# The Impact of R&D Subsidy and IPP on Global Supply Chain Networks System—A Technology Spillover Perspective

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

^{1}. Prior to this, the LED industry has witnessed frequent cases of patent infringement lawsuits involving companies such as Seoul Semiconductor, Everlight Electronics, and Epistar

^{2}. These instances of technology spillover not only harm the interests of the original innovators but also significantly affect the decisions of other members within the global supply chain network [8].

## 2. Literature Review

#### 2.1. Research on Technology Spillovers

#### 2.2. Research on R&D Subsidies and IPP

#### 2.3. Supply Chain Network Equilibrium

## 3. Model Construction

#### 3.1. Problem Description

**.**

**Assumption 1:**

**Assumption 2:**

**Assumption 3:**

#### 3.2. Decisions at the Manufacturer Level

#### 3.3. Decisions at the Retailer Level

#### 3.4. Decisions at the Demand Market Level

#### 3.5. Equilibrium Conditions of Global Supply Chain Networks

## 4. Qualitative Properties of Solutions and Solving Algorithm

#### 4.1. Qualitative Properties of Solutions

**Definition 1**

**.**Let K be a non-empty subset in the n-dimensional Euclidean space ${R}^{n}$, and this subset is a given closed convex set. $F\left(X\right)$is a continuous function defined on K and satisfies ${X}^{*}\in K$. The variational inequality problem can be represented as $VI\left(K,F\right)$, which involves finding a vector set ${X}^{*}\in K$ such that for all ${X}^{*}\in K$, the following condition holds:

**Theorem 1**

**.**When the non-empty subset K satisfies the following conditions: ① K is a bounded non-empty closed convex set, and the function $F\left(X\right)$ satisfies the following condition: ② $F\left(X\right)$ is monotone and continuous on the bounded non-empty closed convex set K, then the variational inequality problem has at least one optimal solution.

**Theorem 2**

**.**When the non-empty subset K satisfies the following conditions: ① K is a bounded non-empty closed convex set, and the function $F\left(X\right)$ satisfies the following condition: ② $F\left(X\right)$ is strictly monotone and continuous on set K, if the solution set of the variational inequality is non-empty, then the variational inequality has a unique solution.

**Definition 2**

**.**If the following condition is satisfied:

**Definition 3**

**.**The solution of a Nash equilibrium decision is a set of strategies, where there exists ${X}^{*}\in K$ such that:

#### 4.2. Solving Algorithm

## 5. Example Analysis

_{1}comprises two manufacturers, two retailers, and one demand market, while C

_{2}consists of one manufacturer, one retailer, and one demand market. The products produced by these three manufacturers are perfect substitutes and are distributed to different demand markets through retailers. The structure of this global supply chain network is depicted in Figure 2.

_{1}have higher technological levels compared to the manufacturers in C

_{2}. This discrepancy is reflected in the R&D efficiency of the manufacturers, where ${M}_{{1}_{1}}$ exhibits higher R&D efficiency than ${M}_{{2}_{1}}$, and ${M}_{{2}_{1}}$ has higher R&D efficiency than ${M}_{{1}_{2}}$. These distinctions are captured by the coefficients of R&D investment cost, denoted as ${C}_{{M}_{{1}_{1}}}^{R\&D}\left({\omega}_{{M}_{{1}_{1}}}\right)=150{\omega}_{{M}_{{1}_{1}}}{}^{2}$, ${C}_{{M}_{{2}_{1}}}^{R\&D}\left({\omega}_{{M}_{{2}_{1}}}\right)=180{\omega}_{{M}_{{2}_{1}}}{}^{2},\mathrm{and}{C}_{{M}_{{1}_{2}}}^{RD}\left({\omega}_{{M}_{{1}_{2}}}\right)=200{\omega}_{{M}_{{1}_{2}}}{}^{2}$.

#### 5.1. The Impact of Technology Spillovers on Equilibrium Results

#### 5.2. The Impact of R&D Subsidies on Equilibrium Results

_{1}and C

_{2}no longer increase, and the benefits of the subsidy become outweighed by subsidy expenditure, leading to a decline in social welfare.

_{1}and 0.1 in C

_{2}, and Scenario II with a subsidy rate of 0.1 in C

_{1}and 0.3 in C

_{2}. Other parameters remain unchanged. The equilibrium decisions and social welfare under different scenarios are presented in Table 5.

