Research on the Pricing Model about Online Celebrity Economy

According to Insight Report on Chinese Internet Celebrities’ Economic Development by I-research, by the end of April 2018, the number of online celebrities who attract more than 100,000 fans had increased by 51% comparing with 2017's. At the same time, the total number of Chinese online celebrity fans maintained a growing trend, reaching at 588 million people. With growth of the number of online celebrities and fans, the scale of the online celebrity market, as well as the ability of participants in industrial chain to get profit are further enhanced. In the process, advertising becomes the main way for online celebrities to get benefit. On this basis, the MCN platform is an abbreviation of multi-channel network platform. This platform is a bilateral market based on information flow. In this platform, offline manufactures (especially advertisers) can find suitable influencers for the promotion of goods and services. Economic benefits can be achieved through cooperation with content providers, and the entire platform benefits by charging appropriate commissions or dividends; MCN platform enterprises are expressed as network channel providers for e-commerce, advertising enterprises and live broadcast industries and communicate with network consumers to get the profit. In the process, MCN platform cooperates with the online celebrity group to provide business support and training, exchanging for registration fee and profit bonus. On the other hand, the manufactures of goods and services need to improve the power of influence through the Internet, and also depends on the MCN platform to explore suitable online celebrity endorsement. Under the push of two-side market demands, MCN platform become the backbone of commercial chain and become the link between the upstream and downstream industry trading. Therefore, the research on platform transaction pricing under online celebrity economy requires with practical guiding significance. In this paper, online celebrity refers to a group of young entrepreneurs who rely on the publicity channels of the Internet to improve their popularity, and then equips with the temperament of personalizing idols, at the time, gain benefits from network consumers and some platform enterprises. On the other hand, MCN platform enterprises are expressed as network channel providers for e-commerce, advertising enterprises and live broadcast industries and communicate with network consumers to get the profit.

This paper mainly studies the domestic and foreign literature on platform pricing. Due to the characteristics of two-side market, most scholars focus on the pricing behavior of the theory of two-side market.

In terms of foreign literature, Caillaudetc [1] proposed a price strategy aiming at solving the excessive competition of the platform in the industrial chain. Rochet etc. [2] discussed the optimal pricing problem of platform under monopoly platform and competitive platform, and draw the conclusion that the price distribution is proportional to the elasticity of bilateral price demand. Armstrong [3] studied the price decision problem about three kinds of platform competition: monopoly platform, bilaterally owned competition platform and unilateral owned competition platform, which concluded that the equilibrium price is related to the cross network effect, charging method and market structure.

Economides etc. [4] pointed out that the net neutrality of the Internet is analyzed with the price tool of two-sided market theory, and it is found that the net neutrality platform increases the total surplus in a certain range of parameter about cross-network externality compared with private platform, while decreases the total surplus in another parameter range.

In terms of domestic literature in China, Ji [5] studied the registration fee, transaction fee and two-step charge could impact the profit and welfare. Wang etc. [6] analyzed the pricing and profit distribution of the platform and content provider in the new video business operation. Xing etc. [7] discussed that the pricing problem of logistics information platform in the two-side market between the vehicle owner and the good owner, and puts forward a relatively perfect pricing model.

It is assumed that both offline manufactures of goods and services and online celebrities are rational. Only when their respective participation constraints are satisfied, they choose to participate in the platform transaction, that is, the utility function of both sides is greater than 0. For offline manufactures of goods and services, this critical value is xi*{\rm{x}}_{\rm{i}}^* where they decided whether join the platform. On the other hand, for the group of online celebrity, this critical value is yj*{\rm{y}}_{\rm{j}}^* . Assuming that the expected number of active offline manufactures of goods and services and active online celebrities is equal to the actual number of these two groups. The number of offline manufactures of goods and services and the group of online celebrity individually is: (4){nc(probility)=xi*=α1λmns−p1tns(probility)=yj*=v+α2λmnc−p2f\left\{ {\matrix{ {{{\rm{n}}_{\rm{c}}}({\rm{probility}}) = {\rm{x}}_{\rm{i}}^* = {{{\alpha _1}\lambda {\rm{m}}{{\rm{n}}_{\rm{s}}} - {{\rm{p}}_1}} \over {\rm{t}}}} \hfill \cr {{{\rm{n}}_{\rm{s}}}({\rm{probility}}) = {\rm{y}}_{\rm{j}}^* = {{{\rm{v}} + {\alpha _2}\lambda {\rm{m}}{{\rm{n}}_{\rm{c}}} - {{\rm{p}}_2}} \over {\rm{f}}}} \hfill \cr } } \right.

