Case analysis of duopoly

With the increasing contribution of innovative technology to economic development, the theoretical research on innovative technology franchising has made great progress. The main entities holding innovative technologies are divided into manufacturer innovators and independent innovators. Kamien and Tauman (1986) and Katz and Shapiro (1986) studied independent innovators; while Wang (1998) and Wang (2002) studied manufacturer innovators. This article conducts a comparative study on the commission licensing strategy and innovation incentives of technological innovation manufacturers in the competitive market structure of downstream synchronous mobile Cournot. 1. Model and basic concepts

Assume that the suppliers in the upstream raw material market have a symmetrical Cournot duopoly competition structure, consisting of I1 and I2. The downstream industry consists of Manufacturer 1 and Manufacturer 2, which produce homogeneous products, forming a Cournot duopoly competition structure. Downstream manufacturers use raw materials provided by upstream manufacturers to produce final products. It is assumed that there are only raw material costs in the production of final products.

Assume that the market demand function faced by the downstream homogeneous product market is linear and can be expressed by P=a-Q=a-(q1+q2). Among them, P is the price, qi is the product supply of the i-th manufacturer, i=1,2. a is the market size, and a larger a represents a larger market size. The general forms of Cournot's equilibrium output qi and equilibrium profit πi are:

q1(c1,c2)=(a-2c1+c2)/3; q2(c1,c2)=(a-2c2+c1 )/3.

π1(c1,c2)=(a-2c1+c2)2/9; π2(c1,c2)=(a-2c2+c1)2/9.

The so-called innovation incentive refers to the maximum expenditure that manufacturers are willing to spend on winning innovation patents. Specifically, when manufacturer 1 is the successful innovator, define ∏⑴ and ∏⑵ as the equilibrium benefits of manufacturer 1 and manufacturer 2 respectively. Similarly, when manufacturer 2 is the successful innovator, and are defined as the equilibrium benefits of manufacturer 1 and manufacturer 2 respectively. Using Фi (ψ) to represent the innovation incentives of manufacturer i, we have:

2. Unfranchised equilibrium profits and innovation incentives of Cournot manufacturer innovation

The downstream industry consists of manufacturers that produce homogeneous products The Cournot duopoly competition structure consists of manufacturer S1 and manufacturer S2. Initially, the marginal production costs of the two are equal, that is, cS1=cS2=ψw. Then Cournot’s equilibrium output and profit are: q0S1=q0S2=(a-ψw)/3, π0S1=π0S2=(a-ψw)2/9.

Now assume that S1 acquires innovative technology and S2’s technology remains unchanged. Then the marginal production costs of manufacturer S1 and manufacturer S2 without a franchise are respectively: cS1=w, cS2=ψw. The Cournot equilibrium output in equation (1) and the Cournot equilibrium profit in equation (2) become: q*S1=(a-2w+ψw)/3=(a-w)/2; π*S1=(a-2w+ψw)2 /9=(a-w)2/4; q*S2=(a-2ψw+w)/3=0; π*S2=(a-2ψw+w)2/9=0; ifw

The total demand for raw materials by downstream manufacturers is: q*=q*S1+ψq*S2=[a(1+ψ)-2w( 1+ψ2)+2ψw]/3; ifw

3. Cournot manufacturer’s innovative commission franchise strategy

The marginal production costs of manufacturer S1 and manufacturer S2 without a franchise are respectively: cS1=w, cS2=ψw. If the innovator licenses its technology in the form of production commission, then: cS1=w, cS2=ηw, where the commission rate per unit product is r=ρw, η=1+ρ≥1. It can be seen that the cost of manufacturer S1 before and after franchising is equal, while the cost of manufacturer S2 changes from ψw before franchising to etaw after franchising.

