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The indirect utility function is the inverse of the expenditure function when the prices are kept constant. I.e, for every price vector p {\displaystyle p} and utility level u {\displaystyle u} : [ 1 ] : 106
the indirect utility function has (assuming an interior solution) the form: (,) = + which is a special case of the Gorman form. ...
One use of the indirect utility concept is the notion of the utility of money. The (indirect) utility function for money is a nonlinear function that is bounded and asymmetric about the origin. The utility function is concave in the positive region, representing the phenomenon of diminishing marginal utility. The boundedness represents the fact ...
Roy's identity (named after French economist René Roy) is a major result in microeconomics having applications in consumer choice and the theory of the firm.The lemma relates the ordinary (Marshallian) demand function to the derivatives of the indirect utility function.
The indirect utility function is a function of commodity prices and the consumer's income or budget. Indirect utility function v(p, w) where p is a vector of commodity prices, and w is an amount of income. Important assumption is that consumers have locally nonsatiated preferences.
Furthermore, the indirect utility function can be written as a linear function of wealth : (,,) = (,) which is a special case of the Gorman polar form. Hence, if all consumers have homothetic preferences (with the same coefficient on the wealth term), aggregate demand can be calculated by considering a single "representative consumer" who has ...
where (,) is the Hicksian demand and (,) is the Marshallian demand, at the vector of price levels , wealth level (or income level) , and fixed utility level given by maximizing utility at the original price and income, formally presented by the indirect utility function (,).
The indirect utility function in this case is (,) = +, which is a special case of the Gorman polar form. [1]: 154, 169 Equivalence of definitions. The ...