Endogenous growth theory

III. R and D

Where are we?

• There seems to be convergence to own steady state, although rate is low

• We expect permanent policy differences to lead to permanent pcGDP differences

• BUT all countries should grow at the same rate• Presumably this is because there is

technological diffusion• However, we still don’t know what this growth

rate is

R and D models

• Technology is produced by an R and D sector

• The sector is profit-motivated• But ideas are non-rival• So how can I make profits out of an

invention?• They can arise from monopoly rents either

naturally (trade secrets, barrier to entry), or artificially (Intellectual property)

The schumpeterian view

• Traditional economics states that monopoly is bad

• But absent monopoly rents there would be no incentives for innovation and entrepreneurship

• Monopoly is bad statically but good dynamically

The hard-core public economics view

• If ideas are a public good, let us subsidize it or provide them publicly

• In principle, we could have zero monopoly power and a subsidy to R and D

• Problem: we can’t define ex-ante what a useful idea is vs. a useless idea

• We need a market test (although for some authors markets only matter for selection)

R and D models of growth

• Horizontal innovation: we introduce new products that are valued by consumers

• There is growth in utility terms if not physical output terms

• Vertical innovation: we introduce new technologies that increase output

• The two can be combined, and quality innovation can also be introduced

What do we need for a model of horizontal innovation?

• A utility function such that– The number of goods can vary– Product variety is appreciated

• An innovation sector that introduces new goods

• Imperfect competition in the goods sector, which creates rents to innovators

The Dixit-Stiglitz paradigm

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Taste for variety

• Because of concavity, consumers gain by having a greater range of goods and consuming proportionally less

• The effect is larger, the more the goods are complements

• If ε<0 the goods are “too complements” and the model does not make sense

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Embodying DS in a growth model(Grossman-Helpman)

• At each date t the R and D sector produces new goods

• The patent owner has monopoly power over the good forever

• The R and D sector has free entry PDV of future monopoly profits = current R and D cost

• The only input in the R and D sector is the labour of researchers

Labour

• Each representative agent is endowed with one unit of labour

• He can work either in the R and D sector or in the production sector

• The wage is the same throughout the economy, equal to wt

Monopolists

• Each monopolist at date t, has a CRTS production function

• Labour is the only input

• Unit productivity

• Takes demand function as given, as well as the aggregate price level (atomistic)

The R and D sector

• One unit of labour produces γ new goods per unit of time

• The PDV of monopoly profits from one additional good is equal to its production cost (free entry)

• The production cost is wt/ γ

Can we get sustained growth?

• The increase in the number of goods is γLR

• For N to grow at a constant rate, so must dN/dt

• But this is impossible if LR is bounded

• So we assume that the productivity of R and D is proportional to the number of goods

The representative consumer problem

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The intra-period allocation of consumption

• Same as in the static Dixit-Stiglitz model

• Income replaced with total expenditure at t, ptCt

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Price normalization

• At any date t, p and w can be multiplied by a small factor and the nominal interest rate adjusted accordingly

• So we need 1 price normalization per period

• We pick pt = 1

• All values are expressed in terms of units of utility

• r = real interest rate in aggregate hedonic consumption units

The monopoly maximization problem

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The R and D problem

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Balanced growth path

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Growth rate determination

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Innovation

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Welfare analysis

• Profits are a small fraction of the social value of innovation not enough people in R and D

• Monopoly markups depress the wage in the production sector too many people in R and D

• The latter, however, is due to the fact that R and D is the only alternative to production work

• Finally, more innovation reduces the cost of future innovations

Transforming this into a model of productivity growth: the Romer

model

• Differentiated goods are now intermediate inputs into production

• “taste for variety” more varieties increase productivity

• Inventing new intermediate goods TFP growth in aggregate production function

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Scale effects

• A key prediction of R and D models is that there are scale effects: dg/dL > 0

• More peoplemore ideasmore growth

• The number of people engaged in R and D has increased substantially

• Yet no sign of accelerating growth

Where do scale effects come from?

• The externality in learning costs prevents growth in ideas from falling

• And this rate goes up with the number of researchers

• In contrast, if this externality were weaker, L would only have a level effect

• But trend growth in population would offset decreasing returns to research just like TFP growth offsets decreasing returns to capital!

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Policy consequences

• Intellectual property, profitability and subsidies no longer have an effect on long-term growth

• These policies only have a level effect

• LT growth only depends on population growth