Economic Models - Convex Optimization

The Advantages of Fiscal Leadership in an Economy 87
We solve this game by solving the second stage (for the policy choices)
first, and then substituting the results back into Eq. (11) to determine the
optimal operating parameters δ and λ cb . From stage 2, we get:
π t (δ, λ cb ) =ˆπ + (1 − δ)β(φ − η)λcb + δ(βφ + γ)λ g 1
α[β(φ − η) + δ(βη + γ)]
(13)
y t (δ, λ cb ) =−u t /α (14)
where
τ t (δ, λ cb ) = (1 − δ)βs(βη + γ)(λcb − λ g 1 )
[β(φ − η) + δ(βη + γ)]λ 9 − (b − θ)u t
α
2
η = ∂m t
∂g t
= −α2 γβs 2 + δφλ g 2
(αβs) 2 + δ 2 λ g 2
(15)
(16)
φ = 1 + αβ − γθs (17)
and
= 1 + αβ + βθs. (18)
Evidently, is positive. We assume φ to be positive as well. One would
certainly expect φ>0 since, with θ0.
Nevertheless, the conflict which stands revealed within the fiscal policy is
important. In order to get φ0.