The following exercise walks you through the main steps of duality. Let the utility function of the consumer over the goods at and y be given by: U (gay) = mag/'3 and let the budget constraint be given by: 1233: + pyy = m. If you solve the above utility maximization problem you will get the following Marshallian demands: mmpmpyml = (elf-) (10%) ympmmw'm) = (ow/:6) (1%) 1. Write down the indirect utility function, 12(pm, pg, m). [2 points] 2. Let a = = %, pm 2 1, 13,, = 2, and m = 10. Calculate the numerical values for mfnampwm), y;(pm,py, m), and vCpmpy, m). [3 points] 3. Duality suggests that this same problem can be interpreted as expenditure minimization. Let U * be the target utility level. Set up the expenditure minimization problem and solve for the Hicksian demand functions: miCpmpy, U*) and y,";(pm,py, U*). [5 points] 4. Using the Hicksian demand functions, write down the minimum expenditure function 60%, pg, U *). [2 points] 5. Let a = 6 = %, 19m = 1, 19,, = 2 as before and U * = v where v is the numerical value of the indirect utility function you found in part (2). Find the numerical values for 50;\