|: (40 points) Luffy consumes rapiers and meat, just like everyone else in the Straw Hat Pirates. The consumption bundle where Luffy consumes x rapiers and y pounds of meat per episode is written as (z, y). Luffy's preferences are represented by the utility function u(z, y) = 4(z+1)+4v/z + 1y+ 2. (g) Write (the mathematical expression for) Luffy's demand function for rapiers and her demand function for meat. 4 points (h) Use your answer to the previous question and complete the table below with Luffy's optimal bundle for different price-income combinations. Px Py m y* 2 4 30 4 4 30 2 4 10 2 4 4 4 points(i) Assume now that Pr = 2 and Py = 4, and draw the following functions in the two graphs below. i. Luffy's Engel curve curve for exes. ii. Luffy's Engel curve curve for whys. 4 points 20 20 18 18 16 16 14 14 12 12 10 10 A N N 8 10 12 14 16 18 20 8 10 12 14 16 18 20 EXES WHYS Assume again that the price of rapier is 2, the price of meat is 4 per pound, and that Luffy's income is 30. Now the local government levies a new tax on rapier that increases its price to 4. (i) How does Luffy's consumption of rapiers change as a consequence of the new tax? 4 point (j) What part of the above change in demand is due to the substitution effect, and what part is due to the income effect? 4 points