Economic Models - Convex Optimization

114 Chirstophe Deissenberg and Pavel Ševčík
Figure 2. Phase diagram of the canonical system, c x = 0.6, p = 2, δ = 0.00025,
β = 1, and ρ = 0.0015.
E U
Table 1. Profits, welfare, and taxes at E U
and E L , c x = 0.6, p = 2, δ = 0.0025, β = 1,
p = 0.0015.
g φ t a
t
E U 1 2.25 1.07 0.12
E L 0.98 2.18 N.A. 0.62
The Pareto-superiority of E U is illustrated in Table 1 (remember that at
the equilibrium g N = g NB ).
The situation captured in Fig. 2 (an unstable equilibrium surrounded
by two stable ones) implies the existence of a threshold such that it is
optimal for R to follow a policy leading in the long-run towards the stable
equilibrium E L = (0,λ L ), whenever the initial value π 0 of π is inferior to
the threshold value, π 0