Chapter 9: Problem 5

Amy, Bill, and Carla all mow lawns for money. Each of them operates a different lawn mower. The accompanying table shows the total cost to Amy, Bill, and Carla of mowing lawns. $$ \begin{array}{cccc} \begin{array}{c} \text { Quantity of } \\\ \text { lawns mowed } \end{array} & \begin{array}{c} \text { Amy's } \\\ \text { total cost } \end{array} & \begin{array}{c} \text { Bill's } \\\ \text { total cost } \end{array} & \begin{array}{c} \text { Carla's } \\\ \text { total cost } \end{array} \\\ 0 & \$ 0 & \$ 0 & \$ 0 \\\ 1 & 20 & 10 & 2 \\\ 2 & 35 & 20 & 7 \\\ 3 & 45 & 30 & 17 \\\ 4 & 50 & 40 & 32 \\\ 5 & 52 & 50 & 52 \\\ 6 & 53 & 60 & 82 \end{array} $$ a. Calculate Amy's, Bill's, and Carla's marginal costs, and draw each of their marginal cost curves. b. Who has increasing marginal cost, who has decreasing marginal cost, and who has constant marginal cost?

Short Answer

Expert verified

Answer: Amy has decreasing marginal costs, Bill has constant marginal costs, and Carla has increasing marginal costs.

Step by step solution

Calculate the marginal costs.

To find the marginal cost (MC) for each person, subtract the total cost of mowing the previous lawn (TCL-1) from the total cost of mowing the current lawn (TCL). That is, MC = TCL - TCL-1. Perform this calculation for Amy, Bill, and Carla for each quantity of lawns mowed.

Analyze the marginal costs.

Observe the computed marginal costs to determine who has increasing, decreasing, and constant marginal costs. An increasing MC is when the MC increases as the quantity of lawns mowed increases; a decreasing MC is when the MC decreases as the quantity of lawns mowed increases; and a constant MC is when the MC remains the same regardless of the number of lawns mowed.

Draw each person's marginal cost curve.

Plot the marginal cost (y-axis) against the quantity of lawns mowed (x-axis) for each person on separate graphs or on a single graph with different colors or symbols to represent each person.

Calculating Marginal Costs:

Refer to the table, and calculate the marginal costs for each person: - Amy: $\operatorname{MC} = (20-0, 35-20, 45-35, 50-45, 52-50, 53-52) = (20, 15, 10, 5, 2, 1)$ - Bill: $\operatorname{MC} = (10-0, 20-10, 30-20, 40-30, 50-40, 60-50) = (10, 10, 10, 10, 10, 10)$ - Carla: $\operatorname{MC} = (2-0, 7-2, 17-7, 32-17, 52-32, 82-52) = (2, 5, 10, 15, 20, 30)$

Analyzing Marginal Costs:

Based on the calculated marginal costs: - Amy has decreasing marginal costs, as the MC decreases as the quantity of lawns mowed increases. - Bill has constant marginal costs, as the MC remains the same regardless of the number of lawns mowed. - Carla has increasing marginal costs, as the MC increases as the quantity of lawns mowed increases.

Drawing Marginal Cost Curves:

To plot the marginal cost curves, set the x-axis as the number of lawns mowed and the y-axis as the marginal cost. The curve for Amy would be downward sloping, Bill's curve would be a horizontal line, and Carla's curve would be an upward-sloping line.