Determine the indirect utility function in brief.

Indirect Utility Function:

The ordinary utility function, u(x), is described over the consumption set X and thus to as the direct utility function. Specified prices p and income m, the consumer selects a utility-maximizing bundle x(p, m). There level of utility achieved while x(p, m) is chosen hence will be the highest level permitted through the consumer’s budget constraint facing p and m, and can be denoted through

v(p, m) = max u(x)

that is px = m.

The function v(p, m) which gives us the maximum utility attainable at specified prices and income is termed as the indirect utility function and therefore this is a compose function of u(•) and x(p, m), which is,

v(p, m) = u(x(p, m)).