microeconomics- consumer preferences

MICROECONOMICS- CONSUMER PREFERENCES ? X

Utility function U ) represents preference relation ? if for any x and y , U (x ? U (y ) if and only

if x ? y . That is , function U assigns a number to x that is at least as large as the number it

assigns to y if and only if x is at least as good as y . The nice thing about utility functions is that

if we know the utility function that represents a consumer 's preferences , we can analyze these

preferences by deriving properties of the

utility function

Consider a typical indifference curve map , and assume that preferences are rational

The line drawn in figure is the line x2 x1 , but any straight line would do as well . Notice

that we could identify the indifference curve Ix by the distance along the line x2 x1 we have

to travel before intersecting Ix . Since indifference curves are downward sloping , each Ix will only

intersect this line once , so each indifference curve will have a unique number associated with it

Further , since preferences are convex , if x y , Ix will lay above and to the right of Iy (i .e . inside

We will call the number associated with Ix the utility of x . Formally we can define a function

u (x1 , x2 ) such that u (x1 , x2 ) is the number associated with the indifference curve on which (x1 , x2 ) lies . It turns out that in to ensure that there is a utility function corresponding to a particular

preference relation , we need to assume that preferences are rational and continuous . The assumption that preferences are rational agrees with how we think consumers should behave , so it is no problem

The assumption that preferences are continuous is what we like to call a technical assumption

by which we mean that is that it is needed for the arguments to be mathematically rigorous (read

true , but it imposes no real restrictions on consumer behavior . Indeed the problems associated

with preferences that are not continuous arise only if we assume that all commodities are infinitely ( MICROECONOMICS- CONSUMER PREFERENCES ( Page 2

divisible (or come in infinite quantities . Since neither of these is true of real commodities , we do

not really harm our model by assuming continuous preferences . Utility is an ordinal concept

Utility is an ordinal (i .e . ing or ranking ) concept

For example , if U (x 6 and U (y 2 then bundle x is strictly to bundle y . However , x is not necessarily three times better ' than y

QUESTION 1 (b

Price of the product : The law of demand states that other demand determinants remaining constant , when the price of a given product falls demand rises and vice-versa . It means , if the price of a given product falls , the market demand for the given product will rise and if the price rises , the market demand for the product will fall . However , the product under consideration should be a normal product and not an inferior good or prestige goods

Income...