Economic growth and economic development 167

Introduction to Modern Economic Growth
H denotes the efficiency units of labor (human capital), given by H =

P

i∈N

hi ,

where N is the set of all individuals in the population and hi is the human capital

of individual i. Assume that H is fixed. Suppose there are no human capital
externalities and factor markets are competitive.
(1) Calculate the steady-state equilibrium of this economy.
(2) Prove that if 10% higher h at the individual level is associated with a%
higher earnings, then a 10% increase in the country’s stock of human capital
H will lead to a% increase in steady-state output. Compare this to the
immediate impact of an unanticipated 10% increase in H (i.e., with the
stock of capital unchanged).
Exercise 3.10. Consider a constant returns to scale production function for country j Yj = F (Kj , Aj Hj ), where Kj is physical capital, Hj denotes the efficiency units
of labor and Aj is labor-augmenting technology. Prove that if Kj /Yj = Kj 0 /Yj 0 in
two different countries j and j 0 , than the rental rates of capital in the two countries,
Rj and Rj 0 will also be equal.
Exercise 3.11. Imagine you have a cross-section of countries, i = 1, ..., N , and for
each country, at a single point in time, you observe labor Li , capital Ki , total output
Yi and the share of capital in national income, αK
i . Assume that all countries have
access to a production technology of the following form
F (L, K, A)
where A is technology. Assume that F exhibits constant returns to scale in L and
K, and all markets are competitive.

(1) Explain how you would estimate relative differences in technology/productivity
across countries due to the term A without making any further assumptions.
Write down the equations that are involved in estimating the contribution
of A to cross-country income differences explicitly.
(2) Suppose that the exercise in part 1 leads to large differences in productivity
due to the A term. How would you interpret this? Does it imply that
countries have access to different production possibility sets?
(3) Now suppose that the true production function is F (H, K, A) where H
denotes efficiency units of labor. What other types of data would you
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