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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 ...
The utility function for perceived gains has two key properties: an upward slope, and concavity. (i) The upward slope implies that the person feels that more is better: a larger amount received yields greater utility, and for risky bets the person would prefer a bet which is first-order stochastically dominant over an alternative bet (that is ...
At this equilibrium point, the slope of the highest indifference curve must equal the slope of the production function. Recall that the marginal rate of substitution is the rate at which a consumer is ready to give up one good in exchange for another good while maintaining the same level of utility. [ 6 ]
For example, if the MRS xy = 2, the consumer will give up 2 units of Y to obtain 1 additional unit of X. As one moves down a (standardly convex) indifference curve, the marginal rate of substitution decreases (as measured by the absolute value of the slope of the indifference curve, which decreases).
The indifference curves are L-shaped and their corners are determined by the weights. E.g., for the function min ( x 1 / 2 , x 2 / 3 ) {\displaystyle \min(x_{1}/2,x_{2}/3)} , the corners of the indifferent curves are at ( 2 t , 3 t ) {\displaystyle (2t,3t)} where t ∈ [ 0 , ∞ ) {\displaystyle t\in [0,\infty )} .
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.
Middle graph: In standard deviation-expected value space, risk averse indifference curves are upward sloped. Right graph : With fixed probabilities of two alternative states 1 and 2, risk averse indifference curves over pairs of state-contingent outcomes are convex.
An example of preferences which are weakly monotonic but not strongly monotonic are those represented by a Leontief utility function. If an agent has monotone preferences which means the marginal rate of substitution of the agent's indifference curve is positive. Given two products X and Y.