C hapter 2 p The Modigliani-Miller theorem When capital markets are perfect and compl e. corDor decisions are trivial," 2.1 Arrow-Debreu model with assets 2.1.1 Primitives (2,F,P X=f: Q-R a is F-measural h=1,,|H ah∈X i=1,2,…,| X2CX,e2∈X,1∈R,u4:X1→R j=1,2,…,|J YCX 2.1.2 Arrow-Debreu model We begin by reviewing the Arrow-Debreu model There is a finite set of states of nature w Q and a single good in each state. The commodity space is R. There is a finite set of firms j E each characterized by a production set Yi cr. There is a finite set of consumers i E I, each characterized by a consumption set Xi, an endowment ei E xi and a utility function w;: Xi- R. Each agent i owns a fraction Bi; of firmChapter 2 The Modigliani-Miller theorem “When capital markets are perfect and complete, corporate decisions are trivial.” 2.1 Arrow-Debreu model with assets 2.1.1 Primitives (Ω, F, P) X = {x : Ω → R | x is F-measurable} h = 1, ..., |H| zh ∈ X i = 1, 2, ..., |I| Xi ⊂ X, ei ∈ Xi, θi ∈ RJ +, ui : Xi → R j = 1, 2, ..., |J| Yj ⊂ X 2.1.2 Arrow-Debreu model We begin by reviewing the Arrow-Debreu model. There is a finite set of states of nature ω ∈ Ω and a single good in each state. The commodity space is RΩ. There is a finite set of firms j ∈ J, each characterized by a production set Yj ⊂ RΩ. There is a finite set of consumers i ∈ I, each characterized by a consumption set Xi, an endowment ei ∈ Xi, and a utility function ui : Xi → R. Each agent i owns a fraction θij of firm j. 1