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Molly’s utility function for recreation (R) and consumption (C) is U(R,C) = R 1/4 C 3/4 . If the price of consumption is 1, Molly’s non-wage income is $90 per day, and she can allocate 15 hours per day to labor or recreation, her reservation wage is: a) $1 per hour b) $1/12 per hour c) $18 per hour d) $2 per hour e) None of the above

User Manman
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Answer:

To find Molly's reservation wage, we need to determine the wage rate at which she would be indifferent between working and enjoying leisure time.

Molly's utility function is given as U(R,C) = R^(1/4) * C^(3/4), where R represents recreation and C represents consumption.

Given that Molly has 15 hours per day to allocate to labor or recreation, we can assume that if she chooses labor, she will have no time for recreation (R = 0) and if she chooses recreation, she will have no time for labor (C = 0).

Using the given information:

- Molly's non-wage income is $90 per day.

- The price of consumption is 1.

Let's consider the scenario where Molly chooses labor (C = 0). In this case, her income would solely come from her wage.

Using the utility function, we can calculate the utility level when C = 0:

U(0, C) = (0)^(1/4) * C^(3/4) = 0

This means that when Molly chooses labor, her utility level is 0, as she has no time for recreation. Therefore, her income from labor should compensate for the loss in utility from not engaging in recreation.

Since her non-wage income is $90 per day, her wage income should also be $90 to keep her utility level at 0. As she has 15 hours per day to allocate to labor, her reservation wage per hour would be:

Reservation wage = Wage income / Hours allocated to labor

Reservation wage = $90 / 15 hours = $6 per hour

Therefore, none of the options provided (a) $1 per hour, b) $1/12 per hour, c) $18 per hour, d) $2 per hour) is the correct reservation wage.

The correct answer is e) None of the above, with the correct reservation wage being $6 per hour.

User Josh Potter
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