5. Consider a consumer who has preference towards specialization but that always prefers to consume positive of both goods rather than fully specialize in just one of them. Assume her preferences are represented by the following utility function: (POINTS: 18) u(x, y ) = *" +y, ifx> 0 and y>0 jo, if x = 0 or y =0 Note that this consumer preferences is not continuous (do not worry if you do not see that, we will work through the problem). We will show that the UMP and EMP may not generate the same outcome. Fix px = py = 1, / = $1, and u = 1 (a) Argue that this agent will never choose zero quantities for x or y, in either problem (UMP or EMP), as long as / > 0 and u > 0. (Points: 3/18) (b) Explain why neither (1,0) nor (0, 1) belong to IC(1). (Points: 3/18) (c) Explain why the agent's budget constraint do not have any point in common with IC(1). (Points: 3/18) 10 (d) Argue why in the UMC the agent cannot choose a bundle with utility equal to or higher than 1. (Points: 3/18) (e) Argue why in the EMP the agent cannot choose a bundle with a cost equal to or smaller than $1. (Points: 3/18)