Barro, Chapter 2
A Robinson Crusoe Economy
Craig Burnside
Economics 302
University of Virginia
Robinson’s Resource Constraint
• Robinson Crusoe is alone on an island. He produces output, y, of a single good
(widgets) that can only be used for consumption, c, and is perishable (i.e. it cannot
be stored to be consumed later). This implies
c = y
• Robinson uses his labor, l, to produce the good. The function f (the production
technology), illustrated in Fig 2.1, tells us how much output Robinson produces for a
given amount of work effort :
y = f(l).
• The slope of f(l) is called the marginal product of labor or MPL. It is illustrated in
Fig 2.2. Notice from either Figure 2.1 or 2.2 that MPL > 0 (working more increases
output) and MPL ↓ if l ↑ (there are diminishing returns to labor). The reason we use
the word marginal product of labor is that for small changes in labor, Δl, the change
in output, Δy, is given by
Δy = MPL × Δl.
• Since c = y we can derive Robinson’s resource constraint:
c = f(l)