DSE Microeco doubts for Mphil\Phd

[Prachi]

Hi Amit,

I have few basic doubts, can you please guide me as to how to proceed with dese ques -

Ques-1: Marshallian demand functions of the following form are given and its asked that are these Marshallian demands generated by a "standard neoclassical" function?

As a hint its written : check the properties of demand functions implied by the demand theory.
 x1(p1,p2,w) = (w/(p1 + p2))^2 = x2(p1,p2,w)

Ans -1: Should I just prove that its homogenous of degree 0 in prices and income. Anything else that i can do here?  

Thanks alot!

[Amit Goyal]

This does not satisfy Walras' Law: p(1)x(1) + p(2)x(2) ≠ w

[Prachi]

Thanks alot! :)

Will check for Walras Law and Homogeneity in such questions.

[Prachi]

Hi Amit,

Can you tell me if the answer to part a) is correct?

Ques.2 A consumer has a direct utility function U(x1,x2) = f(x1) + x2. Good 1 is a discrete good, the only possible levels of consumption of good 1 are x1 = 0 and x1 = 1. Assume f(0) = 0 and p2 = 1.
a) What restriction must p1 satisfy so that x1 = 1 in equilibrium?
b) What is d alzebraic form of indirect utility function?

Ans.2 a) For x1 = 1 to be the equilibrium, (MU1/p1)> (MU2/p2) ........1)
Note : MU1 = f(1) - f(0) = f(1)
MU2/p2 = 1 (as its given that p2 = 1)

This implies that in equilibrium x2=0 and x1 = M/p1, which means that p1 = M ..........2)

From 1) and 2), it can be derived that -
p1 < f(1) , ie M < f(1)

b) V(P,m) = M when f(1) < p1
    and
    V(P,m) = f(1) when f(1) > p1


Thanks alot!