Question

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

Amy has a U-shaped marginal cost curve, indicating increasing and then decreasing marginal cost. Bill's marginal cost is constant. Carla's marginal cost increases with each additional unit.

Step-by-step solution

Define Marginal Costs

Marginal cost is the change in total cost that arises when the quantity produced changes by one unit. To calculate marginal cost for each additional lawn, subtract the total cost of mowing the previous number of lawns from the total cost of mowing the current number of lawns.

Calculate Amy's Marginal Cost

For Amy: - The marginal cost of the 1st lawn is \( 20 - 0 = 20 \). - The marginal cost of the 2nd lawn is \( 35 - 20 = 15 \).- Continue this process for each additional lawn mowed.

Calculate Bill's Marginal Cost

For Bill: - The marginal cost of the 1st lawn is \( 10 - 0 = 10 \).- The marginal cost of the 2nd lawn is \( 20 - 10 = 10 \). - Continue this process for each additional lawn mowed.

Calculate Carla's Marginal Cost

For Carla: - The marginal cost of the 1st lawn is \( 2 - 0 = 2 \).- The marginal cost of the 2nd lawn is \( 7 - 2 = 5 \).- Continue this process for each additional lawn mowed.

Analyze Marginal Cost Trends

Amy's marginal costs decrease and then increase, hence Amy has a U-shaped marginal cost curve. Bill's marginal costs remain constant, so Bill has constant marginal costs. Carla's marginal costs increase with each additional lawn, making her marginal cost curve upward sloping (increasing marginal costs).

Draw Marginal Cost Curves

Plot the calculated marginal costs against the quantity of lawns mowed on a graph for each individual. This will visually represent the marginal cost curves. Each person's plot point is positioned above the quantity that induces the marginal cost.

Key concepts

Microeconomics

Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of scarce resources. It examines how these entities interact within a market to create supply and demand, which in turn determines prices. One of the key concepts in microeconomics is the analysis of costs, including both total costs and marginal costs, which play a crucial role in business decisions.

For example, in our exercise with Amy, Bill, and Carla, microeconomics would be concerned with how each individual decides how many lawns to mow based on their costs and the revenue they expect to receive. Understanding cost structures and the concept of marginal cost, which is central to microeconomic theory, allows these individuals to make informed decisions to maximize their profits.

Total Cost

Total cost in economics refers to the complete cost of production for a business or, in the case of our exercise, the total expense incurred by Amy, Bill, and Carla for mowing lawns. The total cost includes both fixed costs, which do not change regardless of the activity level (such as the purchase price of the lawn mowers), and variable costs, which fluctuate with the level of output (like fuel or maintenance expenses).

An important aspect of total cost is understanding how it varies with the quantity of output produced. In the exercise, each individual has a unique total cost structure. For instance, Amy's total cost starts at $0 for no lawns mowed, and increases as more lawns are mowed. The progression of these costs gives us insight into how efficient each person is at mowing lawns and often indicates the existence of economies or diseconomies of scale. Managers and economists analyze total costs to set prices, determine break-even points, and establish production levels.

Cost Analysis

Cost analysis is an evaluation process that allows a business or individual, like our lawn mowers Amy, Bill, and Carla, to determine the most cost-effective way of achieving a desired level of production or service. This analysis involves weighing the total costs against the benefits of different levels of production or activities to identify the optimal point of operation.

In the context of our exercise, cost analysis would involve examining the different total cost values for Amy, Bill, and Carla as they mow more lawns. By calculating the marginal cost, they can analyze the incremental cost of mowing each additional lawn and make informed decisions about their lawn mowing businesses. For example, if the price they can charge for mowing one additional lawn is greater than the corresponding marginal cost, it may make sense to mow that additional lawn. Cost analysis is a fundamental tool for financial planning and for assessing the profitability of specific actions or strategies.