Question

Prove that the Hicksian demand functions are homogeneous of degree zero in prices. Interpret the economic intuition of this property of Hicksian demand functions in your own words.

Show that

ich (tp, u)) = " (p, u)

Answer 1

to prove that Hicksian demand functions are homogenous of degree zero in prices, we use the relationship between Hicksian and Marshallian demand functions

x ^h (p, u) = x(p, e(p, u))

where e(p, u) is the expenditure function.

We mak use of the fact that e(p, u) is homogeneous of degree 1 in p and Marshallian demand x(p, y) is homogeneous of degree 0 in (p, y):

x^h (tp, u) = x(tp, e(tp, u))

= x(tp, e(tp, u))

= x(tp, te(p, u))

= x(p, e(p, u))

This is the same as the original value of x^h (p, u), so the Hicksian demand function is homogenous of degree zero

The economic interpretation of this property of Hicksian demand functions

The demand functions depend on price and income and if both price and income are increased or decreased by the same factor, then the demand function remains unaffected.This is why Hicksian demand functions are homogenous of degree zero.