Second, by (11), mi(θ-i,θk) ≥ θk for all mi(p,θ-i) = θk for all (θk,θ-ə ∈
Yi∩supp(p) such that ζθk-1 ,θ-i¢ ∈ Yi. By VETO-IC and this property,
P [θik - mi(θik,θ-i)]p(θik,θ-i) (14)
(θik,θ-i)∈Yi
≥ P max{θik - mi (θik-1 , θ-i), 0}p(θik , θ-i)
(θik,θ-i)∈Yi
= P max{θik - mi(θik-1, θ-i), 0}p(θik, θ-i).
(θik-1,θ-i)∈Yi
By the induction hypothesis (9),
θik - mi (θik-1 ,θ-i)=θik - mE (i, θ-i ,p), for all (θik-1 , θ-i) ∈ Yi ∩ supp(p). (15)
By (15) and (12),
P max{θik - mi(θik-1, θ-i), 0}p(θik, θ-i)
(θik-1,θ-i)∈Yi∩supp(p)
= P [θik - mE(i, θ-i,p)]p(θik,θ-i)
(θik-1,θ-i)∈Yi∩supp(p)
= P [θik - mE(i, θ-i, p)]p(θik , θ-i).
(θik-1,θ-i)∈Yi
Thus,
P max{θik - mi (θik-1 , θ-i), 0}p(θik , θ-i)
(θik-1,θ-i)∈Yi
≥ P [θik -mE(p,θ-i)]p(θik,θ-i).
(θik-1,θ-i)∈Yi
This together with (14) imply that
P [θik - mi(θik,θ-i)]p(θik,θ-i) ≥ P [θik - mE(i, θ-i,p)]p(θik,θ-i).
(θik,θ-i)∈Yi (θik-1,θ-i)∈Yi
Thus, by (13),
P [θik - mi(θik,θ-i)]p(θik,θ-i) ≥ P [θik-mE(i,θ-i,p)]p(θik,θ-i),
(θik,θ-i)∈Yi (θik,θ-i)∈Yi
and hence
P mi(θik,θ-i)p(θik,θ-i) ≤ P mE(i, θ-i,p)p(θik,θ-i). (16)
(θik,θ-i)∈Yi (θik,θ-i)∈Yi
Finally, (16) implies that (11) holds as equality, as desired.
19
More intriguing information
1. On the job rotation problem2. Anti Microbial Resistance Profile of E. coli isolates From Tropical Free Range Chickens
3. NATIONAL PERSPECTIVE
4. Research Design, as Independent of Methods
5. The Importance of Global Shocks for National Policymakers: Rising Challenges for Central Banks
6. On Evolution of God-Seeking Mind
7. The name is absent
8. The name is absent
9. Modelling Transport in an Interregional General Equilibrium Model with Externalities
10. Large-N and Large-T Properties of Panel Data Estimators and the Hausman Test