Economic Models - Convex Optimization
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Economic Models - Convex Optimization

Economic Models - Convex Optimization Economic Models - Convex Optimization

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10.03.2015 Views

Cheap-talk Multiple Equilibria and Pareto 113 value of π. In this case, by Eq. (6), implementing the statically optimal actions t a$ , t $ suffices (albeit not optimally so) to insure that π increases locally. In fact, for δ sufficiently large, the thus controlled system will globally converge to a situation where there are only believers, π = 1. However, if δ is small, the regulator cannot implement the actions t a$ , t $ since in that case g NB

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

Cheap-talk Multiple Equilibria and Pareto 113<br />

value of π. In this case, by Eq. (6), implementing the statically optimal<br />

actions t a$ , t $ suffices (albeit not optimally so) to insure that π increases<br />

locally. In fact, for δ sufficiently large, the thus controlled system will<br />

globally converge to a situation where there are only believers, π = 1.<br />

However, if δ is small, the regulator cannot implement the actions t a$ , t $<br />

since in that case g NB

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