Question

Jacked Jackets, Inc. is a successful small business that has purchased a new location for their operations. While it is cost-effective, they are limited to 500 square-footage at the new production facility. As their name suggests, they sew jackets, and they buy materials for these items in bulk as needed. Each worker they hire costs $25 per hour. The company rents a single machine for $40 per day at each location. Using the first location as quantitative reference, the following output parameters exist for these workers:

W2 Labor Daily Output
0 0
1 5
2 10
3 11
4 14
5 15

Assignment

In Excel, assemble a table calculating the following costs:

Average fixed cost

Average variable cost

Average total cost

Marginal Cost

Marginal Product

Value of Marginal Product

Create charts for both the production function and the total cost curve

Using Excel analytics, how many workers should Jacked Jackets hire? Explain your answer. What unspecific factors play a role in this as well?

You should also note that Jacked Jackets typically sell for a net price of $100 per jacket. Also assume the workers on an 8-hour wage schedule. Given this new knowledge, does this impact your previous recommendation?

Answer 1

Jacked Jackets should hire workers up until the point where the Value of Marginal Product equals or exceeds the worker's daily cost. They should create a table to calculate costs, use Excel to chart the production function and the total cost curve, and consider demand, space, and capacity when making hiring decisions.

Step-by-step explanation:

To determine the optimal number of workers Jacked Jackets should hire, we first need to assemble a table with the relevant costs – Average Fixed Cost (AFC), Average Variable Cost (AVC), Average Total Cost (ATC), Marginal Cost (MC), Marginal Product (MP), and the Value of Marginal Product (VMP). We calculate these by using the formulae:

• AFC = Fixed Cost / Quantity of Output
• AVC = Variable Cost / Quantity of Output
• ATC = AFC + AVC
• MC = Change in Total Cost / Change in Quantity of Output
• MP = Change in Output / Change in Labor
• VMP = MP x Net Price per Jacket

The firm's fixed cost is the rental of the machine ($40), and the variable cost is the cost of labor ($25 per hour per worker, with each worker on an 8-hour schedule). Charts for the production function and the total cost curve can be created by plotting the data from the table. Utilizing Excel analytics, we can also calculate the derivative of the total cost function to find out where marginal cost equals marginal revenue (price of the product).

Considering that Jacked Jackets sell their jackets at $100 each, the VMP should be compared with the labor cost. The company should hire workers up to the point where the VMP equals or exceeds the worker's cost ($200 per day). This will maximize profit without increasing costs unnecessarily. Additional factors that may influence the decision include demand forecasts, space constraints, and production capacity.