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Introduction to Modern Economic Growth Assuming that there is positive growth, free entry implies ηV ν, t = 1.. This establishes: Proposition 13.2.. In the above-described lab equipment

Introduction to Modern Economic Growth Assuming that there is positive growth, free entry implies

ηV (ν, t) = 1

Differentiating this with respect to time then yields ˙V (ν, t) = 0, which is only consistent with r (t) = r∗ for all t, thus

r (t) = ηβL for all t

This establishes:

Proposition 13.2 Suppose that condition (13.21) holds In the above-described lab equipment expanding input-variety model, with initial technology stock N (0) > 0, there is a unique equilibrium path in which technology, output and consumption always grow at the rate g∗ as in (13.20)

At some level, this result is not too surprising While the microfoundations and the economics of the expanding varieties model studied here are very different from the neoclassical AK economy, the mathematical structure of the model is very similar to the AK model (as most clearly illustrated by the derived equation for output, (13.12)) Consequently, as in the AK model, the economy always grows at

a constant rate

Even though the mathematical structure of the model is similar to the neoclas-sical AK economy, it is important to emphasize that the economics here is very different The equilibrium in Proposition 13.2 exhibits endogenous technological progress In particular, research firms spend resources in order to invent new inputs They do so because, given their patents, they can profitably sell these inputs to final good producers It is therefore profit incentives that drive R&D, and R&D drives economic growth We have therefore arrived to our first model in which market-shaped incentives determine the rate at which the technology of the economy evolves over time

13.1.5 Pareto Optimal Allocations The presence of monopolistic compe-tition implies that the competitive equilibrium is not necessarily Pareto optimal

In particular, the current model exhibits a version of the aggregate demand exter-nalities discussed in the previous chapter To contrast the equilibrium allocations

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