Lucas 1988

Introduction

Economic development is about understanding why some countries are richer and grow faster than others.
To understand money, we need to look at other parts of society too.
Some countries are way richer than others.
In 1980, rich countries had about U.S. $10,000 per person, while India had $240 and Haiti had $270. That's a huge difference!
How fast countries grow also changes a lot:
- India grew by $1.4\%$ each year.
- Egypt grew by $3.4\%$ each year.
- South Korea grew by $7.0\%$ each year.
- Japan grew by $7.1\%$ each year.
- The United States grew by $2.3\%$ each year.
- Rich countries grew by $3.6\%$ .
- To find out how many years it takes for incomes to double, divide $69$ by the growth rate.
Being rich now doesn't mean a country will grow fast.
Rich countries usually grow at a steady pace, but poorer countries can change quickly.
Some countries like South Korea, Taiwan, Hong Kong, and Singapore grew really fast.
Can governments do things to make their countries grow faster?
We need a way to organize the facts and decide what to do. That thing is called a 'theory.'
A 'theory' is like a computer program that shows how things in the economy work together.
We need to test these theories to see if they match what happens in the real world.
We'll start with a simple model, then make it more complex by adding things like education. Then, we'll see what happens.
We're mostly interested in the 'technology' of how economies work.
We won't talk much about things like people changing or money, even though they're important.

Neoclassical Growth Theory: Review

We'll start with a theory from Robert Solow and Edward Denison.
This theory helps us understand how economies grow and what we can learn from these types of theories. It can also tell us about economic development.
Solow and Denison wanted to explain how the U.S. economy grew. They looked at different things than we do when comparing countries.
A key book is Denison's from 1961, called The Sources of Economic Growth in the United States.
From 1909 to 1957, the U.S. economy grew by $2.9\%$ each year, the hours people worked grew by $1.3\%$ , and the amount of machines and buildings grew by $2.4\%$ .
Solow's model explains why these numbers were stable and about the size they were.
Let's imagine a simple economy with no trade, where everyone is the same and tries to make smart choices. Also, things work in a predictable way.
$N(t)$ is how many people are working at time $t$ , and it grows by $\lambda$ each year.
$c(t)$ is how much each person consumes at time $t$ .
People like to consume over time, which is described by: $\int_{0}^{\infty} e^{-\rho t} \frac{[c(t)^{1-\theta} - 1]}{1-\theta} N(t) dt$ , where $\rho$ is how much people value today over tomorrow and $\theta$ is how much people dislike changes in consumption.
Everything we make is either used for consumption $c(t)$ or to make more machines and buildings $\dot{K}(t)$ .
Total output is $N(t)c(t) + \dot{K}(t)$ , which is the same as net national product.
How much we make depends on machines $K(t)$ , labor $N(t)$ , and technology $A(t)$ , according to: $N(t)c(t) + \dot{K}(t) = A(t) K(t)^{\beta} N(t)^{1-\beta}$ , where $0 - People want to get the most satisfaction from consuming over time, given how much they have to start with$ K(0) $, and how technology$ A(t) $and labor$ N(t) $change.</li><li>To solve this, we use something called a Hamiltonian:$ H(K, \theta, c, t) = \frac{N(t)}{1-\theta} [c^{1-\theta} - 1] + \theta [AK^{\beta}N^{1-\beta} - Nc] $, where$ \theta(t) $is the 'price' of machines and buildings.</li><li>People will choose to consume so that they get the most value out of it:$ c^{-\theta} = \theta(t) $.</li><li>The price of machines and buildings changes over time according to:$ \dot{\theta}(t) = \rho \theta(t) - \frac{\partial H}{\partial K}(K(t), \theta(t), c(t), t) = [\rho - \beta A(t)N(t)^{1-\beta}K(t)^{\beta-1}]\theta(t) $.</li><li>We need to find how machines and buildings change over time$ (K(t), \theta(t)) $given how much we start with$ K(0) $and that we can't have infinite machines and buildings:$ \lim_{t \to \infty} e^{-\rho t} \theta(t)K(t) = 0 $.</li><li>In this model, the best plan is also what would happen if everyone acted in their own self-interest.</li><li>The balanced growth path is when everything grows at a constant rate$ (K(t), \theta(t), c(t)) $.</li><li>Let's say consumption grows at rate$ \kappa $, then the price of machines and buildings falls at rate$ \dot{\theta}(t)/\theta(t) = - \alpha \kappa $.</li><li>Along the balanced path, the return on machines and buildings must be constant:$ \beta A(t) N(t)^{1-\beta} K(t)^{\beta - 1} = \rho + \alpha \kappa $.</li><li>The rate at which things grow depends on how technology changes:$ \kappa = \frac{\mu}{1 - \beta} $.</li><li>The amount we save is constant:$ s = \frac{\dot{K}(t)}{N(t)c(t) + \dot{K}(t)} = \frac{\beta(\kappa + \lambda)}{\rho + \alpha \kappa} $.</li><li>For the balanced path to work, we need to make sure we value the future enough:$ \rho + \alpha \kappa > \kappa + \lambda $.</li><li>No matter how many machines and buildings we start with$ K(0) > 0 $, we'll eventually get to the balanced path.</li><li>Denison's numbers for the U.S. from 1909-1957 are$ \lambda =

The notes primarily discuss economic development in terms of understanding the factors that contribute to the wealth and growth rates of different countries. It introduces the Neoclassical Growth Theory, particularly the Solow-Denison model, to explain economic growth using factors like labor, capital, and technology. The theory also touches on mathematical relationships and conditions necessary for balanced economic growth, using U.S. data from 1909-1957 as an example. The conclusion is that this model helps in understanding the mechanics of economic growth and development, but the provided excerpt stops short of a hard, definitive conclusion beyond the mechanics of the model itself.