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a ,a 20 1 2 M a 1 M a 2 P P a1 a2 10 0 5 10 15 20 t Figure 10: Advertising =11 v 1 ,v 2 1.5 1.0 0.5 P P v1 v2 M v 2 M v 1 0.0 5 10 15 20 t Figure 11: Quality =11 pattern is explained by the fact that the public platform tends to increase the socially beneficial advertising. 5.3 Welfare comparisons In this subsection we compare the social welfare obtained in the three regimes. First, we compare social welfare in the mixed and the zero duopoly. This comparison is illustrated in Figure 13, where in region and in region . According to Figure 13, when advertising is very harmful the zero duopoly is always better than the conventional mixed duopoly, from the social welfare point of view. Otherwise, the conventional mixed duopoly can be socially preferred, as stated in the following proposition. Proposition 1 In the comparisons between the mixed and zero duopoly, we obtain that there exists a critical value of k defined as ∗ (), thatisdecreasing 16 18
x , x 1 2 1.0 0.5 x 1 M x 2 M P P x1 x2 0.0 t 5 10 15 20 Figure 12: Audience shares =11 in t, such that for ≤ ∗ () the zero duopoly is socially better (see region ) and for ≥ ∗ () the mixed duopoly is socially better (region ). Intuitively, the more harmful advertising is, the more likely is that the government commitment to zero advertising is the optimal policy. Additionally, when is small, quality differentiation is more important than horizontal differentiation. Therefore, the smaller is , the more likely is that the optimal policy is the government commitment to zero advertising because this ensures a large audience for the tv-platform providing the highest quality. To see this, note that in the zero duopoly the publicly-owned platform provides the highest quality and obtains a very high audience share (see Figures 1, 2 and 3). Notice that the zero duopoly can be socially better even if advertising is socially desirable (that is, 1) when the degree of horizontal differentiation is low enough. In particular, if 375, wehavethat ∗ () 1 which implies that for some 1. Note that an interesting policy implication of this result is that an advertisingfree public platform (the zero duopoly) tends to be optimal as far as its content is sufficiently similar to the content provided by its private competitor (see the low values for in Figure 13), except in the cases where the social value of advertising is very high. The comparison between the mixed and private duopoly is illustrated in Figure 14, where in regions 1 and 2 , while in region . By comparing the mixed and private duopoly, we find that the private duopoly is optimal when advertising is neutral, i.e. when is near to 1. However, when the negative or positive direct net effect of advertising is large enough, this result can be reversed, as illustrated in Figure 14 and the following proposition. 17 19
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