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A submodular utility function is characteristic of substitute goods. For example, an apple and a bread loaf can be considered substitutes: the utility a person receives from eating an apple is smaller if he has already ate bread (and vice versa), since he is less hungry in that case. A typical utility function for this case is given at the right.
Only if the two products satisfy the three conditions, will they be classified as close substitutes according to economic theory. The opposite of a substitute good is a complementary good, these are goods that are dependent on another. An example of complementary goods are cereal and milk. An example of substitute goods are tea and coffee.
> implies two goods are substitutes. Consumers purchase more B when the price of A increases. Consumers purchase more B when the price of A increases. Example: the cross elasticity of demand of butter with respect to margarine is 0.81, so 1% increase in the price of margarine will increase the demand for butter by 0.81%.
In economics, gross substitutes (GS) is a class of utility functions on indivisible goods.An agent is said to have a GS valuation if, whenever the prices of some items increase and the prices of other items remain constant, the agent's demand for the items whose price remain constant weakly increases.
Constant elasticity of substitution (CES) is a common specification of many production functions and utility functions in neoclassical economics. CES holds that the ability to substitute one input factor with another (for example labour with capital) to maintain the same level of production stays constant over different production levels.
Goods with linear utilities are a special case of substitute goods. Suppose the set of goods is not finite but continuous. E.g., the commodity is a heterogeneous resource, such as land. Then, the utility functions are not functions of a finite number of variables, but rather set functions defined on Borel subsets of the land.
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The concept of the elasticity of substitution was developed by two different economists, each with their own focus. One of these economists was John Hicks, who defined elasticity of substitution as the change in percentage in the relative number of factors of production used, given a particular change in percentage in relative prices or marginal products.