HSE Center for Market Studies and Spatial Economics Vladimir Matveenko Structure of Equilibria in a Sector of Monopolistic Competition in an Endogenous Growth Model with Horizontal Innovations

Paul Romer. Model of growth with horizontal innovations, Journal of Political Economy, 1990. R. Barro and X.Sala-i-Martin. Economic growth. 2nd ed. MIT Press, 2004. R&D Firm Intermediate good Invest Final good Utility Households Consume

Final production Perfect competition in the final product market Profit of a firm

Sector of intermediate goods Profit of a monopolist Monopolist price Demand A mechanism of innovations is based on household saving.

Представления производственной функций в формах Кобба-Дугласа и AK

Equilibrium growth rate of the economy The interest rate and, hence, the growth rate change in the same direction as the profit of the monopolist

In our model

First version of the model

Second version of the model Expenditures E for purchasing intermediate goods are given, in particular, it can be a fixed part of input of the final product. The final output sector firm defines the demand for labor and the demand for each intermediate good. s.t.

Sector of intermediate goods Profit of a monopolist Condition of the strict concavity of the profit function is where Condition of equilibrium This equation always has solution if

Представление производственной функции в форме AK

Proof: The condition of the equilibrium implies Markup of the firm j can be defined as or as PROPOSITION 1. In equilibrium Proof: The condition of the equilibrium implies

For the first version of the model For the second version

PROPOSITION 2. If the elasticities of g and f are both increasing (or both decreasing) and if then in the first version of the model an increase in marginal costs leads to an increase of the equilibrium output and a decrease of the labor in a firm in the sector of monopolistic competition.

Structure of equilibria in the second version of the model Evidently, increases in E/N We are interested in changes in

PROPOSITION 3. The output increases in the clockwise direction if and in the counterclockwise direction if The inequality follows from In particular, the clockwise increase takes place under

is equivalent to PROPOSITION 4. If then the output and the price both increase in the clockwise direction; if then the output increases clockwise and the price increases counterclockwise; if then the output increases counterclockwise and the price increases clockwise.

PROPOSITION 4. If then the output , the price and the profit of the monopolist increase in the clockwise direction; if then the output and the profit of the monopolist increase clockwise and the price increases counterclockwise; if then the output increases clockwise, and the price and the profit increase counterclockwise; if then the output increases counterclockwise and the price and the profit increase clockwise

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