Subsidizing cooperative and noncooperative R&D in duopoly with spillovers

Comparing the effect on private R&D investments of allowing firms to cooperate in R&D with that of providing R&D subsidies reveals that in general the latter policy is more effective than the former in promoting R&D activity. Analyzing the implementation of both policies simultaneously reveals that subsidizing cooperative and noncooperative R&D leads to the same market outcome. The preferred R&D-stimulating policy is to subsidize optimally an agreement according to which firms only share the outcomes of their independent research.     

More on subsidizing cooperative and noncooperative R&D in duopoly with spillovers

In an earlier article in this journal I compared two R&D-stimulating policies: allowing for R&D cooperatives and providing direct R&D subsidies (see Hinloopen, 1997:Journal of Economics 66: 151–175). I also considered the implementation of both policies simultaneously. Since then Amir (1998: Discussion Paper 1/1998, Odense University) has shown that the model I used as a starting point (i.e., that of d'Aspremont and Jacquemin, 1988:American Economic Review 78: 1133–1137) is not well-defined with respect to a crucial parameter (the technological spillover) and subsequently proposes an augmentation of the model. Replicating then my original analysis with this augmented model reveals that all results stated before remain valid. In addition I correct a minor error in Hinloopen (1997) related to the comparison of optimal R&D subsidies.     

Equal treatment and socially optimal R&D in duopoly with one‐way spillovers

This paper examines the standard symmetric two‐period R&D model with a deterministic one‐way spillover structure: know‐how flows only from the high R&D firm to the low R&D firm (but not vice versa). Though firms are ex ante identical, one obtains a unique asymmetric equilibrium (pair) in R&D investments, leading to interfirm heterogeneity in the industry. R&D cooperation by means of a joint lab is considered and compared to the non cooperative solution. The main part of the paper provides a second‐best welfare analysis in which we show that the joint lab yields a socially optimal R&D level subject to an equal treatment (of firms) constraint, which also coincides with the noncooperative solution in the absence of spillovers. We also investigate the welfare costs of this equal treatment constraint and find that they can be quite significant.     

Strategic managerial incentives in a two-period Cournot duopoly

This paper examines the nature of optimal managerial incentives in the context of a duopoly marked by competition between the firm's managers in a dynamic production environment. If the marginal cost of production falls moderately over time or remains unchanged, there exists an equilibrium where one owner requires her manager to maximize profit, whereas the rival-owner requires her manager to maximize sales revenue. The profit-maximizing manager turns his firm into a Stackelberg-leader, while the sales-revenue-maximizing manager turns his firm into a Stackelberg-follower. Further, the profit-maximizing manager may generate a larger firm profit relative to the sales-revenue-maximizing manager.     

Commitment to a strategy of uniform pricing in a two-period duopoly with switching costs

This paper studies decisions by firms of whether to attempt “behavior-based” price discrimination in markets with switching costs by using a two-period duopoly model. When both firms commit themselves to a pricing policy and consumers are “sophisticated” and have rational expectations, there is a dominant strategy equilibrium with both firms engaging in uniform pricing. Both firms are better off in the uniform pricing equilibrium, compared with the discriminatory equilibrium.      

R&D subsidies in a duopoly market with outsourcing to the rival firm

This paper investigates the effects of a public uniform R&D subsidy policy in a downstream duopoly market in which a nonintegrated firm, which faces a lower marginal cost, outsources inputs from its vertically integrated rival. The findings show that, in this market structure, such a policy has relevant effects largely differentiated between downstream competitors, as it can significantly modify the relative market shares and profitability of competing firms. Unlike the standard Cournot setting augmented with R&D, results show that the subsidy policy can have different (counterintuitive) effects on R&D investments, output, and profits of the vertically integrated producer and the vertically separated firm, which hold in both cases of exogenous and endogenous (optimal) subsidy. Our findings offer some testable implications and suggest that a subsidy policy in a market with outsourcing to a rival should also consider the different effects of this approach on competitors.     

