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Complete, such that all points on an indifference curve are ranked equally preferred and ranked either more or less preferred than every other point not on the curve. So, with (2), no two curves can intersect (otherwise non-satiation would be violated since the point(s) of intersection would have equal utility).
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]
A contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. [1] [2] It is a plane section of the three-dimensional graph of the function (,) parallel to the (,)-plane. More generally, a contour line for a ...
At this point, the slope of the isoquant, and the slope of the isocost, will be equal (see intersection of graph D). A firm has incentive to produce at the least cost combination because it is at this point, the related costs of desired production are minimised. [9] As with indifference curves, two isoquants can never cross.
The Hicksian demand function isolates the substitution effect by supposing the consumer is compensated with exactly enough extra income after the price rise to purchase some bundle on the same indifference curve. [2] If the Hicksian demand function is steeper than the Marshallian demand, the good is a normal good; otherwise, the good is inferior.
Let A : (a,b) → R 2 be a parametric plane curve, in coordinates A(t) = (x(t),y(t)), and B be another (unparameterized) curve. Suppose, as before, that the curve A tends to infinity. The curve B is a curvilinear asymptote of A if the shortest distance from the point A(t) to a point on B tends to zero as t → b.
Whether indifference curves are primitive or derivable from utility functions; and; Whether indifference curves are convex. Assumptions are also made of a more technical nature, e.g. non-reversibility, saturation, etc. The pursuit of rigour is not always conducive to intelligibility. In this article indifference curves will be treated as primitive.
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 ...