Because of (4), following outcome could be gotten: (5){nc=λmα1(v−p2)−fp1ft−λ2m2α1α2ns=t(v−p2)−λmα2p1ft−λ2m2α1α2\left\{ {\matrix{ {{{\rm{n}}_{\rm{c}}} = {{\lambda {\rm{m}}{\alpha _1}\left( {{\rm{v}} - {{\rm{p}}_2}} \right) - {\rm{f}}{{\rm{p}}_1}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} \hfill \cr {{{\rm{n}}_{\rm{s}}} = {{{\rm{t}}\left( {{\rm{v}} - {{\rm{p}}_2}} \right) - \lambda {\rm{m}}{\alpha _2}{{\rm{p}}_1}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} \hfill \cr } } \right.

The game among MCN platform and offline manufactures of goods and services and online celebrities is a two-stage dynamic game of complete information. The order of the game is that in the 1^st phase, MCN platform take price to offline manufactures of goods and services and the group of online celebrity in bilateral markets at the same time; In the 2^nd phase, both sides decide whether participate the platform. According to the reverse solution method, the number of offline manufactures of goods and services and the group of online celebrity participating into the platform in the 2^nd phase should be calculated firstly, and then the optimal pricing of the platform is solved according to the number of producers and online celebrity groups. The outcome could be calculated by (4) and (5). (6)πp(p1,p2)=p1nc+(p2+θ)ns=p1[λmα1(v−p2)−fp1]+(p2+θ)[t(v−p2)−λmα2p1]ft−λ2m2α1α2{\pi _p}\left( {{p_1},{p_2}} \right) = {p_1}{n_c} + \left( {{p_2} + \theta } \right){n_s} = {{{p_1}\left[ {\lambda m{\alpha _1}\left( {v - {p_2}} \right) - f{p_1}} \right] + \left( {{p_2} + \theta } \right)\left[ {t\left( {v - {p_2}} \right) - \lambda m{\alpha _2}{p_1}} \right]} \over {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}}}

Hypothesis: (1)

The opportunity cost differences between producers and web celebrity groups are large enough, ft − λ²m²α₁α₂ > 0, and the platform profit function is the joint concave function about p₁, p₂.

For the equation (6), the outcome of the first partial derivative about p₁, p₂ equaling to 0 is: (7){∂πp∂p1=−2fp1−λm(α1+α2)p2+λmα1v−λmα2θft−λ2m2α1α2=0∂πp∂p2=−2tp2−λm(α1+α2)p1+tv−tθft−λ2m2α1α2=0\left\{ {\matrix{ {{{\partial {\pi _p}} \over {\partial {p_1}}} = {{ - 2f{p_1} - \lambda m\left( {{\alpha _1} + {\alpha _2}} \right){p_2} + \lambda m{\alpha _1}v - \lambda m{\alpha _2}\theta } \over {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}}} = 0} \hfill \cr {{{\partial {\pi _p}} \over {\partial {p_2}}} = {{ - 2t{p_2} - \lambda m\left( {{\alpha _1} + {\alpha _2}} \right){p_1} + tv - t\theta } \over {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}}} = 0} \hfill \cr } } \right.

