Consider the following three concepts:
I.Marshall Demand [ ])
II.Indirect Utility [ ])
III.Compensated Demand [ ])
Which of these functions is necessarily homogeneous of degree zero in all its argument?
A)All of them
B)None of them
C)Only I
D)I and III,but not II

Question

Consider the following three concepts:
I.Marshall Demand [ ])
II.Indirect Utility [ ])
III.Compensated Demand [ ])
Which of these functions is necessarily homogeneous of degree zero in all its argument?
A)All of them 
B)None of them 
C)Only I 
D)I and III,but not II

Quizplus · Accepted Answer

A function is said to be homogeneous of degree k if for any scalar λ, f(λx) = λ^kf(x) for all x. 
In other words, changing the scale of all inputs by a factor of λ changes the output by a factor of λ^k.

Now, Marshall Demand function is given by:
x(p,m) = a(p)m/b(p)

where x is the demand for good x, p is the price vector, m is the income and a(p), b(p) are functions of price only. 
It can be shown that this function is indeed homogeneous of degree 0 in p and m, i.e., x(λp,λm) = x(p,m) for any scalar λ.

However, Indirect Utility and Compensated Demand functions are generally not homogeneous of degree 0. Hence, the correct answer is C) Only I.

Consider the Following Three Concepts