Question

Rhonda has hired a worker to stand on the corner and wave a sign advertising her business. It costs her $10 per hour to have this worker stand on the corner. Rhonda is trying to decide how many hours per day she should hire this worker to stand on the corner. Each customer spends an average of $3 when they visit her store. She has been tracking her daily customers as a function of the number of hours per day the worker waves the sign and has found the following information:Hours per day Total Customers0 501 652 753 814 855 88When Rhonda hires the worker to wave the sign for one hour per day, the marginal cost is $ ____ and the marginal benefit is $ ____ . When Rhonda hires the worker to wave the sign for two hours per day, the marginal cost of the second hour is $ ___ and the marginal benefit of the second hour is $ ___ . Enter whole numbers.

Answer 1

When Rhonda hires the worker to wave the sign for one hour per day, the marginal cost is $10 and the marginal benefit is $35. When Rhonda hires the worker to wave the sign for two hours per day, the marginal cost of the second hour is $10 and the marginal benefit of the second hour is $20.

Step-by-step explanation:

The marginal cost is a cost in economics used to measure the amount that will be incurred for making an additional unit of a product or rendering an additional unit of a service. It is generally calculated by dividing the difference in the total cost at two different levels of activity by the difference in the corresponding number of products at the two levels. That is,

`(Difference in Total Cost)/(Difference in levels of activity)`

Since it costs Rhonda $10 per hour the worker waves the sign, it is easy to calculate the total cost at different levels of work. This means 1 hour of waving the sign = $10 × 1 = $10, 2 hours of waving the sign = $10 × 2 = $20, and so on.

Marginal cost for every hour is therefore $10.

The concept also applies to marginal benefit. Benefit here implies revenue from business less cost incurred.

For when the worker waves the sign:

For 0 hour, revenue = $3 (average customer spending) × 50 = $150.

For 1 hour, revenue = $3 × 65 = $195

For 2 hours, revenue = $3 × 75 = $225

Marginal Revenue:

For 1 hour =
`\frac {195-150}{1 hr - 0 hr}` = $45

For 2 hours =
`\frac {225-195}{2hr-1hr}` = $30

Therefore, marginal benefit at 1 hour = $45 - $10 = $35

Marginal benefit at 2 hours = $30 - $10 = $20