Economic growth and economic development 663
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Introduction to Modern Economic Growth
(4) Now consider a hypothetical economy in which the previous highest-quality
producer disappears so that the monopolist can charge a markup of 1/ (1 − β)
instead of the limit price. Show that the BGP growth rate in this hypo-
thetical economy is strictly greater than the growth rate characterized in 2
above. Explain this result.
(5) Let us now go back to the question in Exercise 14.1 and suppose that the
incumbent firm has an advantage in R&D as in that exercise. Show that
if φ is sufficiently high, the incumbent will undertake R&D. Why does this
result differ from the one in Exercise 14.1?
Exercise 14.8. Modify the baseline model of Section 14.1 so that the aggregate
production function for the final good is
∙Z 1
¸
1
1−β
(q(ν, t)x(ν, t | q))
dν Lβ .
Y (t) =
1−β 0
All the other features of the model remain unchanged.
(1) Show that with this production function, a BGP does not exist. Explain
why this is.
(2) What would you change in the model to ensure the existence of a BGP.
Exercise 14.9. Suppose that there is constant exponential population growth at
the rate n. Modify the baseline model of Section 14.1 so that there is no scale effect
and the economy grows at the constant rate (with positive growth of income per
capita). [Hint: suppose that one unit of final good spent on R&D for improving the
machine of quality q leads to flow rate of innovation equal to η/qφ , where φ > 1].
Exercise 14.10. Consider a version of the model of competitive innovations in
which the x’s do not depreciate fully after use (similar to Exercise 13.20 in the
previous chapter). Preferences and the rest of the production structure are the
same as in the baseline model in Section 14.1.
(1) Define an equilibrium.
(2) Formulate the maximization problem of a monopolist with the highest quality machine.
(3) Show that, contrary to Exercise 13.20, the results are different than those
in Section 14.1. Explain why depreciation of machines was not important
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