a moment to verify that the example in Figure \(\PageIndex{1}\) meets the participation and self selection constraints.
- The small bundle must be attractive to the low-demand segment (non-negative surplus). This constraint is met in the example. The price of the small bundle just equals the willingness to pay of the low-demand segment. This is the highest the price can be and still have a bundle that is attractive enough for low-demand segment to participate. Surplus is zero but not negative.
- The large bundle must be attractive to the high-demand segment (non-negative surplus). This constraint is met in the above example. High-demand consumers get $4 of surplus from the large bundle.
- The small bundle must provide a value to the low-demand segment that is at least as good as the large bundle. In this example, the small bundle provides no consumer surplus to the low-demand consumer, but the large bundle provides -$4 of surplus.
- The large bundle must provide a value to the high-demand segment that is at least as good as the small bundle. In this example, it does; the large bundle provides surplus of $4 to the high-demand consumer. This is exactly what could have been obtained from the small bundle.