Micro Question

[jack]

X is planning to go on a weekend trip and he has a few places in mind. However, he has two criteria on the basis of which he is going to decide at which place he wants to go. The primary(the most important) criterion is how safe(S) the place is and the secondary criterion is how far it is from his home(d). He would prefer to go to a place which is safer and ignore the distance. However, in comparing two destination which he thinks are equally safe, he would prefer the one which requires him to travel a lesser distance. The indifference curves in (s.d) domain are

a) horizontal
b) vertical
c) negative sloped
d) Do not exits

[Arushi :))]

i think its d.

[Atika Gupta]

Yes it should be d. Such preferences are called as lexicographic preferences. They violate continuity property and hence, indifference curve for such preferences can not be drawn.
In the question preference map is given by he following:
let, x - (s,d) and y - (s1,d1) be two destinations:
If s>s1; x is preferred to y
If s-s1 and d<d1; x is preferred to y

If you draw the preference map then you can see that indifference curve can not be drawn.

[RajEco]

@atika
Can you please clear my one doubt regarding lexicographic preferences-

U= x2 + y .. Does this represent lexicographic preferences ? if yes.. then we can simply graph it ?

[Atika Gupta]

No, this is not lexicographic preferences.
Infact u can not represent such preferences by a utility function as they violate the property of continuity.

[Anjali]

Thanks @Atika for your explanation.
But how can we identify lexicographic preferences ? Any particular rule ?

[RajEco]

Thanks atika :)

[Atika Gupta]

Hi Anjali,

Formally, following is  lexicographic preference ordering as:
for all x,y belonging to X (where X is the commodity space), xPy if, either
I) x1>y1 ii) x1=y1 and x2>y2.
These are called lexicographic preferences as here commodities are ranked according to lexicographic order.

Following is the another example of lexicographic preferences:
In a two commodity world, a consumer always prefers a consumption bundle with greater total weight to a consumption bundle with lower total weight; however if the total weights are same he prefers the bundle containing more of commodity 1. Draw his preference map.