#### 5.3. The Impact of IPP on Equilibrium Results

_{1}has an IPP intensity of 0.5, while C

_{2}has an intensity of 0.3. In Scenario II, C

_{1}has an intensity of 0.3, while C

_{2}has an intensity of 0.5. Other parameters remain consistent with Case 1. The equilibrium results obtained are shown in Table 7.

_{1}and C

_{1}, as well as social welfare, when compared to Scenario II. Therefore, the analysis indicates that when two countries adopt asymmetric IPP policies, a higher IPP implemented by the high-tech country (C

_{1}) leads to a decrease in the R&D technology level but has positive effects on profits and social welfare.

#### 5.4. Managerial and Policy Implications

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**The data of Figure 3.

Technology Spillover Ratio | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 |
---|---|---|---|---|---|---|---|---|---|---|---|

Total technology level of ${{M}_{1}}_{1}$ | 0.284713 | 0.395751 | 0.513619 | 0.643549 | 0.792005 | 0.949542 | 1.123655 | 1.307413 | 1.503193 | 1.682513 | 1.826896 |

Total technology level of ${{M}_{2}}_{1}$ | 0.209825 | 0.302854 | 0.415493 | 0.54182 | 0.683778 | 0.844096 | 1.012453 | 1.196612 | 1.38832 | 1.591636 | 1.77709 |

Total technology level of ${{M}_{1}}_{2}$ | 0.134563 | 0.230795 | 0.341316 | 0.465337 | 0.605966 | 0.762418 | 0.931832 | 1.115767 | 1.319902 | 1.521798 | 1.712491 |

R&D technology level of ${{M}_{1}}_{1}$ | 0.284713 | 0.37232 | 0.453534 | 0.533824 | 0.61938 | 0.699511 | 0.785242 | 0.866968 | 0.947923 | 0.996641 | 0.998922 |

R&D technology level of ${{M}_{2}}_{1}$ | 0.209825 | 0.274585 | 0.344625 | 0.414354 | 0.484433 | 0.559384 | 0.62706 | 0.697419 | 0.757736 | 0.832751 | 0.900297 |

R&D technology level of ${{M}_{1}}_{2}$ | 0.134563 | 0.198774 | 0.262299 | 0.324532 | 0.387411 | 0.450841 | 0.512378 | 0.573707 | 0.644461 | 0.706804 | 0.772377 |

Profit of ${{M}_{1}}_{1}$ | 20,858.33 | 20,854.01 | 20,849.04 | 20,840.45 | 20,829.99 | 20,820.95 | 20,804.44 | 20,791 | 20,770.67 | 20,758.85 | 20,760.63 |

Profit of ${{M}_{2}}_{1}$ | 20,105.21 | 20,103.13 | 20,099.05 | 20,093.17 | 20,085.51 | 20,075.32 | 20,064.36 | 20,051.34 | 20,038.9 | 20,020.92 | 20,002.8 |

Profit of ${{M}_{1}}_{2}$ | 19,065.9 | 19,065 | 19,061.53 | 19,058.28 | 19,052.67 | 19,042.8 | 19,035.97 | 19,023.29 | 19,011.91 | 18,998.8 | 18,981.05 |

Profit of ${{R}_{1}}_{1}$ | 93,188.07 | 93,226.8 | 93,281.21 | 93,326.42 | 93,388.27 | 93,482.92 | 93,544.03 | 93,653.85 | 93,720.56 | 93,802.43 | 93,892.77 |

Profit of ${{R}_{2}}_{1}$ | 99,430.33 | 99,468.54 | 99,533.63 | 99,569.64 | 99,633.42 | 99,760.77 | 99,804.28 | 99,947.2 | 99,987.33 | 100,066 | 100,177.4 |

Profit of ${{R}_{1}}_{2}$ | 40,895.36 | 40,943.32 | 41,048.85 | 41,089.48 | 41,185.07 | 41,417.12 | 41,465.07 | 41,729.17 | 41,771.95 | 41,898.5 | 42,102.06 |

**Table A2.**The data of Figure 4.

R&D Subsidy | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
---|---|---|---|---|---|---|---|---|

R&D technology level of ${{M}_{1}}_{1}$ | 0.533824 | 0.595142 | 0.666746 | 0.763037 | 0.882394 | 0.996294 | 0.999969 | 0.999978 |

