Figure 3: Transitions between the corner and interior solutions.
the second term overpowers it. Indeed, differentiation of the left-hand side of (C.7), which is
denoted by Φ (Z), with respect to Z yields
dΦ (Z) 1 7ρ
-=Γ~ = —Zδ
dZ ρn
which implies that for smaller values of Z the left-hand side of (C.7) takes a positive slope,
while for larger values of Z that takes a negative slope. Noting that Φ (0) = 0, these results
together imply that the function Φ (Z) displays a U-shaped curve, as illustrated in Fig.3. This
diagram shows that for larger values of c3, as happens with c03 in Fig.3, (C.7) is satisfied at
any value of Z and thus a (Z)=1is a global solution to the HJB equation (C.5), whereas for
smaller values of c3 as happens with c030 in Fig.3, it is satisfied for smaller Z, is then violated,
and finally is satisfied for larger values of Z again. ■
References
Acemoglu, D., S. Johnson and J.A. Robinson, 2001, The colonial origins of comparative
development: An empirical investigation, American Economic Review 91, 1369- 1401.
Auty, R.M., 2001, Resource abundance and economic development, Oxford: Oxford University
Press.
Collier, P. and A. Hoeffler, 2004, Greed and Grievance in Civil War, Oxford Economic Papers,
26
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