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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 ...
A mean-standard deviation indifference curve is defined as the locus of points (σ w, μ w) with σ w plotted horizontally, such that Eu(w) has the same value at all points on the locus. Then the derivatives of v imply that every indifference curve is upward sloped: that is, along any indifference curve dμ w / dσ w > 0.
The observed demand curve would slope upward, indicating positive elasticity. [12] Giffen goods were first noted by Sir Robert Giffen. It is usual to attribute Giffen's observation to the fact that in Ireland during the 19th century there was a rise in the price of potatoes.
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).
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 ]
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.
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.