R&D subsidy and output subsidy in a duopoly: The role of technology spillover and R&D budget

Technology spillover and research and development (R&D) budget are relevant on government subsidies that aim at improving social welfare through enhancing R&D incentives of firms. However, there has not been related literature considering these two factors. To fill this gap, this paper examines the effect of technology spillover and R&D budget on R&D competition of duopolistic firms and government subsidies by constructing a game-theoretic model. We find that while each firm's profit sometimes increases with R&D budget for low coefficient of technology spillover, this profit may decrease with R&D budget for high coefficient of technology spillover due to the intensified R&D competition. We show that when both R&D budget and the coefficient of technology spillover remain high, R&D subsidy leads to higher social welfare than output subsidy and otherwise R&D subsidy results in lower social welfare.     

International spillovers of R&D and marginal social returns

This study analyzes marginal social and private returns of R&D investment through the impact of international spillovers of R&D stocks. We compare the marginal social with marginal private returns using data of 27 OECD and EU countries from 1995 to 2008. We consider two channels of R&D spillovers: embodied in trade flows and disembodied by bilateral technological proximity. We find that marginal social returns on R&D are much larger than the marginal private returns for R&D‐intensive countries, in the embodied spillover channel. We also find that the embodied spillover channel through import flows is more important than the disembodied channel.     

On R&D spillovers, multiple equilibria and indeterminacy

Empirical studies often find significant and positive R&D spillovers across firms. In this note, we incorporate this spillover effect into a scale-invariant quality-ladder model. We find that the modified model features multiple steady states (1) a high-R&D steady state, (2) a low-R&D steady state and (3) a zero-R&D steady state. As for dynamics, when R&D spillovers are small, only the zero-R&D steady state is stable, and it emerges as a no-growth trap. In this case, the economy is subject to sunspot fluctuations around this trap (i.e., local indeterminacy). When R&D spillovers are large, both the zero-R&D and high-R&D steady states are stable and locally indeterminate. In this case, increasing patent breadth may cause the high-R&D steady state to become unstable and the economy to converge to the no-growth trap. Therefore, strengthening patent protection may stifle innovation through the occurrence of a bifurcation.     

Geographical and industrial spillovers in entry decisions across export markets

This article addresses sequential entry decisions in export markets. It focuses on externalities derived from previous export activity in countries close to those for which a potential entry decision is made (geographical spillovers) and externalities derived from previous presence of other firms in the same industry (industrial spillovers). The empirical analysis uses Spanish microdata for the period 2000–2010 in a firm decision model that also integrates country and industry characteristics. The results suggest that these two types of spillovers have a positive effect in explaining entry decisions in new export markets, though both are smaller in magnitude than the effects coming from previous presence in the same specific destination.     

Optimal privatization in a mixed duopoly with consistent conjectures

We show that partially privatizing a public firm alters underlying conjectures, in turn, changing the optimal degree of privatization. The consistent conjectures equilibrium (CCE) generates substantially greater optimal privatization than does any conjecture shared between the firms including the standard Cournot–Nash equilibrium (CNE). Yet, when the private rival is foreign, the CCE generates substantially less privatization than the CNE. The optimal extent of privatization with a domestic rival exceeds that with a foreign rival in the CCE as well as in the CNE.     

Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

Price versus quantity in a mixed duopoly with foreign penetration

We characterize the endogenous competition structure (in prices or quantities) in a differentiated duopoly between a public firm that maximizes domestic welfare and a private firm that can be owned by domestic or foreign investors. The market for which they compete can be domestic or integrated: in the first case Bertrand competition emerges endogenously and in the second case Cournot competition can emerge if the fraction of domestic consumers in the integrated market is low enough. We also determine the optimal degree of foreign penetration showing the optimality of a partial foreign ownership. Finally, we extend the model to increasing marginal cost confirming the robustness of the results.     