R&D technology level of ${{M}_{2}}_{1}$ | 0.414354 | 0.461444 | 0.51081 | 0.591922 | 0.687 | 0.832147 | 0.999731 | 0.999962 |

R&D technology level of ${{M}_{1}}_{2}$ | 0.324532 | 0.36301 | 0.406867 | 0.462707 | 0.542861 | 0.651124 | 0.813702 | 0.999833 |

Profit of ${C}_{1}$ | 233,829.7 | 233,872.8 | 233,955.5 | 234,024.7 | 234,115.2 | 23,4187.7 | 234,188.2 | 234,189.7 |

Profit of ${C}_{2}$ | 60,147.76 | 60,172.96 | 60,246.74 | 60,288.19 | 60,345.66 | 60,497.36 | 60,498.56 | 60,494.31 |

Social welfare | 29,4986.8 | 29,5061.7 | 295,227.7 | 295,354.6 | 295,427.6 | 295,538 | 295,530.2 | 295,528.1 |

**Table A3.**The data of Figure 5.

IPP Intensity | 0.1 | 0.3 | 0.5 | 0.7 | 0.9 |
---|---|---|---|---|---|

R&D technology level of ${{M}_{1}}_{1}$ | 0.660094 | 0.578195 | 0.490665 | 0.41025 | 0.330202 |

R&D technology level of ${{M}_{2}}_{1}$ | 0.51819 | 0.450435 | 0.387597 | 0.31073 | 0.243261 |

R&D technology level of ${{M}_{1}}_{2}$ | 0.424175 | 0.356746 | 0.293903 | 0.23356 | 0.161734 |

Profit of ${{M}_{1}}_{1}$ | 20,825.18 | 20,835.28 | 20,845.82 | 20,851.64 | 20,857.11 |

Profit of ${{M}_{2}}_{1}$ | 20,081.23 | 20,089.4 | 20,095.38 | 20,101.2 | 20,104.32 |

Profit of ${{M}_{1}}_{2}$ | 19,047.69 | 19,055.66 | 19,059.78 | 19,063.68 | 19,065.04 |

Profit of ${{R}_{1}}_{1}$ | 93,431.95 | 93,357.32 | 93,308.01 | 93,248.66 | 93,215.94 |

Profit of ${{R}_{2}}_{1}$ | 99,688.74 | 99,601.87 | 99,562.05 | 99,491.16 | 99,466.98 |

Profit of ${{R}_{1}}_{2}$ | 41,282.54 | 41,136.07 | 41,087.43 | 40,974.6 | 40,957.55 |

## Notes

1 | https://www.toutiao.com/article/7044481355991908894/?channel=&source=news (accessed on 15 January 2023). |

2 | https://www.toutiao.com/article/6644105947713126926/?channel=&source (accessed on 10 May2023). |

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**Figure 3.**The relationship between technology level, enterprise profit, and technology spillover (The date is shown in Table A1).

**Figure 4.**The impact of symmetric R&D subsidy on equilibrium results (The date is shown in Table A2).

**Figure 5.**The impact of IPP on equilibrium results (The date is shown in Table A3).

Symbols | Explanations | |
---|---|---|

Parameters | $I$ | Collection of manufacturers, $i\in \left\{1,\dots ,I\right\}$ |

$J$ | Collection of retailers,$j\in \left\{1,\dots ,J\right\}$ | |

$K$ | Collection of demand markets $k\in \left\{1,\dots ,K\right\}$ | |

$T$ | Collection of countries $t\in \left\{1,\dots ,T\right\}$ | |

${M}_{{i}_{t}}$ | Manufacturer i located in country t | |

${R}_{{j}_{t}}$ | Retailer j located in country t | |

${S}_{{k}_{t}}$ | Demand markets k located in country t | |

$\mu $ | The technology spillover rate between manufacturers $0\le \mu \le 1$, which can be determined based on relevant data disclosed by companies | |

${b}_{{M}_{{i}_{t}}}$ | Subsidies provided by the country where the manufacturer is located for their R&D investment | |

${\phi}_{{M}_{{i}_{t}}}$ | The IPP intensity of manufacturer ${M}_{{i}_{t}}$, $0\le {\phi}_{{M}_{{i}_{t}}}\le 1$, which can be established in accordance with intellectual property policies enacted by individual countries | |

