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An example of how indifference curves are obtained as the level curves of a utility function. A graph of indifference curves for several utility levels of an individual consumer is called an indifference map. Points yielding different utility levels are each associated with distinct indifference curves and these indifference curves on the ...
For example, in consumer theory the objective function is the indifference-curve map (the utility function) of the consumer. The budget line is the constraint. The budget line is the constraint. In the usual case, constrained utility is maximized on the budget constraint with strictly positive quantities consumed of both goods.
The concave portions of the indifference curves and their many-dimensional generalizations, if they exist, must forever remain in unmeasurable obscurity. [ 12 ] The difficulties of studying non-convex preferences were emphasized by Herman Wold [ 13 ] and again by Paul Samuelson , who wrote that non-convexities are "shrouded in eternal darkness ...
An example is shown in Fig. 6, where the purple line is the Pareto set corresponding to the indifference curves for the two consumers. The vocabulary used to describe different objects which are part of the Edgeworth box diverges.
Right graph: With fixed probabilities of two alternative states 1 and 2, risk averse indifference curves over pairs of state-contingent outcomes are convex. In economics and finance , risk aversion is the tendency of people to prefer outcomes with low uncertainty to those outcomes with high uncertainty, even if the average outcome of the latter ...
An example indifference curve is shown below: Each indifference curve is a set of points, each representing a combination of quantities of two goods or services, all of which combinations the consumer is equally satisfied with. The further a curve is from the origin, the greater is the level of utility.
In other words: a preference relation is quasilinear if there is one commodity, called the numeraire, which shifts the indifference curves outward as consumption of it increases, without changing their slope. In the two dimensional case, the indifference curves are parallel. This is useful because it allows the entire utility function to be ...
At this optimal vector, the budget line supports the indifference curve I 2. An optimal basket of goods occurs where the consumer's convex preference set is supported by the budget constraint, as shown in the diagram. If the preference set is convex, then the consumer's set of optimal decisions is a convex set, for example, a unique optimal ...