7. Consider a pure exchange economy with two commodities (called X and Y with quantities given by lower case letters x and y respectively) and two traders, denoted by subscripts 1 and 2, each having an initial endowment vector el = e2 = (1,1). Utility functions are given by u(x1,y1) = 1 and u2(x2,y2) = 2. Each trader's consumption set is the set of all nonnegative vectors in the plane or (equivalently) the closed first quadrant. [85 points total] (b) Do the preference preorders represented by these utility functions satisfy the following properties? Explain each of your answers briefly. [35 points, 5 points each] {i} Transitivity. (ii) Continuity. {iii} Nonsatiation. (iv) Local nonsatiation (|.n.s.) {y} Weak convexity. (vi) Strict {or strong) convexity. (vii) Strict monotonicity