Understanding Agreements on TRIPS and Subsidies in Tandem

Abstract

We provide a theoretical framework to explain why governments seek stronger protection of IPRs and allow R&D subsidies through multilateral trade agreements such as the TRIPS Agreement and the Agreement on Subsidies. Our analysis indicates that it is globally optimal to disseminate knowledge without IPR protection and to subsidize inventive firms when issues of IPR protection and R&D subsidies are considered in tandem. R&D subsidies are a means of amending for damages to investors’ incentives by weak IPR protection. In addition, the TRIPS Agreement is understood as a victory of the interests of exporting countries over those of importing countries.

Appendices

Appendices

1.1 A.1 Proof of Proposition 1

Plugging first-order conditions of the non-cooperative Nash setup into those of the global optimum, $W_{s} + W*_{s} + {\text{CS}}_{s} = 0$; $W_{{s*}} + W*_{{s*}} + {\text{CS}}_{{s*}} = 0$; $W_{\theta } + W*_{\theta } + {\text{CS}}_{\theta } = 0$; $W_{{\theta *}} + W*_{{\theta *}} + {\text{CS}}_{{\theta *}} = 0$, we can show that Nash equilibrium policy levels are globally inefficient. Even though $W_{s} = W_{{s*}} = W_{\theta } = W_{{\theta *}} = 0$, the Nash policy set does not satisfy the first-order conditions of global optimization above because $W*_{s} + {\text{CS}}_{s} \ne 0,W_{{s*}} + {\text{CS}}_{{s*}} \ne 0,W*_{\theta } + {\text{CS}}_{\theta } \ne 0$, and $W_{{\theta *}} + {\text{CS}}_{{\theta *}} \ne 0$ .

1.2 A.2 Proof of Proposition 2

As discussed before, the sign of the reaction curve of R&D subsidies, ds/ds* = −W _ss* /W _ss , is identical to the sign of (W _ss* ). One can show $W_{{ss*}} = - bq*_{{z*}} z*_{s} {\left( {q_{z} z_{{s*}} + q_{{z*}} z*_{{s*}} } \right)} - \theta c_{{z*}} z*_{s} {\left( {q_{z} z_{{s*}} + q_{{z*}} z*_{{s*}} } \right)} = {\left( {q_{z} z_{{s*}} + q_{{z*}} z*_{{s*}} } \right)}{\text{ }}z*_{s} {\left( { - bq*_{{z*}} - {\text{ }}\theta c_{{z*}} } \right)}$. Since ${\left( {q_{z} z_{{s*}} + {\text{ }}q_{{z*}} z*_{{s*}} } \right)}$ and $z*_{s}$ are negative, the sign of (W _ss* ) is equal to the sign of ${\left( { - bq*_{{z*}} - \theta c_{{z*}} } \right)}$. Using Eq. 6 of Kang (2006), one can show $- bq*_{{z*}} - \theta c_{{z*}} = {\left( {2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3} \right)}c*_{{z*}} {\left( {1 - 2\theta } \right)}$. Since $c*_{{z*}}$ is negative, we can show W _ss*  > 0 if θ > 1/2.

1.3 A.3 Effects of IPR Protection Levels on R&D Subsidies

Totally differentiating W _s (θ, θ*) with respect to s, s*, and θ, one can form the following equation: ${\left[ {\begin{array}{*{20}c} {{W_{{ss}} }} & {{W_{{ss*}} }} \\ {{W^{*}_{{s*s}} }} & {{W^{*}_{{s*s*}} }} \\ \end{array} } \right]}{\left[ {\begin{array}{*{20}c} {{{{\text{d}}s} \mathord{\left/ {\vphantom {{{\text{d}}s} {{\text{d}}\theta }}} \right. \kern-\nulldelimiterspace} {{\text{d}}\theta }}} \\ {{{{\text{d}}s*} \mathord{\left/ {\vphantom {{{\text{d}}s*} {{\text{d}}\theta }}} \right. \kern-\nulldelimiterspace} {{\text{d}}\theta }}} \\ \end{array} } \right]} = {\left[ {\begin{array}{*{20}c} {{ - W_{{s\theta }} }} \\ {{ - W^{*}_{{s*\theta }} }} \\ \end{array} } \right]}.$ Using this, we can have the Eq. 5. Since $W_{{s\theta }} = G_{{z*\theta }} z*_{s} + G_{{z*}} z*_{{s\theta }} - s{\left( {\theta ,\theta *} \right)}z_{{s\theta }} ,z*_{s} = {G*_{{z*z}} } \mathord{\left/ {\vphantom {{G*_{{z*z}} } B}} \right. \kern-\nulldelimiterspace} B,z*_{{s\theta }} = {G*_{{z*z\theta }} } \mathord{\left/ {\vphantom {{G*_{{z*z\theta }} } B}} \right. \kern-\nulldelimiterspace} B$, and $z_{{s\theta }} = {G*_{{z*z*\theta }} } \mathord{\left/ {\vphantom {{G*_{{z*z*\theta }} } B}} \right. \kern-\nulldelimiterspace} B$, where $B \equiv G_{{zz}} G*_{{z*z*}} - G_{{zz*}} G*_{{z*z}} > 0$, one can show that $W_{{s\theta }}$ is positive if θ > 1/2, but uncertain otherwise. In addition, using the similar method, one can show that $W*_{{s*\theta }} = G*_{{z\theta }} z_{{s*}} + G*_{z} z_{{s*\theta }} - s*{\left( {\theta ,\theta *} \right)}z*_{{s*\theta }}$, and $W*_{{s*\theta }}$ is positive if θ* > 1/2, but uncertain otherwise. Since W _ss and W* _s*s* are negative as the second-order conditions and ${\text{W}}_{{{\text{s}}\theta }}$ and $W*_{{s*\theta }}$ are positive under the weakly enforced IPR regime (θ and θ* > 1/2), ds/dθ and ds*/dθ are positive if (θ, θ*) ≥ 1/2.

