Economic growth and economic development 594

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 neoclassical 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 marketshaped incentives determine the rate at which the technology of the economy evolves
over time.
13.1.5. Pareto Optimal Allocations. The presence of monopolistic competition implies that the competitive equilibrium is not necessarily Pareto optimal.
In particular, the current model exhibits a version of the aggregate demand externalities discussed in the previous chapter. To contrast the equilibrium allocations
580