08.0-pp-39-54 Lecture 4 Algorithmic Mechanism Design ExercisesExercise 4.1 Consider an arbitrary single-parameter environment, with feasible set X. Prove that the welfare-maximizing allocation rulex(b) = argmax(x1,…,xn)∈Xn∑i=1bixi (4.2)is monotone in the sense of Definition 3.6.[Assume that ties are broken in a deterministic and consistent way,such as lexicographically.] Exercise 4.2 Continuing the previous exercise, restrict now to fea-sible […]