Dynamic Hotelling Duopoly with Linear Transportation Costs

I investigate a spatial duopoly model with linear transportation costs as a differential game where product differentiation is the result of firms’ R&D investments. Two related results obtain, i.e. (i) the steady-state R&D investment (product differentiation) is negatively (positively) related to the cost of capital and time discounting; and (ii) if time discounting and the cost of capital are sufficiently high, the amount of differentiation observed in steady state is sufficiently large to ensure the existence of a unique pure-strategy price equilibrium with prices above marginal cost. The range of time discounting wherein the game produces a price equilibrium in pure strategies is wider under the closed loop solution than under the open loop solution.