Which of the following demand functions is not homogenous of degree zero in p_x ,p_y ,and I?

Question

Quizplus · Accepted Answer

A demand function is said to be homogenous of degree zero in prices and income if multiplying all prices by a constant k while keeping income constant, will not affect the quantities demanded. Similarly, if income is multiplied by a constant k while keeping prices constant, it should not affect the quantities demanded. 
Option D violates this property because it is not homogenous of degree zero in income. If we multiply the income (I) by a constant k, the effect is not just proportional but by k raised to power -1/2. Thus, the function is not satisfying the property of homogeneity of degree zero.

Which of the Following Demand Functions Is Not Homogenous of Degree