Decision variables | ${q}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}}$ | Transaction volume between ${M}_{{i}_{t}}$ and ${R}_{{j}_{t}}$ |

${q}_{{M}_{{i}_{t}}}$ | Total transaction volume of ${M}_{{i}_{t}}$ | |

${p}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}}$ | Wholesale price at which ${M}_{{i}_{t}}$ sells products to ${R}_{{j}_{t}}$ | |

${q}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}{S}_{{k}_{t}}}$ | ${R}_{{j}_{t}}$ and ${S}_{{k}_{t}}$ on the transaction volume of ${M}_{{i}_{t}}$’s products | |

${q}_{{M}_{{i}_{t}}}^{{S}_{{k}_{t}}}$ | The total demand for ${M}_{{i}_{t}}$’s products in the demand market ${S}_{{k}_{t}}$ | |

${p}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}{S}_{{k}_{t}}}$ | The retail price of the product ordered by ${R}_{{j}_{t}}$ from ${M}_{{i}_{t}}$ in ${S}_{{k}_{t}}$ | |

${p}_{{M}_{{i}_{t}}}^{{S}_{{k}_{t}}}$ | The price that ${S}_{{k}_{t}}$ is willing to pay for the product of ${M}_{{i}_{t}}$ | |

Functions | ${d}_{{M}_{{i}_{t}}}^{{S}_{{k}_{t}}}\left({p}_{{M}_{{i}_{t}}}^{{S}_{{k}_{t}}},{L}_{{M}_{{i}_{t}}}\right)$ | The demand function of ${M}_{{i}_{t}}$’s products in ${S}_{{k}_{t}}$ |

${C}_{{M}_{{i}_{t}}}\left({q}_{{M}_{{i}_{t}}},{L}_{{M}_{{i}_{t}}}\right)$ | The production cost function of ${M}_{{i}_{t}}$, which is influenced by the production and total technological level | |

${C}_{{M}_{{i}_{t}}}^{R\&D}\left({\omega}_{{M}_{{i}_{t}}}\right)$ | The R&D cost function for ${M}_{{i}_{t}}$ when the R&D technology level is ${\omega}_{{M}_{{i}_{t}}}$ | |

${C}_{{M}_{{i}_{t}}}^{\mathsf{\Omega}}\left({q}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}}\right)$ | The transaction cost function between ${M}_{{i}_{t}}$ and ${R}_{{j}_{t}}$, borne by ${M}_{{i}_{t}}$ | |

${C}_{{R}_{{j}_{t}}}^{H}\left({q}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}}\right)$ | The handle cost function of ${R}_{{j}_{t}}$ for products from $M$, borne by ${R}_{{j}_{t}}$ | |

${C}_{{R}_{{j}_{t}}}^{\Omega}\left({q}_{{M}_{{i}_{t}}}^{{R}_{{j}_{t}}{S}_{{k}_{t}}}\right)$ | The transaction cost function between ${R}_{{j}_{t}}$ and ${S}_{{k}_{t}}$ regarding ${M}_{{i}_{t}}$’s products, borne by ${R}_{{j}_{t}}$ |

Cost Functions | Functional Form |
---|---|

Production cost function | ${C}_{{M}_{{1}_{1}}}\left({q}_{{M}_{{1}_{1}}},{L}_{{M}_{{1}_{1}}}\right)=0.01{q}_{{M}_{{1}_{1}}}{}^{2}+0.01{q}_{{M}_{{1}_{1}}}\left({q}_{{M}_{{2}_{1}}}+{q}_{{M}_{{1}_{2}}}\right)-0.25{L}_{{M}_{{1}_{1}}}{q}_{{M}_{{1}_{1}}}$ ${C}_{{M}_{{2}_{1}}}\left({q}_{{M}_{{2}_{1}}},{L}_{{M}_{{2}_{1}}}\right)=0.01{q}_{{M}_{{2}_{1}}}{}^{2}+0.02{q}_{{M}_{{2}_{1}}}\left({q}_{{M}_{{1}_{1}}}+{q}_{{M}_{{1}_{2}}}\right)-0.25{L}_{{M}_{{2}_{1}}}{q}_{{M}_{{2}_{1}}}$ ${C}_{{M}_{{1}_{2}}}\left({q}_{{M}_{{1}_{2}}},{L}_{{M}_{{1}_{2}}}\right)=0.01{q}_{{M}_{{1}_{2}}}{}^{2}+0.04{q}_{{M}_{{1}_{2}}}\left({q}_{{M}_{{1}_{1}}}+{q}_{{M}_{{2}_{1}}}\right)-0.25{L}_{{M}_{{1}_{2}}}{q}_{{M}_{{1}_{2}}}$ |

