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I have recently encountered (in a few applications), the Dixit-Stiglitz Pricing index. Consider a Constant elasticity of substitution form of utility $$U=\left(\sum_{i=1}^{N}c_{i}^{1-\frac{1}{\sigma}}\right)$$

This index basically aggregates prices to give a general term as a function of prices that yields a unit cost of utility. How is the index derived?

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