Before presenting the Solow model, it is worth stepping back to consider exactly what a model is and what it is for. In modern economics, a model is a mathematical representation of some aspect of the economy. It is easiest to think of models as toy economies populated by robots.…The best models are often very simple but convey enormous insight into how the world works.– Charles Jones
Consider this discussion, versions of which have been played out countless times in faculty offices around the world:
Professor: Welcome. How can I help you?
Student: I am having trouble with the Solow Model. It is confusing.
Professor: Yes, this is a difficult model. What exactly is the problem?
Student: I can see how increasing the rate of population growth (n) or the depreciation rate (δ) will hurt the economy –
Professor: The nifty canonical graph, also known as the Solow diagram [which the professor quickly sketches as in Figure 3.1.1], makes that obvious, don't you think? The line rotates up and steady-state capital per worker in efficiency units falls, so steady-state output and consumption per worker in efficiency units will also fall. Ta-da!
Student: I see that for n and δ, but g is where I get really baffled. Why would technological progress hurt the economy? Shouldn't an increase in g help, with more consumption as we produce more output with the same resources?
Professor: You are forgetting that the x axis on the canonical graph is capital per worker in efficiency units. That's not the actual economy –
Student: I know that. You emphasized this point a lot in class. But here's my question then: Where is the actual economy? How can I see what is happening there? Does the canonical graph have some secret trap door that reveals the impact of g on the economy itself, not in efficiency units but in actual output per worker?
Professor: Um, no, there are no secret trap doors. The canonical graph just provides an ingenious way to find the steady-state in a model with constant technological progress. That is all it does.