What are the properties of indirect utility function?
Properties of the indirect utility function:
While u(x) is continuous and monotonic onto R^{L}_{+} and (p, m) > 0, the indirect utility function has the given properties as follows:
a. v(p, m) is nonincreasing in p; which is, when p′> p, v(p′, m) < v(p, m). Likewise, v(p, m) is nondecreasing in m.
b. v(p, m) is homogeneous of degree 0 into (p, m).
c. v(p, m) is quasiconvex in p; which is, {p: v(p, m) < k} is a convex set for each k.
d. v(p, m) is continuous at all p >> 0, m > 0.