Trade in Intermediate Goods, Endogenous Growth and Intellectual Property Rights

Abstract

The present chapter develops a product cycle model of North-South trade and integrates the Romer (1990) model and Helpman (1993) model. In this chapter, North innovates the variety of intermediate goods, and South imitates it. Final goods are not traded, while a variety of capital-intensive intermediate goods are traded. The effect of intellectual property rights on economic growth is studied. It is shown that a unique steady-state balanced growth equilibrium may exist, or there may be multiple steady-state equilibria, and tighter intellectual property rights may lead to both a higher and a lower steady-state balanced growth rate depending on the human capital endowment of both the countries.

Appendix

Profit of intermediate good firm of North is

$$ \pi_x^n = p_n^nx_n^n + p_s^nx_s^n-{r_n}(x_n^n + x_s^n). $$

Using Eq. (6.15), we have

$$ \pi_x^n = \alpha {p^n}{x^n}, $$

(6.39)

where ${x^n}$ is given by Eq. (6.2).

From Eq. (6.23), we have

$$ P_A^n = \frac{{\pi_x^n}}{{({r^n} + m)}}. $$

(6.40)

From Eq. (6.15) we know that $p_n^n = p_s^n = {p^n}$. Hence, replacing ${p^n}$ by $p_n^n$ given by Eq. (6.11) in Eq. (6.39), we have

$$ \pi_x^n = \alpha (1-\alpha){P_n}{T_n}{(H_n^Y)^\alpha }{(x_n^n)^{-\alpha }}(x_n^n + x_s^n). $$

(6.41)

Using Eqs. (6.40) and (6.41), we have

$$ P_A^n = \frac{1}{{({r^n} + m)}}\alpha (1-\alpha){P_n}{T_n}{(H_n^Y)^\alpha }{(x_n^n)^{-\alpha }}(x_n^n + x_s^n). $$

(6.42)

Using Eqs. (6.20) and (6.42), we have

$$ w_A^n = P_A^n{\delta_n}A = \frac{1}{{({r^n} + m)}}\alpha (1-\alpha){P_n}{T_n}{(H_n^Y)^\alpha }{(x_n^n)^{-\alpha }}(x_n^n + x_s^n){\delta_n}A. $$

Now, using Eqs. (6.13), (6.14) and (6.18), we have

$$ \frac{{x_n^s}}{{x_n^n}}=(\frac{{{r_s}}}{{{r_n}}}{)^{-\frac{1}{\alpha }}}{(1-\alpha)^{-\frac{1}{\alpha }}}$$

and

$$ \frac{{x_s^n}}{{x_n^n}}=(\frac{{{P_s}{T_s}}}{{{P_n}{T_n}}}{)^{\frac{1}{\alpha }}}\frac{{H_s^Y}}{{H_n^Y}}. $$

Equating $w_A^n$ and $w_Y^n$ given by the Eq. (6.25) and using the expressions of $\frac{{x_n^s}}{{x_n^n}}$ and $\frac{{x_s^n}}{{x_n^n}},$ we have $H_n^Y$ given by Eq. (6.26).