“Input Complementarity and Substitutability in Imperfectly Competitive Multi-Tier Supply Chains”
Abstract: We study a two-tier supply chain in which oligopolistic downstream firms need complementary inputs for their production processes. Each of these complementary inputs is offered by a host of suppliers that imperfectly compete against each other. Hence, input categories (e.g., fabric and dye) complement each other, whereas there are substitute varieties within each category (e.g., different types of fabric), thus presenting a theoretical framework that opens up avenues for flexible structural estimation of rich enough supply chains. We use this framework to examine the equilibrium relationship between downstream firms’ marginal costs and the (imperfect) complementarity and substitution patterns exhibited by their inputs. We find that collusion among suppliers results in greater marginal costs for downstream firms than competition if and only if the number of suppliers within each input category is high enough. We also find that integration of a supplier into the production of substitute varieties within an input category always results in greater downstream firms’ marginal costs. By contrast, integration of a supplier into the production of complementary inputs results in greater downstream firms’ marginal costs if and only if there is sufficient competition within each input category.
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