Question

Magnificent Blooms is a florist specializing in floral arrangements for weddings, graduations, and other events. Magnificent Blooms has a fixed cost associated with space and equipment of \(\$ 100\) per day. Each worker is paid \(\$ 50\) per day. The daily production function for Magnificent Blooms is shown in the accompanying table. a. Calculate the marginal product of each worker. What principle explains why the marginal product per worker declines as the number of workers employed increases? b. Calculate the marginal cost of each level of output. What principle explains why the marginal cost per floral arrangement increases as the number of arrangements increases?

Short answer

Answer: The Marginal Cost per floral arrangement increases as the number of arrangements increase due to the Law of Diminishing Returns. As more output is produced, the marginal product per worker declines, which means that it takes more resources (workers) to produce each additional floral arrangement, and the cost of those resources also increases.

Step-by-step solution

1. Understand the given information

Magnificent Blooms is a florist company with a fixed cost of \(100 per day and a variable cost of \)50 per day for each worker. The company has provided the daily production function in the form of a table.

2. Explain the concept of Marginal Product

Marginal Product (MP) is the additional output produced by using one additional unit of an input (in this case, a worker). MP is calculated as the change in total output divided by the change in quantity of input.

3. Calculate the Marginal Product of each worker

To calculate the marginal product of each worker, find the change in total output as each additional worker is employed. For example: MP of worker 1 = (Output with 1 worker - Output with 0 workers) MP of worker 2 = (Output with 2 workers - Output with 1 worker) MP of worker 3 = (Output with 3 workers - Output with 2 workers) Continue this process for each worker according to the given production function table.

4. Explain the reason for the decline in Marginal Product

The principle that explains why the marginal product per worker declines as the number of workers employed increases is the Law of Diminishing Marginal Returns. As more workers are employed, they have to share the available equipment and workspace, which leads to lower efficiency and less additional output produced by each additional worker.

5. Explain the concept of Marginal Cost

Marginal Cost (MC) is the additional cost incurred when producing an additional unit of output. It is calculated as the change in total cost divided by the change in output.

6. Calculate the Marginal Cost of each level of output

To calculate the marginal cost of each level of output, use the following formula: MC = Change in total cost / Change in output The total cost is the sum of the fixed costs and variable costs. In this case, fixed cost is \(100 per day, and the variable cost is \)50 per day per worker. For example: MC of the 1st floral arrangement = ((\(100 + 50 * 1) - \)100) / (Output with 1 worker - Output with 0 workers) MC of the 2nd floral arrangement = ((\(100 + 50 * 2) - (\)100 + 50 * 1)) / (Output with 2 workers - Output with 1 worker) MC of the 3rd floral arrangement = ((\(100 + 50 * 3) - (\)100 + 50 * 2)) / (Output with 3 workers - Output with 2 workers) Continue this process for each level of output according to the given production function table.

7. Explain the reason for the increasing Marginal Cost per floral arrangement

The principle that explains why the marginal cost per floral arrangement increases as the number of arrangements increases is the Law of Diminishing Returns. As more output is produced, the marginal product per worker declines, meaning that to produce each additional floral arrangement, it takes more and more resources (workers), and the cost of those resources also increases.

Key concepts

Marginal Cost

When analyzing a business like Magnificent Blooms, understanding Marginal Cost (MC) is crucial. Marginal cost refers to the added expense associated with producing one additional unit of output. It is calculated by the change in total cost divided by the change in output. This formula can be expressed as:\[ \text{MC} = \frac{\Delta \text{Total Cost}}{\Delta \text{Output}} \]For Magnificent Blooms, the total cost combines fixed costs like rent or equipment, and variable costs such as wages paid to workers, which total \$50 per worker each day.
To determine the marginal cost for each additional floral arrangement, you need to assess how costs shift with each increase in production. As production grows, you incur greater expenses despite hiring additional workers. This is primarily because these workers become less productive due to resource sharing, thereby increasing the overall costs for each new arrangement produced.

Law of Diminishing Returns

The Law of Diminishing Returns is a valuable principle in understanding how productivity changes with added resources. According to this law, if you add more units of a variable resource (such as workers) to a set amount of fixed resources (like workspace and equipment), there will come a point where each new worker adds less to the total output than the worker added before. For Magnificent Blooms, initially, hiring additional workers takes advantage of the fixed resources efficiently. However, as more workers join, they have to share the same equipment and workspace, which leads to congestion, ultimately reducing the additional output produced by each worker. This showcases the diminishing marginal product per worker, where each additional worker contributes progressively less to the total production.
As seen in the calculations, initially, hiring may boost productivity significantly. But with each extra worker, this boost will decrease, indicating less efficiency, which explains why the marginal cost of producing additional units eventually climbs.

Production Function

A production function illustrates the relationship between inputs used in production and the resulting output. It's a fundamental concept to grasp how factors of production like labor and capital result in various levels of output.
For Magnificent Blooms, the production function is displayed in their daily evaluations expressed in a table format. Changes in input, particularly labor, show varying levels of output. The combination of inputs aimed at maximizing output reflects efficiency under given conditions.
Utilizing the production function allows businesses to optimize their resource allocation. Identifying the point at which additional input fails to significantly increase output helps streamline operations. This relates directly to the Law of Diminishing Returns and affects calculations such as marginal cost. Through understanding the production function, Magnificent Blooms can make informed decisions on workforce levels and resource management to maintain efficiency while minimizing rising costs.