Suppose that a consumer has wealth, W, consumers from a set of differentiated varieties wn, and...

  

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Suppose that a consumer has wealth, W, consumers from a set of differentiated varieties wn, and solves the following CES maximization problem: max u = (9 (w) dw) % F s.t. Lop(w)q (w) dw X (1) where > 0 is the elasticity of substitution between varieties, q(w) is the quantity consumed of variety w and p(w) is the price of variety w din (a) Show that w is the elasticity of substitution, i.e. for any w, w' en, = all/ din (b) What happens as co?1?0? Suppose that a consumer has wealth, W, consumers from a set of differentiated varieties wn, and solves the following CES maximization problem: max u = (9 (w) dw) % F s.t. Lop(w)q (w) dw X (1) where > 0 is the elasticity of substitution between varieties, q(w) is the quantity consumed of variety w and p(w) is the price of variety w din (a) Show that w is the elasticity of substitution, i.e. for any w, w' en, = all/ din (b) What happens as co?1?0?