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Chapter 21: Problem 14

Three college students are considering operating a tutoring business in economics. This business would require that they give up their current jobs at the student recreation center, which pay \(6,000 per year. A fully equipped facility can be leased at a cost of \)8,000 per year. Additional costs are \(1,000 a year for insurance and \).50 per person per hour for materials and supplies. Their services would be priced at $10 per hour per person. a. What are fixed costs? b. What are variable costs? c. What is the marginal cost? d. How many students would it take to break even?

Short Answer

Expert verified
Answer: The marginal cost is $0.50.

Step by step solution

01

a. Fixed Costs

Fixed costs are the expenses that don't change with the level of output. In this case, the fixed costs include the cost of leasing a facility (\(8,000) and the annual insurance cost (\)1,000). Adding these together, the fixed costs are \(8,000 + \)1,000 = $9,000 per year.
02

b. Variable Costs

Variable costs are the expenses that change with the level of output. In this case, the variable cost is \(0.50 per person per hour for materials and supplies. The price for their services is \)10 per hour per person. Let x represent the number of students tutored per hour, then the variable cost function is V(x) = $0.50x.
03

c. Marginal Cost

In this context, marginal cost is the additional cost to provide tutoring services for one more student per hour. Since the fixed costs do not change with output, the only component that affects the marginal cost is the variable cost. The marginal cost is the same as the variable cost for one more student, which is $0.50.
04

d. Breakeven Point

To find the breakeven point, we need to determine how many students should be tutored to cover all the fixed costs and variable costs. The revenue should be equal to the total costs. Let x represent the number of students tutored per hour. The revenue function is R(x) = \(10x, and the total cost function is C(x) = \)9,000 + $0.50x (fixed costs + variable costs). To find the breakeven point, we set the revenue function equal to the total cost function: \(10x = \)9,000 + $0.50x Solving for x, we get: \(9.50x = \)9,000 x = \dfrac{9,000}{9.50} x = 947.37$ Since it is not possible to tutor a fraction of a student, the three college students would need to tutor 948 students per hour to break even.

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