According to the hypothesis, all the second partial derivatives about p₁, p₂ are less than 0, which means that Hessian matrix is negative definitely |Δ| > 0. (8)Δ=(−2fft−λ2m2α1α2−λm(α1+α2)ft−λ2m2α1α2−λm(α1+α2)ft−λ2m2α1α2−2tft−λ2m2α1α2)\Delta = \left( {\matrix{ {{{ - 2{\rm{f}}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} & {{{ - \lambda {\rm{m}}\left( {{\alpha _1} + {\alpha _2}} \right)} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} \cr {{{ - \lambda {\rm{m}}\left( {{\alpha _1} + {\alpha _2}} \right)} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} & {{{ - 2{\rm{t}}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} \cr } } \right)

Solving the equation system (7), the following outcome could be obtained: (9){p1*=λmt(α1−α2)(v+θ)4ft−λ2m2(α1+α2)2p2*=2ft(v−θ)−λ2m2(α1+α2)(α1v−α2θ)4ft−λ2m2(α1+α2)2\left\{ {\matrix{ {{\rm{p}}_1^* = {{\lambda {\rm{mt}}\left( {{\alpha _1} - {\alpha _2}} \right)({\rm{v}} + \theta )} \over {4{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{{\left( {{\alpha _1} + {\alpha _2}} \right)}^2}}}} \hfill \cr {{\rm{p}}_2^* = {{2{\rm{ft}}({\rm{v}} - \theta ) - {\lambda ^2}{{\rm{m}}^2}\left( {{\alpha _1} + {\alpha _2}} \right)\left( {{\alpha _1}{\rm{v}} - {\alpha _2}\theta } \right)} \over {4{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{{\left( {{\alpha _1} + {\alpha _2}} \right)}^2}}}} \hfill \cr } } \right.

According to the equation (5), (6) and (9), the outcome could be solved as: (10){nc*=λmt(α1+α2)(v+θ)4ft−λ2m2(α1+α2)2ns*=2t(v+θ)4ft−λ2m2(α1+α2)2\left\{ {\matrix{ {{\rm{n}}_{\rm{c}}^* = {{\lambda {\rm{mt}}\left( {{\alpha _1} + {\alpha _2}} \right)({\rm{v}} + \theta )} \over {4{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{{\left( {{\alpha _1} + {\alpha _2}} \right)}^2}}}} \hfill \cr {{\rm{n}}_{\rm{s}}^* = {{2{\rm{t}}({\rm{v}} + \theta )} \over {4{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{{\left( {{\alpha _1} + {\alpha _2}} \right)}^2}}}} \hfill \cr } } \right.(11)πp*(p1,p2)=p1nc+(p2+θ)ns=t(v+θ)24ft−λ2m2(α1+α2)2\pi _p^*\left( {{p_1},{p_2}} \right) = {p_1}{n_c} + \left( {{p_2} + \theta } \right){n_s} = {{t{{(v + \theta )}^2}} \over {4ft - {\lambda ^2}{m^2}{{\left( {{\alpha _1} + {\alpha _2}} \right)}^2}}}

According to the equation (8), cross network effects, value-added service revenues, and the number of times about offline manufactures of goods and services participating in transactions could affect equilibrium prices. Proposition 2 could be gotten by sensitivity analysis for α₁, α₂, θ, m.

It is assumed that, due to internal or external reasons of the platform, the platform can only charge to one side of bilateral users and be free for another side. The purpose of the platform is to attract the offline manufactures of goods and services or online celebrities, especially in the initial stage of information platform.

Assuming that two platforms k₁, k₂ are located in x = 0 and x = 1 respectively, utility function for manufacturers of offline goods and services in the boundary line is: (37)uck1=mα1λnsk1−p1k1−txi=uck2=mα1λnsk2−p1k2−t(1−xi){\rm{u}}_c^{{{\rm{k}}_1}} = {\rm{m}}{\alpha _1}\lambda {\rm{n}}_{\rm{s}}^{{{\rm{k}}_1}} - {\rm{p}}_1^{{{\rm{k}}_1}} - {\rm{t}}{{\rm{x}}_{\rm{i}}} = {\rm{u}}_{\rm{c}}^{{{\rm{k}}_2}} = {\rm{m}}{\alpha _1}\lambda {\rm{n}}_{\rm{s}}^{{{\rm{k}}_2}} - {\rm{p}}_1^{{{\rm{k}}_2}} - {\rm{t}}\left( {1 - {{\rm{x}}_{\rm{i}}}} \right)

