Fall Semester ’05-’06
Akila Weerapana
Lecture 4: The Solow Diagram
I. OVERVIEW
•In the last lecture, we discussed the importance of economic growth, and the importance of
models. We then derived a model of economic growth: the Solow growth model, which basi-
cally consisted of two equations: a production function and a capital accumulation equation.
•In today’s lecture, we will first transform these equations into per-capita terms: in other
words write the equations in terms of output and capital per-capita. This will make the
model more tractable. We will then use these two equations to draw a diagram known as the
Solow diagram.
•We will then use this diagram to do various “comparative statics” exercises where we analyze
the impact of changes in saving rates, population growth rates, the capital stock etc. on
economic growth in the short run and in the long run.
II. THE PER-CAPITA VERSION OF THE SOLOW MODEL
•In order to make working with the model a little easier, we transform the model into per-
capita terms. Define the following per-capita variables y=Y
L(output per worker) and k=K
L
(capital per worker)
•Note that every person is a worker in this model. I will use per-capita and per-worker
interchangeably.)
•The production function can be written in per-capita terms as Y
L=KαL1−α
L≡Kα
Lαwhich
means that y=kα
•The capital accumulation equation can be written in per-capita terms as well.
k=K
L⇒
˙
k
k=˙
K
K−
˙
L
L
˙
k
k=(sY −δK)
K−n≡(sY )
K−δ−n
˙
k
k=(sY/L)
K/L −(δ+n)≡(sy)
k−(δ+n)
⇒˙
k=sy −(δ+n)k
•This equation states that net investment per worker (the change in the capital stock per
worker) is the difference between gross investment per worker (sy) and the level of break-even
investment per worker (n+δ)k.
•The intuition underlying this equation is not too difficult to follow:
