3. (a) Derive the Hicksian demand functions and the expenditure function for the following utility function: u($1, 12, 13) = (21)1/6(x2)1/6(x3)1/3, x1 2 0, 12 2 0, 13 2 0 (b) Using your results from part (a), derive the indirect utility function. (c) Rob currently earns an income of $1000. He shops at a store where the per-unit prices of r1, 12 and x3 are $3, $3 and $3 respectively. A new store opens up which advertises lower prices of $1, $1, $1 for ri, 12 and r3. But Rob will have to pay a membership fee of F to be able to shop at this new store. What is the maximum fee F that Rob will be willing to pay? [Utility theory is a powerful tool, and has been used to study a wide range of issues. The next question will expose you to one of the many applications of this theory; you may see more applications in other economics courses.]