What is indirect utility function? How will you derive an indirect utility function from a direct utility function? Explain Roy’s identity.
Let qi denotes commodity I and pi is the price of that commodity. Let y denotes money income of the consumer. Suppose vi = pi/y. The budget constraint written as:
n
1 =∑ viqi (1)
i=1
Since optimal solutions in the demand functions are homogeneous of degree zero in income and prices, nothing essential is lost by this transformation to ‘normalised’ prices. The utility function U = f(q1,qn) together with equation (1) gives the following first order conditions of utility maximization:
fi – λvi = 0 for all I – 1,….n
n
and 1 =∑ viqi (2)
i=1
Ordinary demand functions obtained by solving equation (2): qi = Di (v1,….,vn)
The indirect utility function g(v1,…..vn) is defined by
- U = f[D(v1,….,vn), Dn(v1,….,vn) = g(v1,….,vn) (3)
It gives the maximum utility as a function of
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