<Ol> <Li> Defined only in the non-negative quadrant of commodity quantities (i.e. the possibility of having negative quantities of any good is ignored). </Li> <Li> Negatively sloped . That is, as quantity consumed of one good (X) increases, total satisfaction would increase if not offset by a decrease in the quantity consumed of the other good (Y). Equivalently, satiation, such that more of either good (or both) is equally preferred to no increase, is excluded . (If utility U = f (x, y), U, in the third dimension, does not have a local maximum for any x and y values .) 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 between a bundle A and another bundle B because they lie on the same indifference curve, even in the case in which the quantity of both goods in bundle B is higher . Because of monotonicity of preferences and non-satiation, a bundle with more of both goods must be preferred to one with less of both, thus the first bundle must yield a higher utility, and lie on a different indifference curve at a higher utility level . The negative slope of the indifference curve implies that the marginal rate of substitution is always positive; </Li> <Li> 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). </Li> <Li> Transitive with respect to points on distinct indifference curves . That is, if each point on I is (strictly) preferred to each point on I, and each point on I is preferred to each point on I, each point on I is preferred to each point on I. A negative slope and transitivity exclude indifference curves crossing, since straight lines from the origin on both sides of where they crossed would give opposite and intransitive preference rankings . </Li> <Li> (Strictly) convex . With (2), convex preferences imply that the indifference curves cannot be concave to the origin, i.e. they will either be straight lines or bulge toward the origin of the indifference curve . If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the other good are required to keep satisfaction unchanged . </Li> </Ol> <Li> Defined only in the non-negative quadrant of commodity quantities (i.e. the possibility of having negative quantities of any good is ignored). </Li> <Li> Negatively sloped . That is, as quantity consumed of one good (X) increases, total satisfaction would increase if not offset by a decrease in the quantity consumed of the other good (Y). Equivalently, satiation, such that more of either good (or both) is equally preferred to no increase, is excluded . (If utility U = f (x, y), U, in the third dimension, does not have a local maximum for any x and y values .) 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 between a bundle A and another bundle B because they lie on the same indifference curve, even in the case in which the quantity of both goods in bundle B is higher . Because of monotonicity of preferences and non-satiation, a bundle with more of both goods must be preferred to one with less of both, thus the first bundle must yield a higher utility, and lie on a different indifference curve at a higher utility level . The negative slope of the indifference curve implies that the marginal rate of substitution is always positive; </Li> <Li> 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). </Li>

Which of the following is not the assumption of indifference curve