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

0H12

(a) Is Karina's preference monotone in C and H? Explain in detail.

(b) Draw an indifference curve in (H, C) space that yields U = 32. Make sure to

Plot hours worked (H) in horizontal axis and (C) in vertical axis.

Plot two points: one where H = 0 and another where H = 12.

(c) Karina's income is hourly wage (w) times the hours worked (H). Suppose w = $30 per hour. How many hours would Karina work to maximize her utility? How much C will Karina consume? Assume that Karina has no other sources of income.