In the recent macro literature the effect of competition has been analyzed by comparing economies with the same market structure but different degrees of substitutability. In this note, we argue that this approach may mingle the price effect of competition with a pure allocation effect. To illustrate the limitations of using the elasticity of substitution as a measure of competition, we present an example in which changes in the elasticity alter equilibrium allocations, but changes in the degree of market power do not. We use a simple static general equilibrium model in which sectors have different productivity. Then, higher substitutability always shifts resources towards the more productive sectors. Instead, changes in the market structure (monopolistic competition versus Bertrand duopoly) do not affect the relative price of consumption goods if the markups are symmetric, implying that the induced changes in competition do not have any price effect on equilibrium allocations.