Logarithmic quasi-homothetic preferences

We study a class of symmetric, quasi-homothetic preferences that result in demands logarithmic in own prices when these have a negligible impact on aggregate price indices (as in monopolistic competition models). Thus marginal revenues are computationally friendly, and decreasing whenever demands are elastic. Preferences can be represented either by an additive negative exponential direct utility function, or by an expenditure function which depends on two price indices. A parameter accounts for any number of commodities. Another one affects the relevant demand elasticities, which are not constant. Commodities can be either substitutes or complements according to the size of consumption.