HSE Center for Market Studies

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• 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

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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.
RD Firm
Intermediate good
Invest
Final good
Utility
Households
Consume
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• Final production
• Perfect competition in the final product market
• Profit of a firm

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Sector of intermediate goods

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

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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

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In our model
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First version of the model
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• 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.

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• 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

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

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• For the first version of the model
• For the second version

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• 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.

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Structure of equilibria in the second version of
the model

• Evidently, increases in E/N
• We are interested in changes in

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• 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

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• is equivalent to
• 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.

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• 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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Thank you