洪慧敏,辽宁春晚2018宋小宝,女教师升迁笔记
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Before turning to why mixed bundling is sustainable, let us consider why the other product configurations are not. Under pure bundling, the price of the bundle is 16. This price is susceptible to entry by, say, a producer of good 1 at a price of 14. This component price is less than the 16 that group 1 pays for the bundle under mixed bundling, and it is sufficient to cover costs even if only group 1 buys the bundle. A pure component selling, in which the price of each of the two goods is 11, is not sustainable either. Group B pays a total of 22 for the two components, so entry with the bundle at a price of 20 attracts group B and is profitable. When the bundle and just good 1 are offered, the price of the bundle is 17. Entry by a supplier of good 2 at a price of 11 is then profitable. For the same reason, it is not sustainable to offer just the bundle and good 2.
Having seen how entry can prevent a set of offerings from being sustainable, we can now understand why mixed bundling is sustainable in this case. All possible products are offered in mixed bundling, so it is not possible to enter with a new product. We do, however, need to consider whether cutting the price of an existing product (or products) to attract an additional block of customers would be profitable. At these prices, it is not. For example, to sell the bundle at a price that is low enough to attract groups 1 and 2; one would still have to charge 16. But that would not be low enough to attract groups 1 and 2, which can purchase only the good they want under mixed bundling for 14. Similarly, cutting the price of the components to attract group B would not be profitable. If group B purchased the components, the prices would still have to be 11. Group B would then pay 22 for both goods, which is more than the 20 it pays for the bundle under mixed bundling.
There are a number of factors that give rise to mixed bundling in this example. First, there are marginal cost savings from bundling. At the same time, the marginal cost of the bundle exceeds the marginal cost of just one of the components. So, putting fixed costs aside, there would be an advantage to having the separate components available to those who want just one of them. Also, the demand for each of the three possible products is substantial; and, while fixed costs are present, they are not so great as to preclude offering one of the goods.
The results in Table 3 depend, of course, on the assumed values for each of the seven variables in the model. Small changes in each variable would affect prices, but mixed bundling would still be the qualitative outcome. With larger changes, however, the qualitative outcome would change as well. Since mixed bundling means that all three of the possible products are offered, any change would eliminate one or more of the products offered.
For example, consider a reduction in the number of people who want just good 1. The fixed cost of offering good 1 would then have to be spread over a smaller customer base so the price of good 1 would have to increase. When the number of people who want only good 1 is sufficiently small, the price of good 1 would exceed the price of the bundle. Consumers who want just good 1 would then buy the bundle (anSd discard good 2). Good 1 would disappear from the market, leaving good 2 and the bundle as the only products offered. In that case, good 2 is tied to good 1.
Just as a reduction in the number of people who want good 1 causes the price of good 1 to go up, an increase in X1 causes the price to drop. With a sufficiently large increase in the demand for good 1 alone, the price can drop enough that people who want both goods find it cheaper to buy them separately. The bundle disappears from the market. The result is pure components selling, which does not entail tying.
Table 4 shows the change in product offerings that could result from sufficiently large increases and decreases of each of the seven variables in the model. (As we note, in some cases, even a large change will not alter the product offerings.) The first row of the table reports the results described above. The left half of that row says that with a sufficiently large decrease in X1, the set of products offered becomes the bundle and good 2 while good 1 is no longer offered. The right hand half of the first row shows that with a sufficiently large increase in the demand for good 1, the set of products offered are goods 1 and 2 while the bundle is no longer offered.
As Table 4 indicates, there are two cases in which mixed bundling are the qualitative outcome no matter how much the variable change (in the given direction). One of these is a reduction in fixed costs. That result makes intuitive sense. Fixed costs in the model can cause a potential product not to be offered. Given the other assumed values in Table 4, fixed costs of 600 are low enough that all three of the possible products can be offered profitably. A reduction in the fixed cost of a product offering would only reinforce the possibility of providing for each group the product tailored to its particular demand.
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