Question

Question 2: 8 marks (1, 1, 1, 2, 3) Deborah’s utility over consumption (C), hours worked (H), and hours spent in commute (S) is: (1) U (C, H) = C1/2 – H – S. The maximum number of hours that Deborah can work productively is 10. Thus (2) 0 ≤ H ≤ 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) If H > 0, S = 2. Else if H = 0, S = 0. Assume that ≥ 0 and ≥ 0. For simplicity, we also assume that there are no other costs (e.g., ticket costs, parking fee) associated with commuting.

(2 marks) Deborah’s income is hourly wage (w) times the hours worked (H). Suppose w = $32 per hour and price of C is $1. How many hours would Deborah work to maximize her utility? How much C will Deborah choose? Assume that Deborah has no other sources of income.

(3 marks) Deborah has received a new job 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 answer.

Answer 1

To maximize her utility, Deborah would work 10 hours and consume 2 units of C.

Step-by-step explanation:

In order to maximize her utility, Deborah must find the combination of hours worked (H) and consumption (C) that will provide her with the highest level of satisfaction. To determine the optimal number of hours Deborah should work, we need to find the intersection of her budget constraint and her indifference curve.

Her budget constraint is determined by the number of hours she can work (10) and her hourly wage ($32). Her indifference curve represents the various combinations of H and C that provide her with the same level of satisfaction. By solving the optimization problem, we can find that Deborah would choose to work 10 hours and consume 2 units of C.

Therefore, Deborah would work 10 hours and consume 2 units of C to maximize her utility.