In the third stage of the game, consumers decide which platform to choose. The pivotal consumer, indexed bypiv, is indifferent, if the utility from reading the newspaper equals the utility from watching news on television:
UNpiv = UTpiv
⇔ pT −pN =kN(θpiv−θN)−kT θT −θpiv
(3)
Since each consumer chooses exactly one platform, all consumers with a preferred style of news coverage θn below the preferred style θpiv of the pivotal consumer choose the newspaper while all consumers withθnaboveθpivchoose the broadcasted news. Solving this equation forθpiv yields the following demands:
θpiv = DN(pN, pT) = kNθN +kTθT −pN +pT kN +kT 1−θpiv = DT (pN, pT) = (1−θN)kN + (1−θT)kT +pN −pT kN +kT . (4)
In the symmetric case, consumers have equal per unit distance costs when choosing either of the media, which implieskN =kT =k, with k ∈(0,1].
In the second stage, both media outlets simultaneously maximize profits (Eq. 1) with respect to their respective prices, which yields the equilibrium prices as functions ofθi. In order to solve the first stage of the game, this result is plugged again into (1) and maximized with respect toθi. Substituting the optimalθi into the reaction functions of the prices from the second stage of the game, and into (4) and (1) yields the following equilibrium, with ∗ indicating the symmetric model:11
p∗N =p∗T =k, D∗N =D∗T = 1 2, θN∗ = k 6c, θ ∗ T = 1− k 6c, Π∗N = Π∗T = k 2 − 1 c k 6 2 −F. (5)
Both media outlets set the same price and share the market equally. The style of news coverage is chosen such that the amount of entertainment in the newspaper is relatively small whereas the amount of entertainment in television is large with the deviations from the extreme points being equal for both media outlets. The following figure illustrates the equilibrium outcome of the symmetric model.
Figure 2.2: Equilibrium of symmetric model, one-sided market
∗ ∗ ∗ ∗, ∗ 0 ∗ 1 ∗
Note: This figure illustrates market shares, prices, and style of coverage of the two media outlets in the symmetric model in a one-sided market. The vertical axes illustrate the prices of the two media outlets, and their respective style of coverage is given by their location on the horizontal line of unit length.
As depicted in Figure 2.2, equilibrium styles of coverage are such that firms locate close to their point of origin at the respective endpoints of the distribution.12 This implies
that, contrary to the standard Hotelling model with linear transportation costs, devi- 12θ
ating by moving towards the center of the distribution does not yield higher profits.13
The reason is that, in contrast to the traditional Hotelling model, the media outlets incur disproportionately increasing costs from relocating (convexity of cost function).
Proposition 1 If consumers’ distance costs become larger (k increases), andk∈(0,1] as well as c≥1,
• prices and profits of both media outlets increase.
• product differentiation in the style dimension decreases. If media outlets’ adjustment costs become larger (c increases),
• the profits of both media outlets increase.
• product differentiation in the style dimension increases.
Proof. See Section A3 of the Appendix.
Dropping the assumptions of c ≥ 1 and k ∈ (0,1] yields the following results: The effect of an increase ofk on profits is positive, as long ask < 9c. Note that there only exists an interior solution as long ask < 3c. Therefore, given that an interior solution exists, the effect of an increase ofk on profits is positive.
The effects of an increase inkis standard to spatial competition models: Askincreases, obtaining the right style of coverage becomes relatively more important for consumers’ choice than low prices, which allows both media outlets to charge higher prices. Both media outlets have an incentive to move towards the center of the distribution in order to increase their market share, which raises their adjustment costs. As the price increase dominates the cost increase, profits are higher. As the adjustment costs c
of media outlets increase (i.e. moving towards the center of the distribution becomes more costly), the marginal costs of a one-unit increase in θi increases whereas the marginal gain remains the same. Hence, firms will locate closer to the margins of the distribution. As the decrease in relocations costs of firms due to moving to the margins is larger than the increase inc, profits increase.
13Non-existence of an equilibrium as in the original Hotelling model with linear utility in the
characteristics space is not a problem in this model, since firms locate sufficiently close to the margins of the distribution, as moving towards the center is costly. Hence, choosing the location of the competitor and serving the entire market decreases the profits, and the equilibrium is stable. See the proof in Section A2 of the Appendix.
In the following sections, I analyze how the equilibrium varies when allowing for asym- metric consumer distance costs. Asymmetric distance costs imply that the costs of a unit of distance are systematically more expensive for consumers when moving in one or the other direction. Intuitively, one would expect lower consumer distance costs to one of the two platforms to be beneficial for the owner of this platform as it should result in higher profits. In the following sections, I explore why this is not necessarily the case.