In our previous two chapters we explored how the age structure of the population
In our previous two chapters we explored how the age structure of the population affects the economy. Now we focus on how the rate of population growth affects the economy.
The model of economic growth by Robert Solow (1956) is very well-known, simple, and easy to manipulate, so we’ll have a look at it and see what it predicts about the economic consequences of population growth. Its message will not be about efficiency, because efficiency is held constant in the Solow model. It will not be about hours worked or about the fraction of the population that works, because in the Solow model, labour is measured as the number of people in the population: everyone is assumed to work full-time.
The Solow model’s message will be about the capital-labour ratio, K/L, and the importance of accumulating capital to keep up with the number of workers.
The Solow model uses the aggregate production function Y = A F(K,L)
Y = aggregate output of the economy. There’s just one thing produced.
A = efficiency. This is held constant.
F(K,L) = the production function. The production function exhibits constant returns to scale; that is to say, if you double K and double L, F(K,L) doubles in size.
K = physical capital. This time we are not using K+ as we did in Chapter 16. K+ represents a number of different kinds of capital, and different kinds of capital may present mathematical complications. For example, if we include human capital, we might reasonably expect that human capital accumulation would affect efficiency, A, and we’d need an equation to show how that happens. If we included non-renewable natural resource capital, we’d need an equation to show how the resource stock is being depleted.
L = labour. This is identical to the number of people in the population. It grows at rate n.
Why is efficiency A held constant? We might think of including an equation that shows how efficiency grows, either exogenously (automatically) or endogenously (in response to something in the model, such as population growth). However, if A is allowed to grow, then output Y exhibits increasing returns to scale. Doubling K and L while increasing A would result in more than double the output. If increasing returns to scale were in place, output Y and consumption could grow forever in the presence of population growth. Sustainability would be too easy, at least mathematically.
Because efficiency growth such as technological change makes sustainability so easily to achieve, it’s more interesting to hold technological change constant and see what happens when technology and other forms of efficiency don’t improve.
We think of efficiency A as possibly changing depending on the age structure of the workforce, but in the Solow Model there is no change to the age structure.
This model is almost as simple as the Malthusian model. One difference is that in Solow’s model the population growth rate never changes. A second difference is that in Solow’s model, there is not only labour, but also physical