Assuming the whole market is covered, the outcome is expressed as following: (38){nck1=12+λmα1(nsk1−nsk2)−(p1k1−p1k2)2tnck2=1−nck1\left\{ {\matrix{ {n_c^{{k_1}} = {1 \over 2} + {{\lambda m{\alpha _1}\left( {n_s^{{k_1}} - n_s^{{k_2}}} \right) - \left( {p_1^{{k_1}} - p_1^{{k_2}}} \right)} \over {2t}}} \hfill \cr {n_c^{{k_2}} = 1 - n_c^{{k_1}}} \hfill \cr } } \right.

Similarly, if two platforms are located in y = 0 and y = 1, utility function for the group of online celebrity is: (39)usk1=v+α2λmnck1−p2k1−fyj=usk2=v+α2λmnck2−p2k2−f(1−yj){\rm{u}}_{\rm{s}}^{{{\rm{k}}_1}} = {\rm{v}} + {\alpha _2}\lambda {\rm{mn}}_{\rm{c}}^{{{\rm{k}}_1}} - {\rm{p}}_2^{{{\rm{k}}_1}} - {\rm{f}}{{\rm{y}}_{\rm{j}}} = {\rm{u}}_{\rm{s}}^{{{\rm{k}}_2}} = {\rm{v}} + {\alpha _2}\lambda {\rm{mn}}_{\rm{c}}^{{{\rm{k}}_2}} - {\rm{p}}_2^{{{\rm{k}}_2}} - {\rm{f}}\left( {1 - {{\rm{y}}_{\rm{j}}}} \right)

Assuming the whole market is covered, the outcome is expressed as following: (40){nsk1=12+λmα2(nck1−nck2)−(p2k1−p2k2)2fnsk2=1−nsk1\left\{ {\matrix{ {n_s^{{k_1}} = {1 \over 2} + {{\lambda m{\alpha _2}\left( {n_c^{{k_1}} - n_c^{{k_2}}} \right) - \left( {p_2^{{k_1}} - p_2^{{k_2}}} \right)} \over {2f}}} \hfill \cr {n_s^{{k_2}} = 1 - n_s^{{k_1}}} \hfill \cr } } \right.

Solving the equation (38) and (40), the outcome is expressed as following: (41){nck1=12+λmα1(p2k2−p2k1)+f(p1k2−p1k1)2(ft−λ2m2α1α2)nsk1=12+λmα2(p1k2−p1k1)+t(p2k2−p2k1)2(ft−λ2m2α1α2)nck2=12−λmα1(p2k2−p2k1)+f(p1k2−p1k1)2(ft−λ2m2α1α2)nsk2=12−λmα2(p1k2−p1k1)+t(p2k2−p2k1)2(ft−λ2m2α1α2)\left\{ {\matrix{ {n_c^{{k_1}} = {1 \over 2} + {{\lambda m{\alpha _1}\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right) + f\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \hfill \cr {n_s^{{k_1}} = {1 \over 2} + {{\lambda m{\alpha _2}\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right) + t\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \hfill \cr {n_c^{{k_2}} = {1 \over 2} - {{\lambda m{\alpha _1}\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right) + f\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \hfill \cr {n_s^{{k_2}} = {1 \over 2} - {{\lambda m{\alpha _2}\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right) + t\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \hfill \cr } } \right.

