Increasing Compatibility Among Three Firms

Effect of Increased Compatibility

"Network Externalities" proves the following Proposition: "When compatibility costs are purely fixed costs, any move to complete compatibility that raises industry profits is socially beneficial." In other words, if any two firm networks join to increase their profits, the change is good for the entire society. Intuitively, this makes sense, since the consumers are happier when the products they choose are more compatible with each other, and the firms increase their total profits when they can attract more consumers. Here is how this relates to the results obtained in the previous slides.

In any Fulfilled Expectations Cournot Equilibrium, the industry profit equals the sum of the squares of the firm outputs. Furthermore, the total consumer surplus in such an equilibrium is equal to half the square of the total industry output. Finally, the social benefit of a FECE can be calculated by adding the total industry profits and the consumer surplus.

For instance, in case of the three-firm symmetric equilibrium under full incompatibility (choice "C" in Slide 1 of this topic), the outputs of all three firms are 7.07. The industry profits are then:

`industry profits = 3 * 7.072 = 149.95`
On the other hand, the consumer surplus is:
`consumer surplus = (3 * 7.07)2/2 = 224.93`
This means that the total social benefit is:
`social benefit = industry profits + consumer surplus = 149.95 + 224.93 = 375.88`

Similarly, we can compute these numbers for the network monopoly (equilibrium "B" in Slide 2 of this topic) under partial compatibility:

`industry profits = 2 * 13.732 = 257.65`
`consumer surplus = (2 * 13.73)2/2 = 377.03`
`social benefit = industry profits + consumer surplus = 634.68`

Now we can check that these two equilibria satisfy the proposition above. A switch from the first to the second is towards more compatibility. Furthermore, the industry profits are higher in the second case. Thus, the proposition holds in this case, since the total social benefit increases as well.

The same pattern continues as we move from any partial compatibility equilibrium to the fully-compatible case.

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