4.3 Equilibrium of the game
4.3.2 Comparative statics
In this section, I analyze how an increase in the ad effectivenessβt, or an increase in the importance`of type preferences affect equilibrium outcomes. An increase inβt reflects the effects of the advertising market becoming more important to media outlets:
Proposition 2 Starting from the interior equilibrium where |∆3β|< `≤1, a marginal increase in the ad effectiveness βt yields the following effects:
• Consumer prices of a given type decrease in their own type’s ad effectiveness. The effect of an increase in the other type’s ad effectiveness is ambiguous for ∆β ≷0, and depends on the sign of ∆β, as well as on the intensity of type preferences, `.
• Consumer market shares and advertising prices increase in their own type’s ad effectiveness, and decrease in the ad effectiveness of the other type.
Proof. See Section A2 of the Appendix.
In a two-sided markets setup where a firm provides two platforms with one being more valuable to consumers from one side of the market than the other platform, one would expect firms to shift consumer demand from the less profitable to the more profitable platform by unilaterally lowering consumer prices. In this model, however, this is not the case. The first derivatives of consumer prices with respect to the ad effectiveness βtshow that consumer prices do not only decrease in their own type’s ad effectiveness, but may also decrease in the other type’s ad effectiveness.25 More specifically, for the case of offline platforms yielding the higher return on the advertising market than online platforms (∆β > 0), online consumer prices decrease in βOF F, if and only if
` > 2∆3β, i.e. if consumers’ utility from obtaining their preferred type is sufficiently large. If the online ad effectiveness is larger than the offline ad effectiveness (∆β <0), online consumer prices decrease inβOF F on the whole parameter range.26
This is due to the evolution of consumer prices being determined by a direct and two indirect effects. In the following, I briefly sketch the mechanism for the example of
∆β >0.27 IfβOF F increases, offline prices go down due to the direct effect of consumer
25For ∆β = 0, consumer prices of a platform of a given type unambiguously decrease in the ad effectiveness of the other type.
26Analogically, if ∆β >0, offline consumer prices decrease in βON on the whole parameter range.
If ∆β<0, prices decrease inβON, if and only if` > 2∆3β.
27Note that offline prices are always lower than online prices, if ∆β>0.
contacts selling at a higher price to advertisers than consumer contacts on the platform with the lower ad effectiveness. Furthermore, ∆β becomes larger, which implies that the average return per consumer increases. This leads to the online prices decreasing as well, which is captured by the negative indirect effect. If, however, βON increases, there is again a negative direct effect on online prices, but two indirect effects on offline prices, that work in different directions. An increase inβON implies (i) that the average return per consumer increases, which is the negative indirect effect on offline prices, and (ii) ∆β becomes smaller such that it is less important for media outlets which platform to attract consumers to. This results in a positive indirect effect of an increase in βON on offline prices. The positive indirect effect only dominates the evolution of offline prices, if consumers’ type preferences ` are sufficiently small.
However, for the largest part of the parameter range, an increase in the ad effectiveness of any media type has negative effects on consumer prices.28
The reaction of consumer market shares to an increase inβtis such that online market shares increase in βON, and decrease inβOF F, and vice versa for offline market shares.
This is due to the direct (negative) effect dominating the indirect (negative) effect on consumer prices: The incentive to lower consumer prices consists of two components, out of which only one remains if the ad effectiveness of the other media type increases.
Hence, given that βOF F increases, the incentive to lower prices in the offline market is twofold, as the marginal return of advertisements increases, and price competition increases. For the online platform, in contrast, only the competition effect plays a role. This leads to offline platforms making larger price cuts than online platforms, and thus becoming ceteris paribus more attractive to consumers.
With respect to the profits, conventional wisdom would suggest that overall revenues of media outlets increase if advertising space can be sold at a higher price (due to an increase inβt). This, however, is not the case. The reason is that revenues are shifted between the advertising and the consumer market such that the net effect of an in-crease in the profitability of the advertising sector is zero. If advertisers are completely inelastic, media outlets can extract the maximum surplus from them. Therefore, the incentive to attract consumers is sufficiently strong such that, in equilibrium, the gains from advertising revenues are mitigated by the price cuts and the resulting loss on the consumer market.
28This is due to the losses from reducing the price for the intra-marginal units being lower than the losses due to a reduction of the market shares if prices remained higher.
After having analyzed the effects of the advertising market of a type-t-platform becoming more important to media outlets, the following part is devoted to analyzing an increase in the importance ` of type preferences. The higher `, the higher the costs consumers have to bear when switching to their less preferred media type.
One-dimensional models would predict the following: If consumers’ distance costs increase, firms capitalize on these distance costs, and will thus increase prices, which, in turn, will lead to higher profits. Again, this is not the case, because this framework accounts for additional effects that cannot be captured in one-dimensional models.
Proposition 3 Starting from the interior equilibrium where |∆3β|< `≤1 and
∆β ≷ 0, a marginal increase in the importance ` of type preferences for consumer utility (increase in distance costs) yields the following effects:
• Consumer prices increase.
• Market shares as well as advertising prices of the offline platforms increase (de-crease), if ∆β < 0 (∆β > 0). For online platforms, these relations are the reverse.
If ∆β = 0, an increase in ` does not affect the equilibrium results.
Proof. See Section A3 of the Appendix.
As ` increases, the relative importance of low prices for consumers’ decision which platform to choose, diminishes. This allows media outlets to increase the prices on all of their platforms.29 The increase in the importance of type preferences weakens the effect of media outlet i setting different prices on their platforms of a given style. If, for instance, ∆β > 0, the ad effectiveness of offline platforms is higher than the ad effectiveness of online platforms, which implies that media outletisets lower consumer prices in the offline market than in the online market. Since the lower price of the offline platform attracts less consumers as ` increases, the offline market shares decrease, if
∆β >0. Following a similar logic, the market shares of online platforms decrease in `, if ∆β <0. The main reason for the effects of an increase in `to deviate from standard models is that any reaction to an increase in`is subject to the ad effectiveness deviating across media types.
29This argument is similar to one-dimensional spatial competition models where firms increase their prices, if consumers’ demand elasticity decreases.
As profits only depend on the intensityk of style preferences, any effects induced by a change in type preferences or ad effectiveness only lead to redistribution between the online and offline profits, or between the profits from advertising or from consumers, respectively. This, however, is profit-neutral for media outlets. An increase in the distance cost parameter in the style dimension,k, induces the same effect as in standard models: An increase in k leads to higher prices of both firms, as well as to higher profits.30 Hence, a key result of this section is that adding an additional dimension to a spatial competition framework does not lead to higher profits, which contradicts the intuition gained from one-dimensional models.