Explain about the money metric utility functions.

The Money Metric Utility Functions:

It is a nice construction including the expenditure function which comes up into a variety of places within welfare economics. See some prices p and some specified bundle of goods x. Some given question can be asked there as: how much money would a specified consumer require at the prices p to be as well off as he could be through consuming the bundle of goods x. When identify the consumer's preferences, simply solve the given problem as:

m(p, x) ≡ min_z pz

that is u(z) = u(x).

which is as m(p, x) ≡ e(p, u(x)).

This type of function is termed as money metric utility function. This is also termed as the "minimum income function," or as "direct compensation function," and with a variety of other names. As, for fixed p, m(p, x) is only a monotonic transform of the utility function and for itself a utility function.

A similar construct is there for indirect utility termed as the money metric indirect utility function that is known by

µ(p; q, m) ≡ e(p, ν (q, m)).

It is µ(p; q, m) measures how much money one would require at prices p to be as well off as one would be facing prices q and acquiring income m. Only as in the direct case, µ(p; q, m) is only a monotonic transformation of an indirect utility function.