Transaction cost function borne by manufacturers | ${C}_{{M}_{{1}_{1}}}^{\Omega}\left({q}_{{M}_{{1}_{1}}}\right)=0.01{q}_{{M}_{{1}_{1}}}{}^{2}+0.1{q}_{{M}_{{1}_{1}}}$ ${C}_{{M}_{{2}_{1}}}^{\Omega}\left({q}_{{M}_{{2}_{1}}}\right)=0.01{q}_{{M}_{{2}_{1}}}{}^{2}+0.1{q}_{{M}_{{2}_{1}}}$ ${C}_{{M}_{{1}_{2}}}^{\Omega}\left({q}_{{M}_{{1}_{2}}}\right)=0.01{q}_{{M}_{{1}_{2}}}{}^{2}+0.1{q}_{{M}_{{1}_{2}}}$ |

Technology R&D cost function | ${C}_{{M}_{{1}_{1}}}^{R\&D}\left({\omega}_{{M}_{{1}_{1}}}\right)=150{\omega}_{{M}_{{1}_{1}}}{}^{2}$ ${C}_{{M}_{{2}_{1}}}^{R\&D}\left({\omega}_{{M}_{{2}_{1}}}\right)=180{\omega}_{{M}_{{2}_{1}}}{}^{2}$ ${C}_{{M}_{{1}_{2}}}^{R\&D}\left({\omega}_{{M}_{{1}_{2}}}\right)=200{\omega}_{{M}_{{1}_{2}}}{}^{2}$ |

Transaction cost function between manufacturers and retailers borne by retailers | ${C}_{{R}_{{1}_{1}}}^{H}\left({q}_{{R}_{{1}_{1}}}\right)=0.1{q}_{{R}_{{1}_{1}}}{}^{2}$ ${C}_{{R}_{{2}_{1}}}^{H}\left({q}_{{R}_{{2}_{1}}}\right)=0.1{q}_{{R}_{{2}_{1}}}{}^{2}$ ${C}_{{R}_{{1}_{2}}}^{H}\left({q}_{{R}_{{1}_{2}}}\right)=0.1{q}_{{R}_{{1}_{2}}}{}^{2}$ |

Transaction cost function between retailers and markets | ${C}_{{R}_{{1}_{1}}}^{\Omega}\left({q}_{{R}_{{1}_{1}}}\right)=0.05{q}_{{R}_{{1}_{1}}}{}^{2}+0.5{q}_{{R}_{{1}_{1}}}$ ${C}_{{R}_{{2}_{1}}}^{\Omega}\left({q}_{{R}_{{2}_{1}}}\right)=0.05{q}_{{R}_{{2}_{1}}}{}^{2}+0.5{q}_{{R}_{{2}_{1}}}$ ${C}_{{R}_{{1}_{2}}}^{\Omega}\left({q}_{{R}_{{1}_{2}}}\right)=0.05{q}_{{R}_{{1}_{2}}}{}^{2}+0.5{q}_{{R}_{{1}_{2}}}$ |

$\mathit{\mu}$ | $0$ | $0.1$ | $0.2$ | $0.3$ | $0.4$ | $0.5$ | $0.6$ | $0.7$ | $0.8$ | $0.9$ | $1$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Wholesale price | ${p}_{{M}_{{1}_{1}}}$ | 60.68 | 60.66 | 60.64 | 60.61 | 60.58 | 60.55 | 60.51 | 60.47 | 60.43 | 60.39 | 60.35 |

${p}_{{M}_{{2}_{1}}}$ | 80.12 | 80.10 | 80.08 | 80.06 | 80.03 | 80.00 | 79.96 | 79.93 | 79.88 | 79.84 | 79.80 | |

${p}_{{M}_{{1}_{1}}}$ | 120.10 | 120.09 | 120.07 | 120.05 | 120.03 | 120.00 | 119.97 | 119.93 | 119.89 | 119.85 | 119.81 | |

