1. provide a careful proof: (a) Prove that a firm’s cost function, c(w,y), is concave in w. (b) Recall the lexicographic preference ordering on X?R+2: for any x,y?X,x?y iff either (i) x1>y1or (ii) x1=y1 and x2=y2. Prove that the lexicographic ordering is complete and transitive. (c) Consider an n-good exchange economy?i,eii?? where ? = {1, …, I}. Assume that each ?i satisfies local non-satiation and can be represented by a utility function ui. Prove that any Walrasian equilibrium allocation (WEA) of this economy is Pareto efficient.
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