A consumer is faced with the followlling Utility Function, U(x_(1 ) x_2) = (x_1^ + x_2^ ) 1/, where 0

A consumer is faced with the followlling Utility Function, U(x_(1 ) x_2) = (x_1^ρ + x_2^ρ ) 1/ρ, where 0<ρ<1. The consumer also faces the prices p_1 and p_2 and has income level m. Set up the Lagrangian 0ptimisation function for the consumer and Compute the optimal consumption bundle for the consumer. [5 MARKS]

The solution in (a) represents the Marshallian demand function for x_(1 ) and x_2. Using the solution in (a) compute the indirect utility function. [5 MARKS]

Derive the corresponding expenditure function for the consumer and the Hicksian demand function. [5 MARKS]