1.4 A.4 Global Optimum

Using previous maximization problems for output, R&D investment, and R&D subsidies, one can show $H_{\theta } = - G_{{z*}} {\left( {{G*_{{z*\theta }} } \mathord{\left/ {\vphantom {{G*_{{z*\theta }} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)} + G_{\theta } - {\left( {{G_{{z*}} } \mathord{\left/ {\vphantom {{G_{{z*}} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)}s*_{\theta }$ and $H_{{*\theta }} = - G*_{z} {\left( {{G_{{z\theta }} } \mathord{\left/ {\vphantom {{G_{{z\theta }} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)} + G*_{\theta } - {\left( {{G*_{z} } \mathord{\left/ {\vphantom {{G*_{z} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)}s_{\theta }$. In addition, using a derivative of an integral, we can show the derivative of consumer surplus with respect to IPR protection level: ${\text{CS}}_{\theta } = P\frac{{d{\left( {q + q*} \right)}}} {{d\theta }} - P\frac{{d{\left( {q + q*} \right)}}} {{d\theta }} - {\left( {q + q*} \right)}\frac{{{\text{d}}P}} {{{\text{d}}\theta }} = - {\left( {q + q*} \right)}{\left[ {\frac{{{\text{d}}P}} {{{\text{d}}q}}\frac{{{\text{d}}q}} {{{\text{d}}\theta }} + \frac{{{\text{d}}P}} {{{\text{d}}q*}}\frac{{{\text{d}}q*}} {{{\text{d}}\theta }}} \right]}$. Since (dP/dq) = (dP/dq*) = −b, we can rewrite this as follows: ${\text{CS}}_{\theta } = b{\left( {q + q*} \right)}{\left[ {{\left( {z_{s} s_{\theta } + z_{{s*}} s*_{\theta } + z_{\theta } } \right)}{\left( {q_{z} + q*_{z} } \right)} + {\left( {z*_{s} s_{\theta } + z*_{{s*}} s*_{\theta } + z*_{\theta } } \right)}{\left( {q_{{z*}} + q*_{{z*}} } \right)} + q_{\theta } + q*_{\theta } } \right]}$. It turns out ${\text{CS}}_{\theta }$ is always positive because the third importing country will be better off since weak IPR protection will lead higher subsidies, inducing higher production of the final goods and lower prices. For $H_{\theta }$ and $H*_{\theta }$, one can rewrite these as follows: $H_{\theta } = G_{{z*}} {\left[ {z*_{\theta } - {\left( {{z*_{s} } \mathord{\left/ {\vphantom {{z*_{s} } {z_{s} }}} \right. \kern-\nulldelimiterspace} {z_{s} }} \right)}z_{\theta } } \right]} + G_{\theta } + G_{{z*}} {\left[ {z*_{{s*}} - {\left( {{z*_{s} } \mathord{\left/ {\vphantom {{z*_{s} } {z_{s} }}} \right. \kern-\nulldelimiterspace} {z_{s} }} \right)}z_{{s*}} } \right]}s*_{\theta }$ and $H*_{\theta } = G*_{z} {\left[ {z_{\theta } - {\left( {{z_{{s*}} } \mathord{\left/ {\vphantom {{z_{{s*}} } {z*_{{s*}} }}} \right. \kern-\nulldelimiterspace} {z*_{{s*}} }} \right)}z*_{\theta } } \right]} + G*_{\theta } + G*_{z} {\left[ {z_{s} - {\left( {{z_{{s*}} } \mathord{\left/ {\vphantom {{z_{{s*}} } {z*_{{s*}} }}} \right. \kern-\nulldelimiterspace} {z*_{{s*}} }} \right)}z*_{s} } \right]}s_{\theta }$. Interestingly, the first two terms, $G_{{z*}} {\left[ {z*_{\theta } - {\left( {{z*_{s} } \mathord{\left/ {\vphantom {{z*_{s} } {z_{s} }}} \right. \kern-\nulldelimiterspace} {z_{s} }} \right)}z_{\theta } } \right]} + G_{\theta }$ and $G*_{z} {\left[ {z_{\theta } - {\left( {{z_{{s*}} } \mathord{\left/ {\vphantom {{z_{{s*}} } {z*_{{s*}} }}} \right. \kern-\nulldelimiterspace} {z*_{{s*}} }} \right)}z*_{\theta } } \right]} + G*_{\theta }$, are identical to $W_{\theta }$ and $W*_{\theta }$ in Kang (2006) that we considered both exporting countries simultaneously set IPR protection and R&D subsidies, and the final terms, $G_{{z*}} {\left[ {z*_{{s*}} - {\left( {{z*_{s} } \mathord{\left/ {\vphantom {{z*_{s} } {z_{s} }}} \right. \kern-\nulldelimiterspace} {z_{s} }} \right)}z_{{s*}} } \right]}s*_{\theta }$ and $G*_{z} {\left[ {z_{s} - {\left( {{z_{{s*}} } \mathord{\left/ {\vphantom {{z_{{s*}} } {z*_{{s*}} }}} \right. \kern-\nulldelimiterspace} {z*_{{s*}} }} \right)}z*_{s} } \right]}s_{\theta }$, are new parts representing the sequential policy moves of governments. Checking signs of every component in $H_{\theta }$ and $H*_{\theta }$, one can conclude that $H_{\theta } + H*_{\theta } + {\text{CS}}_{\theta } > 0$ implying the globally optimal IPR protection level is 1. In addition, plugging this result to the optimal subsidy rates that we found in the second stage, we conclude the globally optimal subsidies are positive.

