jnu sis doubts

[shietal]

can someone please help me with the following questions

1. the utility function u(x) = x^a - 1/ a
concave and increasing
convex and increasing
concave and decreasing
convex and decreasing

2 the consumption set
c = (x,y) belongs to R ^2 x>= x degree>0 y>=y degree >0 is
bounded
convex
convex and bounded
neither convex nor bounded

how to measure the elasticity of demand for imports from offer curves?

JNU 2013

I need help in q 21, q 24

is the 25th answer c

please help

thanks

[Granpa Simpson]

1. The function is increasing because the first derivative is positive for the defined a and is concave because the second derivative is negative for all values a defined.

2. The given set is convex and is bounded below, but it is not bounded above. A set is called bounded if it is both bounded above and below, so in this case it is not bounded, it is only convex.

[ViV]

@Subhayu: How do you know this Consumption set is convex?

[Granpa Simpson]

@Viv: U draw the consumption set and and arbitrarily take any two points and make them join by a st line, all points of the st. line joining the two points will always lie within the set, so the set is convex.

[Dreyfus]

@subhayu...can convex set for consumption be refer to convex preferences?

[The Villain]

Could u pls show how did u plot it

[Anjali]

Subhayu could you please explain ques 1 ? Is a constant here ?

[Dreyfus]

@Anjali.. 'a' is constant here and it is given in the ques that 0<a<1

[Granpa Simpson]

@Vaibhav: Preferences are said to be convex if the set "at least as good as" a convex set, or in other words you can say a preference pattern to be convex if the upper contour set is convex, the ones that occur with normal IC's is an example. This is again ensured by the concept of quasiconcavity..!!!!!

[Dreyfus]

@subhayu...that means in this case especially ...we can say that since preferences are convex ...therefore set is convex...
As extremes are not possible here...am I right?

[Granpa Simpson]

Consumers preference ordering is given by the utility function, since in this case there is nothing specified about the utility function, you cannot infer anything about his/her preferences. Its just that the consumption set is convex, a consumer's preference ordering is said to be convex if you get IC's whose upper contour set in convex. In this case you do not know how this consumer's IC's look like, so you cannot also tell that whether the upper contour set is convex or not. Consumption set and preferences are not the same, consumption sets are general sets however preferences are relations or you may say a mapping, so it needs a specific functional form to get identified.

[The Villain]

@Subhayu..how to plot the diag..i'm not getting it.

[Granpa Simpson]

[Granpa Simpson]

Sorry Ron for such a bad and untidy diagram..nywa that will give u a basic idea...!!!

[The Villain]

Its okk man...Thanxx a lot.I got it..Where can i practice such quest fr?

[Granpa Simpson]

Regarding Sets and functions you can find this type of practice questions in Simon & Blume, however if you just want to get the concept right I think Varian is the best book to go through..!!!

[ViV]

Thanks Subhayu

[Granpa Simpson]

My pleasure bro..!!!!