Economic growth and economic development 717

Introduction to Modern Economic Growth
also acquire skills. Conclude from this that there exists a cutoff level of
¯ do not get education.
¯ such that all Kx > K
talent, K,
(2) Show that, along BGP relative supplies take the form:
¯
Γ(K)
H
=
¯ .
L
1 − Γ(K)

Explain why such a simple expression would not hold away from the BGP.
¯ [Hint: agent with talent K
¯ has to be indif(3) How would you determine K?
ferent between acquiring skills and not].
Show that the relative supply of skills as a function of the skill premium
must satisfy
Γ (ln ω/ (r∗ + υ − g ∗ ))
H
=
,
L
1 − Γ (ln ω/ (r∗ + υ − g∗ ))
where r∗ and g ∗ refer to the BGP interest-rate and growth rate.
(4) Determine the BGP skill premium by combining this equation with (15.27)
and (15.30). Can there be multiple equilibria? Explain the intuition.
Exercise 15.29. * Consider an economy with a constant population and risk neutral consumers discounting the future at the rate r. Utility is defined over the final
good, which is produced as

Y (t) =

∙Z

0

n

y (ν, t)

ε−1
ε

dν

ε
¸ ε−1

where ε > 1 and intermediate y (ν, t) can be produced using either skilled or unskilled labor. In particular, when a new intermediate is invented, it is first produced
using skilled labor only, with the production function y (ν, t) = h (ν, t), and eventually, another firm may find a way to produce this good using unskilled labor with
the production function y (ν, t) = l (ν, t). Assume that when there exist n goods in
the economy and m goods can be produced using unskilled labor, we have
˙ (t) = bm Xm (t)
n˙ (t) = bn Xn (t) and m
where Xn (t) and Xm (t) are expenditures on R&D to invent new goods and to transform existing goods to be produced by unskilled labor. A firm that invents a new
good becomes the monopolist producer, but can be displaced by a new monopolist
who finds a way of producing the good using unskilled labor.
703