Strategic R&D policy under multiproduct duopoly and quality-price competition

ABSTRACT

This paper analyses strategic R&D policy in a third-country trade model where multiproduct firms with different production technologies compete in a vertically differentiated market. I show that the optimal R&D policies for both countries are subsidies when the product market is under price competition.

KEYWORDS:

• Mutiproduct firms
• strategic R&D policy
• subsidies

JEL CLASSIFICATION:

• D43
• F13
• L13

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ According to the study on US firms by Bernard et al. (2007), 57.8% of exporting firms produce multiple products, and 99.6% of export value can be accounted for by multiproduct firms in the year 2000.

² Similarly, Eckel and Neary (2010) name the core competence variety which incurs the lowest marginal cost.

³ Following Park (2001), asymmetry in the R&D cost functions can be adopted in such a way that $I_H(a)=g\times I_L(a)$ with a large enough $g>1$. According to Park (2001), these types of cost functions ensure the uniqueness and stability of the equilibrium.

⁴ The price equilibrium is similar to Eaton 1994. See footnote 6 in Eaton and Schmitt1994.

⁵ In theory, both firms can produce and sell the product with quality $\hat{q}$. For convenience, I assume the low-tech firm supplies this product. Because the profit on the product is zero, our results do not depend on the assumption.

⁶ I have already shown that consumer $t\in [0,\hat{q}]$ will purchase the products produced by the low-tech firm. Notice that $\frac{\mathrm{\partial }u(t,q)}{\mathrm{\partial }q}=t-\alpha q$ is decreasing in $q\in [0,\hat{q}]$ but always positive for any $t\in (\alpha \hat{q},\hat{q}]$. Therefore, consumer $t\in (\alpha \hat{q},\hat{q}]$ will maximize his or her utility by purchasing good with $\hat{q}$.

⁷ The second-order conditions are as follows: $\frac{{\mathrm{\partial }}^2{\mathrm{\Pi }}_H}{\mathrm{\partial }{a}_H^2}=\frac{\mathrm{\partial }\hat{q}}{\mathrm{\partial }{a}_H}-(1-s_H)\frac{{\mathrm{\partial }}^2{I}_H}{\mathrm{\partial }{a}_H^2}<0$.

⁸ $W_i(s_i,s_j)$ is assumed to be concave in $s_i$ to satisfy the second-order conditions. The reader is referred to Park 2001 pp. 974–975 for further detailed derivation.