Retail price | ${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{1}}}$ | 322.47 | 322.50 | 322.55 | 322.59 | 322.64 | 322.73 | 322.78 | 322.88 | 322.94 | 323.00 | 323.08 |

${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{2}}}$ | 327.26 | 327.30 | 327.35 | 327.38 | 327.43 | 327.55 | 327.58 | 327.72 | 327.74 | 327.81 | 327.91 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{1}}}$ | 332.93 | 332.96 | 333.03 | 333.05 | 333.10 | 333.24 | 333.26 | 333.41 | 333.42 | 333.48 | 333.59 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{2}}}$ | 329.23 | 329.26 | 329.32 | 329.35 | 329.40 | 329.52 | 329.55 | 329.68 | 329.71 | 329.77 | 329.87 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{1}}}$ | 338.38 | 338.41 | 338.48 | 338.50 | 338.56 | 338.69 | 338.71 | 338.85 | 338.87 | 338.93 | 339.04 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{2}}}$ | 341.31 | 341.35 | 341.42 | 341.43 | 341.49 | 341.66 | 341.65 | 341.84 | 341.82 | 341.87 | 341.99 | |

Prduction | ${q}_{{M}_{{1}_{1}}}$ | 742.87 | 742.94 | 742.99 | 743.09 | 743.16 | 743.16 | 743.27 | 743.27 | 743.41 | 743.50 | 743.50 |

${q}_{{M}_{{2}_{1}}}$ | 757.54 | 757.61 | 757.70 | 757.74 | 757.81 | 757.95 | 757.97 | 758.12 | 758.11 | 758.15 | 758.23 | |

${q}_{{M}_{{1}_{2}}}$ | 1500.41 | 1500.55 | 1500.69 | 1500.83 | 1500.97 | 1501.11 | 1501.25 | 1501.39 | 1501.52 | 1501.64 | 1501.73 | |

SW | 294,552.25 | 294,669.95 | 294,882.43 | 294,986.78 | 295,184.38 | 295,609.05 | 295,727.67 | 296,205.11 | 296,311.03 | 296,555.41 | 296,926.53 |

${\mathit{b}}_{{\mathit{M}}_{{\mathit{i}}_{\mathit{t}}}}$ | 0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | |
---|---|---|---|---|---|---|---|---|

Wholesale price | ${p}_{{M}_{{1}_{1}}}$ | 60.61 | 60.60 | 60.58 | 60.56 | 60.53 | 60.50 | 60.49 |

${p}_{{M}_{{2}_{1}}}$ | 80.06 | 80.05 | 80.04 | 80.02 | 80.00 | 79.97 | 79.93 | |

${p}_{{M}_{{1}_{1}}}$ | 120.05 | 120.04 | 120.04 | 120.03 | 120.02 | 120.00 | 119.97 | |

Retail price | ${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{1}}}$ | 322.59 | 322.61 | 322.65 | 322.69 | 322.73 | 322.80 | 322.80 |

${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{2}}}$ | 327.38 | 327.40 | 327.44 | 327.47 | 327.51 | 327.59 | 327.61 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{1}}}$ | 333.05 | 333.07 | 333.11 | 333.14 | 333.18 | 333.28 | 333.28 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{2}}}$ | 329.35 | 329.37 | 329.41 | 329.45 | 329.49 | 329.58 | 329.58 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{1}}}$ | 338.50 | 338.52 | 338.57 | 338.61 | 338.65 | 338.75 | 338.77 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{2}}}$ | 341.43 | 341.45 | 341.51 | 341.54 | 341.57 | 341.69 | 341.69 | |

Production | ${q}_{{M}_{{1}_{1}}}$ | 743.09 | 743.14 | 743.17 | 743.25 | 743.35 | 743.42 | 743.56 |

${q}_{{M}_{{2}_{1}}}$ | 757.74 | 757.78 | 757.86 | 757.93 | 758.02 | 758.18 | 758.26 | |

${q}_{{M}_{{1}_{2}}}$ | 1500.83 | 1500.92 | 1501.03 | 1501.18 | 1501.37 | 1501.61 | 1501.82 |

