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The negative slope of the indifference curve reflects the assumption of the monotonicity of consumer's preferences, which generates monotonically increasing utility functions, and the assumption of non-satiation (marginal utility for all goods is always positive); an upward sloping indifference curve would imply that a consumer is indifferent ...
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 ...
A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set.
Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve (more precisely, to the slope multiplied by −1) passing through the consumption bundle in question, at that point: mathematically, it ...
The preferences are weakly convex, but not strictly convex: a mix of two equivalent bundles may be either equivalent to or better than the original bundles. The indifference curves are L-shaped and their corners are determined by the weights.
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 ...
The function's slope represents the best fit line going through the indifference curves, representing wages and the probability of injury while at work. [15] The function is upward sloping due to the parallel relationship between wages and the undesirable qualities of a job; the more undesirable the job is, the higher the wages employees are ...
This translates to a linear expansion path in income: the slope of indifference curves is constant along rays beginning at the origin. [1]: 482 This is to say, the Engel curve for each good is linear. Furthermore, the indirect utility function can be written as a linear function of wealth :