The equilibrium output of the two downstream manufacturers are: q*S1=(a-2w+ηw)/3, q*S2=(a-2ηw+w)/3, when w

1. The optimal supply strategy of upstream manufacturers. The upstream manufacturer supplies raw materials to the two downstream manufacturers at the same time. When 1<η<5, the market profits of I1 and I2 are both 4a2/[27(1+η)]; when η≥5, the authorized manufacturer no longer Production. If we only supply raw materials to technological innovation manufacturers, the market profits of I1 and I2 are: a2/18 when η≥2; [a2(η-1)]/2(2η- 1)2. Through comparison, it can be concluded that when 1<η<1.4, supplying raw materials to both downstream manufacturers is more profitable. Therefore, the commission strategy of technological innovation manufacturers is feasible only when 1<η≤1.4.

2. Optimal commission licensing strategy for downstream manufacturers. When 1<η<1.4, the total revenue of downstream technology innovation manufacturers after licensing is: ∏RS1=πRS1+rqRS2=[a2(5η-1)2]/[81(η+1)2]+(η-1 )*{2a/[3（n+1)]}*{[a(5-n)]/[9（n+1)]}=[a2(19n2+26n-29)/81（n+1 )2]. At this time, the franchising strategy of the technological innovation manufacturer is: when 1<ψ≤1.4, η=ψ, and the total revenue of S1 is [a2(19η2+26η-29)/81(η+1)2]; when ψ≥ When 1.4, η=1.4, the total income of S1 is 31a2/324.

Through comparison, the following proposition can be obtained: Proposition 1: Given that the upstream is a duopoly market structure, the optimal strategy of royalties for downstream Cournot manufacturers with the same initial conditions has the following conclusions: 1) When 1≤ When ψ<1.3099 or ψ≥1.6596, technological innovation manufacturers will not grant licenses. 2) When 1.3099≤ψ<1.4, technological innovation manufacturers will license, and η=ψ. 3) When 1.4≤ψ<1.6596, technological innovation manufacturers will license, and η=1.4.

IV. Comparison of innovation incentives of Cournot manufacturers’ technological innovation manufacturers before and after franchising

As known from the previous analysis, the innovator’s innovation incentives ФNi (ψ) without franchising: when 1<ψ< When 2, it is [a2(7ψ2-7ψ+4)2]/[324(ψ2-ψ+1)2]-[a2(4ψ2-7ψ+7)2]/[324(ψ2-ψ+1)2 ]; when ψ≥2, it is a2/9. Under the condition of royalty concession, when 1<ψ<1.3099 or 1.6596<ψ<2, the technological innovation incentive of downstream manufacturers is [a2(7ψ2-7ψ+4)2]/[324(ψ2-ψ+1)2] -[a2(4ψ2-7ψ+7)2]/[324(ψ2-ψ+1)2]; when ψ≥2, the technological innovation incentive is a2/9; when 1.3099<ψ<1.4, the downstream manufacturer’s The innovation incentive is [2a2(ψ2+2ψ-3)]/[9(ψ+1)]; when 1.4<ψ<1.6596, the innovation incentive of downstream manufacturers is 11a2/162.

By comparison, the following proposition can be obtained:

Proposition 2: Given the upstream duopoly market structure, the technological innovation incentives of two downstream Cournot manufacturers with the same initial production technology The following conclusions are drawn: 1) When the scale of innovation is small, that is, 1.3099<ψ<1.441, the royalty strategy increases the innovation incentives of manufacturers; 2) When the scale of innovation is large, that is, 1.441<ψ<1.6596, the royalty strategy makes The innovation incentives of manufacturers decrease; 3) Under other conditions, the innovation incentives of downstream manufacturers remain unchanged.

The research in this article is useful for upstream manufacturers to determine the optimal supply strategy, for downstream innovators to determine technology licensing strategies, for prompting downstream technology inferiors to pay attention to innovation or optimize cooperation with raw material suppliers, and for the government to formulate scientific and technological innovation policies. has great significance. The government can encourage R&D activities of certain enterprises and guide manufacturers that are expected to be more beneficial to society to innovate and achieve success.