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.