Scenario I | Scenario II | ||
---|---|---|---|

R&D technology level | ${\omega}_{{M}_{{1}_{1}}}$ | 0.7625 | 0.5966 |

${\omega}_{{M}_{{2}_{1}}}$ | 0.5898 | 0.4618 | |

${\omega}_{{M}_{{1}_{2}}}$ | 0.3627 | 0.4604 | |

Wholesale price | ${p}_{{M}_{{1}_{1}}}$ | 60.5594 | 60.5946 |

${p}_{{M}_{{2}_{1}}}$ | 80.0219 | 80.0479 | |

${p}_{{M}_{{1}_{2}}}$ | 120.0481 | 120.0244 | |

Retail price | ${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{1}}}$ | 322.6799 | 322.6169 |

${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{2}}}$ | 327.4532 | 327.4127 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{1}}}$ | 333.1125 | 333.0934 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{2}}}$ | 329.4376 | 329.3813 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{1}}}$ | 338.6066 | 338.5242 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{2}}}$ | 341.5091 | 341.4774 | |

Production | ${q}_{{M}_{{1}_{1}}}$ | 743.2241 | 743.1574 |

${q}_{{M}_{{2}_{1}}}$ | 757.8880 | 757.8276 | |

${q}_{{M}_{{1}_{2}}}$ | 1501.1121 | 1500.9849 | |

Manufacturer’s profit | ${\pi}_{{M}_{{1}_{1}}}$ | 20,832.8702 | 20,839.2603 |

${\pi}_{{M}_{{2}_{1}}}$ | 20,089.6397 | 20,092.0412 | |

${\pi}_{{M}_{{1}_{2}}}$ | 19,058.6739 | 19,055.7499 | |

Retailer’s profit | ${\widehat{\pi}}_{{R}_{{1}_{1}}}$ | 93,415.1350 | 93,360.8373 |

${\widehat{\pi}}_{{R}_{{2}_{1}}}$ | 99,651.7727 | 99,614.8874 | |

${\widehat{\pi}}_{{R}_{{1}_{2}}}$ | 41,222.2231 | 41,126.1401 | |

Social welfare | SW | 295,322.0579 | 295,094.8394 |

Firms’ profits within C_{1} | 233,989.4175 | 233,907.0263 | |

Firms’ profits within C_{2} | 60,280.8970 | 60,181.8900 |

The Strength of IPP | $\mathit{\phi}=0.1$ | $\mathit{\phi}=0.3$ | $\mathit{\phi}=0.5$ | $\mathit{\phi}=0.7$ | $\mathit{\phi}=0.9$ | |
---|---|---|---|---|---|---|

Wholesale price | ${p}_{{M}_{{1}_{1}}}$ | 60.56 | 60.59 | 60.63 | 60.65 | 60.67 |

${p}_{{M}_{{2}_{1}}}$ | 80.02 | 80.05 | 80.07 | 80.09 | 80.11 | |

${p}_{{M}_{{1}_{2}}}$ | 120.01 | 120.04 | 120.06 | 120.08 | 120.09 | |

Retail price | ${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{1}}}$ | 322.68 | 322.62 | 322.58 | 322.52 | 322.49 |

${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{2}}}$ | 327.49 | 327.41 | 327.38 | 327.31 | 327.30 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{1}}}$ | 333.16 | 333.08 | 333.05 | 332.98 | 332.97 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{2}}}$ | 329.45 | 329.38 | 329.35 | 329.28 | 329.26 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{1}}}$ | 338.61 | 338.53 | 338.50 | 338.43 | 338.42 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{2}}}$ | 341.55 | 341.46 | 341.44 | 341.37 | 341.36 | |

Production | ${q}_{{M}_{{1}_{1}}}$ | 743.17 | 743.12 | 743.03 | 742.98 | 742.88 |

${q}_{{M}_{{2}_{1}}}$ | 757.87 | 757.78 | 757.73 | 757.64 | 757.59 | |

${q}_{{M}_{{1}_{2}}}$ | 1501.04 | 1500.90 | 1500.76 | 1500.62 | 1500.48 | |

Manufacturer’s profit | ${\pi}_{{M}_{{1}_{1}}}$ | 20,825.18 | 20,835.28 | 20,845.82 | 20,851.64 | 20,857.11 |

${\pi}_{{M}_{{2}_{1}}}$ | 20,081.23 | 20,089.40 | 20,095.38 | 20,101.20 | 20,104.32 | |

