Theoren215. Suppose f,9,hy:Rn×R→ R are C" functions,i=1,…,m, G=(01,…,9m)2,H≡(h1,…,bk)2, L(x,a,A,p)≡f(x,a)+入·G(x,a)+·H(x,a) If r*(a is a solution of the following problem max f(a, a) t.G(x,a)≥0 H(x,a)=0, and A*(a) and u*(a) are the corresponding Lagrange multipliers, then under some con- ditions we have F(a)OL(x,a,入 x=x(a),A=X(a),p=*(a) Example 2. 16. Consider F(a, b) in Example 2. 12. Example 2.17. Consider the following economic problem v(p1,…,pn,D)≡maxa(x1,…,xn) st.p1x1+……+pnxn≤I ee Sydsaeter et al(2005, p 149)Theorem 2.15. Suppose f, gi, hj : Rn × Rl → R are C1 functions, i = 1, . . . , m, j = 1,..., k. Let G ≡ (g1,...,gm)T , H ≡ (h1,...,hk)T , and L(x, a, λ, μ) ≡ f(x, a) + λ · G(x, a) + μ · H(x, a). If x∗(a) is a solution of the following problem F(a) ≡ max x∈Rn f(x, a) s.t. G(x, a) ≥ 0, H(x, a)=0, and λ∗ (a) and μ∗(a) are the corresponding Lagrange multipliers, then under some con￾ditions1 we have ∂F(a) ∂a = ∂L(x, a, λ, μ) ∂a     x=x∗(a), λ=λ∗(a), μ=μ∗(a) .  (2.3) Example 2.16. Consider F(a, b) in Example 2.12.  Example 2.17. Consider the following economic problem: v(p1,...,pn, I) ≡ max x≥0 u(x1,...,xn) s.t. p1x1 + ··· + pnxn ≤ I.  1See Sydsaeter et al (2005, p.149). 2 — 11