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

separable utility function

Economics

A utility function is separable if it can be written in the form

$u = U (v_{1} (x^{1}), v_{2} (x^{2}), …, v_{m} (x^{m}))$

where x¹,…, x^m form a partition of the available products. (Assume three goods are available and denote the consumption of good i by x_i, i = 1, 2, 3. Then x¹ = (x₁, x₂), x² = (x₃) is an example of a partition.) The implication of separability is that the marginal rate of substitution between any two goods in x^j is unaffected by the consumption level of any good not in x^j. If a consumer has separable preferences then the demand for a good in x^j depends on the expenditure allocated to all goods in x^j and the prices of goods in x^j. This is a form of two-stage budgeting: the consumer first decides how much to spend on each category of goods (meaning, for each element of the partition), and then allocates the expenditure between goods within a category. A utility function is additively separable if

$u = v_{1} (x^{1}) + v_{2} (x^{2}) + … + v_{m} (x^{m}) .$

This is a special case of separability. Additive separability is frequently used to represent preferences over consumption at different points in time.

单词	separable utility function
释义	separable utility function Economics A utility function is separable if it can be written in the form $u = U (v_{1} (x^{1}), v_{2} (x^{2}), …, v_{m} (x^{m}))$ where x¹,…, x^m form a partition of the available products. (Assume three goods are available and denote the consumption of good i by x_i, i = 1, 2, 3. Then x¹ = (x₁, x₂), x² = (x₃) is an example of a partition.) The implication of separability is that the marginal rate of substitution between any two goods in x^j is unaffected by the consumption level of any good not in x^j. If a consumer has separable preferences then the demand for a good in x^j depends on the expenditure allocated to all goods in x^j and the prices of goods in x^j. This is a form of two-stage budgeting: the consumer first decides how much to spend on each category of goods (meaning, for each element of the partition), and then allocates the expenditure between goods within a category. A utility function is additively separable if $u = v_{1} (x^{1}) + v_{2} (x^{2}) + … + v_{m} (x^{m}) .$ This is a special case of separability. Additive separability is frequently used to represent preferences over consumption at different points in time.
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