1.5 A.5 Joint Optimum

Using results of Appendix A.4., we can rewrite Eq. 17 as follows: $H_{\theta } + H*_{\theta } + \lambda _{1} - \lambda _{2} = - G_{{z*}} {\left( {{G*_{{z*\theta }} } \mathord{\left/ {\vphantom {{G*_{{z*\theta }} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)} + G_{\theta } - {\left( {{G_{{z*}} } \mathord{\left/ {\vphantom {{G_{{z*}} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)}s*_{\theta } - G*_{z} {\left( {{G_{{z\theta }} } \mathord{\left/ {\vphantom {{G_{{z\theta }} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)} + G*_{\theta } - {\left( {{G*_{z} } \mathord{\left/ {\vphantom {{G*_{z} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)}s_{\theta } + \lambda _{1} - \lambda _{2} = 0$. Given this equation, we analyze every possible case for the optimization problem.

Case 1: θ = 0.

In this case, the slackness condition implies that λ ₁ ≥ 0 and λ ₂ = 0, having $\lambda _{1} = - {\text{ }}H_{\theta } - H*_{\theta }$. Checking signs of the components when θ = 0, we can show that λ ₁ is negative. It violates the slackness condition, which means that it has a contradiction.

Case 2: θ = 1.

In this case, the slackness condition implies that λ ₁ = 0 and λ ₂ ≥ 0, having $\lambda _{2} = H_{\theta } {\text{ }} + H*_{\theta }$. Checking the signs of components when θ = 1, we can show that the sign of λ ₂ is negative. It violates the slackness condition, which means that it has a contradiction.

Case 3: 0 < θ < 1.

In this case, the slackness condition implies that λ ₁ = λ ₂ = 0, having $H_{\theta } + H*_{\theta } = 0$. One can rewrite this condition as follows: $- G_{{z*}} {\left( {{G*_{{z*\theta }} } \mathord{\left/ {\vphantom {{G*_{{z*\theta }} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)} + G_{\theta } - {\left( {{G_{{z*}} } \mathord{\left/ {\vphantom {{G_{{z*}} } {G*_{{z*z*}} }}} \right. \kern-\nulldelimiterspace} {G*_{{z*z*}} }} \right)}s_{{*\theta }} - G*_{z} {\left( {{G_{{z\theta }} } \mathord{\left/ {\vphantom {{G_{{z\theta }} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)} + G_{{*\theta }} - {\left( {{G*_{z} } \mathord{\left/ {\vphantom {{G*_{z} } {G_{{zz}} }}} \right. \kern-\nulldelimiterspace} {G_{{zz}} }} \right)}s_{\theta } = 0$. Since $G*_{{z*\theta }} < 0$, $G*_{{z*z*}} < 0,G_{{zz}} < 0,G_{{z\theta }} > 0$, and $G_{\theta } + G*_{\theta } > 0$, we can conclude that G _z* and $G^{*}_{z}$ must be negative to hold the above equation. According to Proposition 1 in Kang (2006), the optimal IPR policy will be given as 0 < θ ^C < 1/2. In addition, the optimal R&D subsidy is still positive under the strongly enforced IPR regime.