“expenditure function”的概念、定义、翻译、参考文献-科学参考

expenditure function

Economics

单词	expenditure function
释义	expenditure function Economics The minimum cost for a consumer of achieving a given utility level. Consider a consumer choosing the quantities, x₁ and x₂, of two goods to minimize expenditure subject to a utility constraint. The cost minimization problem is ${min}_{{x_{1}, x_{2}}} p_{1} x_{1} + p_{2} x_{2} subject to U (x_{1,} x_{2}) \geq U .$ The solution is described by the two compensated demand functions x₁ = h₁(p₁,p₂,U) and x₂ = h₂(p₁,p₂,U). Substituting the optimal choices back into the objective gives the minimized level of expenditure as $E (p_{1}, p_{2}, U) \equiv p_{1} h_{1} (p_{1}, p_{2,} U) + p_{2} h_{2} (p_{1}, p_{2}, U) .$ The function E(p₁,p₂,U) is the expenditure function. Shephard’s lemma states that ∂E/∂p_i = h_i(p₁,p₂,U), a result that is useful for calculating the welfare consequences of a price change. See also indirect utility function.
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