Solving the demand function of equation (41) and profit function of equation (3), the profit functions of these two platforms could be gotten. (42){πpk1=p1k1[12+λmα1(p2k2−p2k1)+f(p1k2−p1k1)2(ft−λ2m2α1α2)]+(p2k1+θ)[12+λma2(p1k2−p1k1)+t(p2k2−p2k1)2(12(k1−λ2α1α2)]πpk2=p1k2=p1k2[12+λmα1(p2k1−p2k2)+f(p1k1−p1k2)2(ft−λ2m2α1α2)]+(p2k2+θ)[12+λma2(p1k−p1k2)+t(p2k1−p2k2)2(ft−λ2m2α1α2)]\left\{ {\matrix{ {\pi _p^{{k_1}} = p_1^{{k_1}}\left[ {{1 \over 2} + {{\lambda m{\alpha _1}\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right) + f\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \right] + \left( {p_2^{{k_1}} + \theta } \right)\left[ {{1 \over 2} + {{{\lambda _{m{a_2}}}\left( {p_1^{{k_2}} - p_1^{{k_1}}} \right) + t\left( {p_2^{{k_2}} - p_2^{{k_1}}} \right)} \over {2\left( {{1 \over 2}\left( {{k_1} - {\lambda ^2}{\alpha _1}{\alpha _2}} \right)} \right.}}} \right]} \hfill \cr {\pi _p^{{k_2}} = p_1^{{k_2}} = p_1^{{k_2}}\left[ {{1 \over 2} + {{\lambda m{\alpha _1}\left( {p_2^{{k_1}} - p_2^{{k_2}}} \right) + f\left( {p_1^{{k_1}} - p_1^{{k_2}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \right] + \left( {p_2^{{k_2}} + \theta } \right)\left[ {{1 \over 2} + {{\lambda m{a_2}\left( {p_1^k - p_1^{{k_2}}} \right) + t\left( {p_2^{{k_1}} - p_2^{{k_2}}} \right)} \over {2\left( {ft - {\lambda ^2}{m^2}{\alpha _1}{\alpha _2}} \right)}}} \right]} \hfill \cr } } \right.(43)Δ(hessian)=(−fft−λ2m2α1α2−λm(α1+α2)2(ft−λ2m2α1α2)−λm(α1+α2)2(ft−λ2m2α1α2)−tft−λ2m2α1α2)\Delta ({\rm{hessian}}) = \left( {\matrix{ {{{ - {\rm{f}}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} & {{{ - \lambda {\rm{m}}\left( {{\alpha _1} + {\alpha _2}} \right)} \over {2\left( {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}} \right)}}} \cr {{{ - \lambda {\rm{m}}\left( {{\alpha _1} + {\alpha _2}} \right)} \over {2\left( {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}} \right)}}} & {{{ - {\rm{t}}} \over {{\rm{ft}} - {\lambda ^2}{{\rm{m}}^2}{\alpha _1}{\alpha _2}}}} \cr } } \right)

Because Δ is negative definitely, the maximum of these profit functions could be solved by setting the first derivation equal to 0. (44){p1k1=p1k2=t−λmα2p2k1=p2k2=f−θ−λmα1\left\{ {\matrix{ {{\rm{p}}_1^{{{\rm{k}}_1}} = {\rm{p}}_1^{{{\rm{k}}_2}} = {\rm{t}} - \lambda {\rm{m}}{\alpha _2}} \hfill \cr {{\rm{p}}_2^{{{\rm{k}}_1}} = {\rm{p}}_2^{{{\rm{k}}_2}} = {\rm{f}} - \theta - \lambda {\rm{m}}{\alpha _1}} \hfill \cr } } \right.(45)πpk1=πpk2=f+t−λm(α1+α2)2\pi _p^{{k_1}} = \pi _p^{{k_2}} = {{f + t - \lambda m\left( {{\alpha _1} + {\alpha _2}} \right)} \over 2}

The equation (44) shows that when there are two competing platforms, the optimal pricing of the two MCN platforms for the manufactures of goods and services and the group of online celebrity are equal, and the price increases as the enlarge of degree of differentiation between different offline manufactures of goods and services and between different online celebrities. But the price goes down with the development of platform technology and with improvement of the quantity about offline manufactures of goods and services.

On the other hand, the optimal price decreases as the increase of the cross network effect of both sides. Meanwhile, the price of online celebrities decreases as the increase of value-added service benefits to the platform. It can be seen from (45) that the equilibrium profit of the two platforms is equal, which increases as the rise of the differentiation degree of bilateral users and decreases with the rise of network effect.