Question

I What does it mean that preferences are reflexive, complete and transitive?

ii What characterises convex preferences?

iii Explain what the assumption of monotonicity of preferences imply.

vi If the five properties above (reflexive, complete transitive, convexity and monotonicity) are satisfied, preferences are said to be “well-behaved”. Explain, which of these properties that make sure that:i.indifference curves cannot slope upwards, ii.indifference curves (for an individual) cannot cross each other, iii.indifference curves are bowed into the origin.

Answer 1

(QUESTION-1)

# Preferences are reflexive if for all X , X greater equal to X, ( X is at least as good as itself ). The assumption is probably the weakest of five assumptions. Reflexive preferences can be explained with the help of an example as:-

I like one apple and one mango at least as well as one apple and one mango.

# Preferences are considered to be as complete if for any two consumption points X and X^' either (X is at least as good as X') or ( X' is atleast as good as X ), or both.

For example, X may be one apple and one mango, X' might be one orange and one carrot. The property says that when presented with these two alternatives, a person can decide that ( X is at least as good as X' ) or vice versa. Completeness asserts that a person can do this for every possible pair of choices in the set of alternatives.

# Transitive preferences means if ( X is greater equal to X' ) and ( X' is greater equal to X'' ) then it should imply that:-

( X is greater equal to X'' )

Transitivity is also intuitive and plausible.

(QUESTION - 2 )

Convex preferences are an individual's ordering of various outcomes, typically with regard to the amount of various goods consumed with a property that " Averages are better than the extremes ". The concept corresponds to the concept of diminishing marginal utility.

A set of convex shaped indifference curves displays convex preferences. Given a convex indifference curve containing the set of all bundles 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.

(QUESTION- 3 )

The assumption of monotonicity of preferences implies that any increase in consumption will be welcomed by a consumer, independent of the reference consumption bundle.

(QUESTION- 4 )

(1) Indifference curve can not slope upward - A set of indifference curves can be upward sloping if we violate assumption number 3 i.e " More is preferred to less ". When a set of indifference curves is upward sloping, it means one of the goods is a " bad " in that the consumer prefers less of the good rather than more of the good.

(2) Indifference curve can not cross each other - Transitivity means that the consumer's preference are consistent in the sense that if she prefers bundle B to A and prefers bundle C to B than she will prefer C to A . This implication of the transitivity assumption is that indifference curves can never cross each other.

(3) Indifference curves are bowed into the origin - The reason behind this is that most people don't like extremes. This means the assumption of convexity of preference makes sure that indifference curves are bowed towards origin.