Economic growth and economic development 597

Introduction to Modern Economic Growth
optimal allocation involves a constant growth rate given by
´
1³
gS =
η (1 − β)−1/β βL − ρ
θ

starting with any N (0) > 0.

Proof. Most of the proof is provided in the preceding discussion. Exercise
13.9 asks you to show that the Pareto optimal allocation always involves a constant
growth rate and no transitional dynamics.

Ô

Intuitively, the Pareto optimal growth rate is greater than the equilibrium growth
rate because the social planner values innovation more. The greater social value of
innovations stems from the fact that the social planner is able to use the machines
more intensively after innovation, since the monopoly markup reducing the demand
for machines is absent in the social planner’s allocation. It is interesting to observe
that one of the advantages of the lab equipment model studied in this section is that
the only source of inefficiency in the equilibrium allocation is a pecuniary externality, and results from the monopoly markups (and is thus related to the aggregate
demand externalities discussed in the previous chapter). Other models of endogenous technological progress we will study in this chapter incorporate technological
spillovers and thus generate inefficiencies both because of the pecuniary externality
isolated here and because of the standard technological spillovers.
13.1.6. Policy in Models of Endogenous Technological Progress. The
divergence between the decentralized equilibrium and the socially planned allocation
introduces the possibility of Pareto-improving policy interventions. There are two
natural alternatives to consider:
(1) Subsidies to Research: by subsidizing research, the government can increase

the growth rate of the economy, and this can be turned into a Pareto
improvement if taxation is not distortionary and there can be appropriate
redistribution of resources so that all parties benefit.
(2) Subsidies to Capital Inputs: inefficiencies also arise from the fact that the
decentralized economy is not using as many units of the machines/capital
inputs (because of the monopoly markup); so subsidies to capital inputs
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