Economic growth and economic development 175

Introduction to Modern Economic Growth progress can gather speed (see, for example, Chapter 23) Alternatively, some natural (steady) progress of technology that may have been going on in the background needs to reach a critical threshold for the process of growth to begin These stories are quite plausible World population has indeed increased tremendously over the past one million years and the world’s inhabitants today have access to a pool of knowledge and technology unimaginable to our ancestors Could these long-run developments of the world economy also account for cross-country differences? Is the increase in world population a good explanation for the take off of the world economy? Let us focus on population to give a preliminary answer to these questions The simplest way of thinking of the relationship between population and technological change is the Simon-Kremer model (after the demographer Julian Simon and the economist Michael Kremer) This model is implicitly one of the entire world economy, since there are no cross-country differences and proponents of this model not try to explain differences across countries by their populations Imagine that there is a small probability that each individual will discover a new idea that will contribute to the knowledge pool of the society Crucially, these random discoveries are independent across individuals, so that a larger pool of individuals implies discovery of more new ideas, increasing aggregate productivity Let output be determined simply by technology (this can be generalized so that technology and capital determine output as in the Solow model, but this does not affect the point we would like to make here): Y (t) = A (t) L (t)α Z 1−α , where α ∈ (0, 1), Y (t) is world output, A (t) is the world stock of technology, L (t) is world population, and Z is some other fixed factor of production, for example, land, which we normalized to Z = without loss of any generality Imagine we are in a continuous time world and suppose that (4.1) A˙ (t) = λL (t) , where λ represents the rate at which random individuals make discoveries improving the knowledge pool of the society, and the initial level of world knowledge A (0) > is taken as given Population, in turn, is a function of output, for example because 161