### Working paper

## Input-output linkages and optimal product diversity

We consider a monopolistic competition model with endogenous choice of technology in the closed economy case. The aim is to make comparative statistics of equilibrium and social optimal solutions with respect to "technological innovation"; parameter which influences on costs. Key findings: with the growth of innovation and investment in the production increase; behavior of the equilibrium variables depends only on the elasticity of demand; behavior of the socially optimal variables depends only on the elasticity of utility; behavior of the equilibrium and socially optimal variables does not depend on the properties of the cost as a function of R&D.

The article deals with the theory of monopolistic competition under demand uncertainty. The authors consider the economy with labor immobility consisting of the high-tech sector with monopolistic competition and the standard sector with perfect competition. Preferences between sectors are specified by the Cobb – Douglas production function. It is assumed that companies make output decisions under preferences uncertainty and consumers’ distribution by sectors will be known by the time of realization. It means that firms are informed about consumer demand with accuracy up to a multiplicative uncertainty which is generated by random parameters in the Cobb – Douglas utility function. The paper shows that demand uncertainty leads to consistent growth of prices and wages in high-tech sector in relation to salaries in the second sector. The impact of uncertainty on welfare is ambiguous. In particular, under the known expected value of uncertainty customers derive benefit from exaggerated companies’ expectations about clients’ desire to consume high-tech goods.

We propose a general equilibrium model to study the spatial inequality of consumers and firms within a city. Our mechanics rely on Dixit and Stiglitz monopolistic competition framework. The firms and consumers are continuously distributed across a two-dimensional space, there are iceberg-type costs both for goods shipping and workers commuting (hence firms have variable marginal costs based on their location). Our main interest is in the equilibrium spatial distribution of wealth. We construct a model that is both tractable and general enough to stand the test of real city empirics. We provide some theoretical statements, but mostly the results of numerical simulations with the real Moscow data.

We consider standard monopolistic competition models in the spirit of Dixit and Stiglitz or Melitz with aggregate consumer's preferences defined by two well- known classes of utility functions – the implicitly defined Kimball utility function and the variable elasticity of substitution utility function. These two classes gene- ralize classical constant elasticity of substitution utility function and overcome its lack of flexibility. It is shown in [Dhingra, Morrow, 2012] that for the monopolis- tic competition model with aggregate consumer’s preferences defined by the va- riable elasticity of substitution utility function the laissez-faire equilibrium is effi- cient (i.e. coincides with social welfare state) only for the special case of constant elasticity of substitution utility function. We prove that the constant elasticity of substitution utility function is also the only one which leads to efficient laissez- faire equilibrium in the monopolistic competition model with aggregate consu- mer’s preferences defined by the utility function from the Kimball class. Our main result is following: we find that in both cases a special tax on firms' output may be introduced such that market equilibrium becomes socially efficient. In both cases this tax is calculated up to an arbitrary constant, and some considerations about the «most reasonable» value of this constant are presented.