Question 3 A certain household comprises of a couple, Adam (A) and Betty (B). They have lexicographic preferences over two goods G1 and G2 A wants to consume as much of G1 as possible, before moving on to G2 whereas, for B, it is the opposite, she wants to consume as much of G2 as possible before moving on to G1.1 Given their varying preferences, they decide to shop separately, after dividing the household income equally. The household income is $8. One difference to the usual setting there are government restrictions in place so that no individual is allowed to buy more than two units of either good. Hint: Do n_ot use mathematical brute force (like Calculus) to solve this problem. A simple diagram with appropriate budget lines, etc. should suice. 1) Suppose prices are p = (101,112) = (1, 2). Denote the optimal choice of A and B as a = (a1, a2) and b = (b1, ()2) respectively. Solve and calculate this explicitly. 2) Now suppose the prices change to q =(q1,q2) = (2,1). Again. obtain the optimal choices for A and B, denote them by (1: ((31,02) and d: (d1,d2). 3) Now, you are an outside observer. All that you observe is that at p the household chose the bundle x = a + b was chosen and price q the bundle y = c + d was chosen. If you had mistakenly assumed that the household was a one individual, would you conclude that this individual is behaving rationally, i.e. maximizing a preference relation? Comment