During the height of pandemic in 2021, 60% of total hours worked were from home. While the numbers will come down once the pandemic is over, experts believe that work from home (WFH) is here to stay for some occupations.

Karina spends 2 hours every day in commuting from home to work and then back (1 hour each way). Her utility over consumption (C), hours worked (H), and hours spent in commute (S) is given by:

U(C, H) = C - 1.5(H + S)²

Assume that (a) price of C is $1 (b) S = 2. For simplicity, assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting. Spending more than 12 hours in work reduces worker productivity to zero, so we assume that:

0 H 12

(a) During the pandemic, Karina has worked from home. Research on working from home (WFH) shows that individuals typically spend about 50% of the time saved (from commuting) in working and 50% in leisure activities.

(i) We model working from home as a reduction of S from S = 2 to S = 0. How much of those 2 hours saved does Karina spends in work? Does it match with the research finding?

(ii) To save costs, Karina's employer is considering a wage cut for its employees working from home. Karina will be prepared to accept a cut in hourly wages (w) if w does not fall below ____________________ (write up to two decimal places). [Note: Karina accepts a wage cut as long as her utility does not fall below pre-WFH utility]

(iii) Wage cuts have been strongly resisted by the employees as they realized that they need extra space to work productively from home. For example, it will cost Karina R dollars more per day. Karina will opt for WFH if and only if her utility from doing so is higher than her utility under the status quo (with 2 hours' commuting time). This means Karina will opt for WFH if and only if R is less than ___________________. Explain.

[Assume Karina opts for WFH if she is indifferent between WFH and commuting]