Define the preference relation ~ defined in the positive quadrant X = R2 as: A bundle x is weakly preferred to another bundle y, if and only if min {r1 + 212, 2x1 + 12} > min{y1 + 2y2, 2y1 + 92} a. [10 points] Show that this preference relation represents rational preferences. b. [10 points] Draw the upper contour set, the lower contour set and the indifference set for the bundle x = (1,1). Draw the upper contour set, the lower contour set and the indifference set for the bundle x = (1 , 2 ) . c. [10 points] Does this preference relation satisfy strict convexity? What about convexity? Give an explanation and derive mathematically] d. [5 points] For what value of p1/P2 will the Walrasian demand be unique? e. [5 points] For what value of p1/p2 will the unique Walrasian demand be r2 # 0? what about r1 * 0