${\pi}_{{M}_{{1}_{2}}}$ | 19,047.69 | 19,055.66 | 19,059.78 | 19,063.68 | 19,065.04 | |

Retailer’s profit | ${\widehat{\pi}}_{{R}_{{1}_{1}}}$ | 93,431.95 | 93,357.32 | 93,308.01 | 93,248.66 | 93,215.94 |

${\widehat{\pi}}_{{R}_{{2}_{1}}}$ | 99,688.74 | 99,601.87 | 99,562.05 | 99,491.16 | 99,466.98 | |

${\widehat{\pi}}_{{R}_{{1}_{2}}}$ | 41,282.54 | 41,136.07 | 41,087.43 | 40,974.60 | 40,957.55 |

Scenario I | Scenario II | ||
---|---|---|---|

R&D technology level | ${\omega}_{{M}_{{1}_{1}}}$ | 0.5329 | 0.5395 |

${\omega}_{{M}_{{2}_{1}}}$ | 0.4160 | 0.4164 | |

${\omega}_{{M}_{{1}_{2}}}$ | 0.2952 | 0.3573 | |

Wholesale price | ${p}_{{M}_{{1}_{1}}}$ | 60.6171 | 60.6037 |

${p}_{{M}_{{2}_{1}}}$ | 80.0641 | 80.0530 | |

${p}_{{M}_{{1}_{2}}}$ | 120.0492 | 120.0489 | |

Retail price | ${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{1}}}$ | 322.6002 | 322.6003 |

${p}_{{M}_{{1}_{1}}}^{{S}_{{1}_{2}}}$ | 327.4134 | 327.3882 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{1}}}$ | 333.0985 | 333.0501 | |

${p}_{{M}_{{2}_{1}}}^{{S}_{{1}_{2}}}$ | 329.3784 | 329.3575 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{1}}}$ | 338.5359 | 338.5151 | |

${p}_{{M}_{{1}_{2}}}^{{S}_{{1}_{2}}}$ | 341.4999 | 341.4381 | |

Production | ${q}_{{M}_{{1}_{1}}}$ | 743.0240 | 743.1026 |

${q}_{{M}_{{2}_{1}}}$ | 757.7829 | 757.7489 | |

${q}_{{M}_{{1}_{2}}}$ | 1500.8068 | 1500.8515 | |

Manufacturer’s profit | ${\pi}_{{M}_{{1}_{1}}}$ | 20,842.2260 | 20,839.7405 |

${\pi}_{{M}_{{2}_{1}}}$ | 20,092.5104 | 20,093.5001 | |

${\pi}_{{M}_{{1}_{2}}}$ | 19,059.2996 | 19,055.0483 | |

Retailer’s profit | ${\widehat{\pi}}_{{R}_{{1}_{1}}}$ | 93,335.2745 | 93,337.1849 |

${\widehat{\pi}}_{{R}_{{2}_{1}}}$ | 99,602.5924 | 99,576.1128 | |

${\widehat{\pi}}_{{R}_{{1}_{2}}}$ | 41,154.9177 | 41,104.9414 | |

Social welfare | SW | 295,095.8970 | 295,015.9036 |

Firms’ profits within C_{1} | 233,872.6032 | 233,846.5383 | |

Firms’ profits within C_{2} | 60,214.2174 | 60,159.9896 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Q.; Zhou, X.; Li, D.; Liu, A.; Lev, B.
The Impact of R&D Subsidy and IPP on Global Supply Chain Networks System—A Technology Spillover Perspective. *Systems* **2023**, *11*, 460.
https://doi.org/10.3390/systems11090460

**AMA Style**

Zhu Q, Zhou X, Li D, Liu A, Lev B.
The Impact of R&D Subsidy and IPP on Global Supply Chain Networks System—A Technology Spillover Perspective. *Systems*. 2023; 11(9):460.
https://doi.org/10.3390/systems11090460

**Chicago/Turabian Style**

Zhu, Qiuyun, Xiaoyang Zhou, Die Li, Aijun Liu, and Benjamin Lev.
2023. "The Impact of R&D Subsidy and IPP on Global Supply Chain Networks System—A Technology Spillover Perspective" *Systems* 11, no. 9: 460.
https://doi.org/10.3390/systems11090460