Stackelberg leadership in a dynamic duopoly with stochastic capital accumulation

I propose a dynamic duopoly model where firms enter simultaneously but compete hierarchically á la Stackelberg at each instant over time. They accumulate capacity through costly investment, with capital accumulation dynamics being affected by an additive shock the mean and variance of which are known. The main findings are the following. First, the Stackelberg game is uncontrollable by the leader; hence, it is time consistent. Second, the leader invests more than the follower; as a result, in the steady state, the leader’s capacity and profits are larger than the follower’s. Therefore, the present analysis does not confirm Gibrat’s Law, since the individual growth rate is determined by the timing of moves.JEL Classification: C61, C73, D43, D92, L13Financial support within the project The post-entry performance of firms: technology, growth and survival lead by Enrico Santarelli, co-financed by the University of Bologna and MIUR, is gratefully acknowledged. I thank Uwe Cantner, Roberto Cellini, Roberto Golinelli, Helen Louri, Enrico Santarelli, Antonello Scurcu, Peter Thompson, two anonymous referees and the audience at the final workshop of the project (Bologna, November 22-23, 2002) for useful comments and discussion. The usual disclaimer applies.     

Profit-sharing in a unionized cournot duopoly

The main purpose of this paper is to analyze when it is optimal for firms in a unionized duopoly to introduce profit-sharing. It is shown that a firm only prefers a profit-sharing system if its own union does not have “too much” bargaining power, and if the union in the other firm does not have “too much” bargaining power. However, if a firm introduces profit-sharing, the employment increases, and the price in the goods market decreases. Hence, even if it is not in the own interest of a firm to introduce profit-sharing, it may be in the interest of the society.     

R&D spillovers and productivity: Evidence from U.S. manufacturing microdata

This paper deals with the estimation of the impact of technology spillovers on productivity at the firm level. Panel data for American manufacturing firms on sales, physical capital inputs, employment and R&D investments are linked to R&D data by industry. The latter data are used to construct four different sets of `indirect' R&D stocks, representing technology obtained through spillovers. The differences between two distinct kinds of spillovers are stressed. Cointegration analysis is introduced into production function estimation. Spillovers are found to have significant positive effects on productivity, although their magnitudes differ between high-tech, medium-tech and low-tech firms. First version received: April 1997/final version received: April 1999     

Low-quality leadership in a vertically differentiated duopoly with Cournot competition

We model a vertically differentiated duopoly with quantity-setting firms as an extended game in which firms noncooperatively choose the timing of moves at the quality stage, to show that at the subgame, perfect equilibrium sequential play obtains, with the low-quality firm taking the leader’s role.     

Market share dynamics in a duopoly model with word-of-mouth communication

We analyze dynamic price competition in a homogeneous goods duopoly, where consumers exchange information via word-of-mouth communication. A fraction of consumers, who do not learn any new information, remain locked-in at their previous supplier in each period. We analyze Markov perfect equilibria in which firms use mixed pricing strategies. Market share dynamics are driven by the endogenous price dispersion. Depending on the parameters, we obtain different ‘classes’ of dynamics. When firms are impatient, there is a tendency towards equal market shares. When firms are patient, there are extended intervals of market dominance, interrupted by sudden changes in the leadership position.     

Open Innovation in a dynamic Cournot duopoly

In recent years Open Innovation (OI) processes have been receiving growing attention from the empirical and theoretical economic literature, where a debate is taking place on the aspects of complementarity or substitutability between internal R&D and OI spillover. By means of a differential game approach, we analyze the case of substitutability in an OI setup in a Cournot duopoly where knowledge spillovers are endogenously determined via the R&D process. The game produces multiple steady states, allowing for an asymmetric solution where a firm may trade off the R&D investment against information absorption from the rival. The technical analysis and the numerical simulations point out that the firm which commits to a higher level of OI absorption produces a smaller output and enjoys higher profits than its rival.