1. 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

2. Paul Romer. Model of growth with horizontal innovations, Journal of Political Economy, 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

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

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

5. Представления производственной функций в формах Кобба-Дугласа и AK

6. 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

7. In our model

8. First version of the model

10. 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.

12. 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

13. Представление производственной функции в форме AK

14. 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

15. For the first version of the model
For the second version

16. 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.

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

18. 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

19. 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.

20. 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

21. Thank you