Deborah's utility over consumption (C), hours worked (H), and hours spent in commute (S) is: (1) U(C, H)=C\"2HS. The maximum number of hours that Deborah can work productively is 10. Thus (2) 0 s H s 10. On the days which Deborah works, she spends 2 hours in commuting from home to work and then back (one hour each way). (3) lfH>0,S=2.ElseifH=0,S=0. Assume that C 2 0 and S 2 0. For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting. (a) (1 mark) Explain why Deborah's preferences are not strongly monotone in C and H. Use an example to support your answer. (3 marks) Deborah has received a newjob offer which pays $w* an hour. However, it requires relocation closer to city where prices are at least 30% higher. More concretely, price of C is $1.30 instead of $1. On the plus side, relocation will cut down Deborah's commuting time from 2 hours per day to 30 minutes per day (15 minutes each way). That is, S will decline from S = 2 to S = 0.5. Deborah is a utility maximizer. Deborah will accept the offer if and only if w* > Fill in the blank. Explain your