Economic growth and economic development 504

Introduction to Modern Economic Growth
More interesting than the underinvestment result is the imbalance in the physical
to human capital ratio of the economy, which did not feature in the previous two
environments we discussed. The following proposition summarizes this imbalance
result in a sharp way:
Proposition 10.5. Consider the positive activity equilibrium described in Proposition 10.3. Output is equal to 0 if either λ = 0 or λ = 1. Moreover, there exists
λ∗ ∈ (0, 1) that maximizes output.
Proof. See Exercise 10.19.

Ô

Intuitively, dierent levels of λ create different types of “imbalances” between
physical and human capital. A high level of λ implies that workers have a strong
bargaining position, and this encourages their human capital investments. But
symmetrically, it discourages the physical capital investments of firms, since they
will only receive a small fraction of the output. Therefore, high level of λ (as long as
we have λ < 1) creates an imbalance with too high a level of human capital relative
to physical capital. This imbalance effect becomes more extreme as λ → 1. In this

limit, workers’ investment behavior is converging to the first-order condition of the
¯ i (k) for all k > 0). However, simultaneously, the
ˆ i (k) → h
social planner (i.e., h
ˆ is converging to zero, and this implies
physical capital investment of each firm, k,
ˆ i (k) → 0, and production collapses. The same happens, in reverse, when λ is
that h

too low. Now there is too high a level of physical capital relative to human capital.
An intermediate value of λ∗ achieves a balance, though the equilibrium continues to
be inefficient as shown in Proposition 10.5.

Physical-human capital imbalances can also increase the role of human capital in
cross-country income differences. In the current model, the proportional impact of
a change in human capital on aggregate output (or on labor productivity) is greater
than the return to human capital, since the latter is determined not by the marginal
product of human capital, but by the bargaining parameter λ. The deviation from
competitive factor prices, therefore, decouples the contribution of human capital to
productivity from market prices.
At the root of the inefficiencies and of the imbalance effect in this model are
pecuniary externalities. Pecuniary externalities refer to external effects that work
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