The paper proves the existence of a subgame perfect Nash
equilibrium in a vertically differentiated duopoly with uncovered market,
for a large set of symmetric and asymmetric distributions of consumers,
including, among others, all logconcave distributions. The proof relies on the
’income share elasticity’ representation of the consumers’ density function,
which ensures the analytical tractability of the firms’ optimality conditions
at a high level of generality. Some illustrative examples of the solution are
offered, in order to assess the impact of distributive shocks on the equilibrium
market configuration.