Question

From the data supplied in Table 1 , determine the cost of each unit produced. $$ \begin{aligned} &\text { Table }\\\ &\begin{array}{|c|c|c|} \hline \text { Output } & \text { Average Fixed Cost } & \underline{\text { Average Variable Cost }} \\ \hline 0 & \$ 10.00 & 0 \\ \hline 1 & 10.00 & \$ 20.00 \\ \hline 2 & 5.00 & 19.50 \\ \hline 3 & 3.33 & 19.00 \\ \hline 4 & 2.50 & 18.50 \\ \hline 5 & 2.00 & 18.00 \\ \hline 6 & 1.67 & 17.50 \\ \hline 7 & 1.42 & 17.29 \\ \hline 8 & 1.25 & 17.25 \\ \hline 9 & 1.11 & 17.33 \\ \hline 10 & 1.00 & 17.50 \\ \hline \end{array} \end{aligned} $$

Short answer

Based on the given data in Table 1, the cost of each unit produced for different outputs is as follows: - For Output = 1, Cost per unit = $30.00 - For Output = 2, Cost per unit = $24.50 - For Output = 3, Cost per unit = $22.33 - ... continue to do the same for other output rows as well.

Step-by-step solution

Calculate Total Cost for each output row

Use the given formula to calculate the Total Cost for each output row: $$ \text{Total Cost} = \text{Average Fixed Cost} \times \text{Output} + \text{Average Variable Cost} \times \text{Output} $$ - For Output = 1, Total Cost = \(10.00 \times 1 + \)20.00 \times 1 = $30.00 - For Output = 2, Total Cost = \(5.00 \times 2 + \)19.50 \times 2 = $49.00 - For Output = 3, Total Cost = \(3.33 \times 3 + \)19.00 \times 3 = $67.00 - ... continue to do the same for other output rows as well.

Calculate the cost of each unit produced

To find the cost of each unit produced, you'll divide the Total Cost for each output row by its corresponding Output: $$ \text{Cost per unit} = \frac{\text{Total Cost}}{\text{Output}} $$ - For Output = 1, Cost per unit = \(\frac{\)30.00}{1} = $30.00 - For Output = 2, Cost per unit = \(\frac{\)49.00}{2} = $24.50 - For Output = 3, Cost per unit = \(\frac{\)67.00}{3} = $22.33 - ... continue to do the same for other output rows as well. In conclusion, the cost of each unit produced can be calculated by first finding the Total Cost for each output row and then dividing it by the corresponding Output.

Key concepts

Understanding Average Fixed Cost

Average Fixed Cost (AFC) is a crucial concept in cost analysis. It represents the fixed cost per unit of output. These costs do not vary with the level of production. For example, expenses like rent or salaried personnel are constant irrespective of how many units you produce. To find the AFC, you divide the total fixed costs by the number of units produced: \[ \text{AFC} = \frac{\text{Total Fixed Cost}}{\text{Output}} \]One important aspect of AFC is that as production increases, the AFC per unit decreases. This phenomenon is known as spreading overhead. Let's consider this as a strategy to achieve cost efficiency. If an increase in production volume lowers the fixed cost burden per individual unit, your business can potentially improve overall profitability.
Through this simple calculation, businesses gain insight into how effectively they are using their fixed assets, which is vital for strategic planning.

Exploring Average Variable Cost

Average Variable Cost (AVC) pertains to costs that fluctuate with your level of production, such as raw materials and hourly wages. It is calculated by dividing the total variable costs by the output:\[ \text{AVC} = \frac{\text{Total Variable Cost}}{\text{Output}} \]Understanding AVC is important as it helps businesses gauge the efficiency of variable inputs and control costs. In Table 1 of the given exercise, for instance, you'll notice a general downward trend in AVC as production increases from 1 to 10 units. This could mean that as you produce more units, you utilize resources more efficiently, potentially getting discounts on bulk purchases of materials.
Monitoring AVC is essential for businesses wanting to maximize profits because variable costs often represent a significant portion of total expenses. Keeping track of AVC also assists in pricing strategies and ensuring competitiveness within the market.

Grasping Total Cost Calculation

Total Cost (TC) combines all costs of production, both fixed and variable. This measurement provides a comprehensive view of a business's expenses. The Total Cost for each level of output is calculated as:\[ \text{Total Cost} = (\text{Average Fixed Cost} \times \text{Output}) + (\text{Average Variable Cost} \times \text{Output}) \]Calculating TC is significant because it forms the basis for understanding overall profitability and financial performance. In the exercise, for example, you add up fixed and variable costs for each output level to determine the TC.
By evaluating TC, businesses understand how costs change with production volume. This understanding can guide decisions on scaling operations, entering new markets, or adjusting production strategies to improve margin.

Decoding Unit Cost

Unit cost, also known as cost per unit, helps determine the expense associated with producing a single unit of output. It's a useful metric in assessing pricing strategies and cost efficiency. You calculate it by dividing the Total Cost by the amount of output:\[ \text{Unit Cost} = \frac{\text{Total Cost}}{\text{Output}} \]This calculation reveals the average cost to produce a specific quantity of goods. It helps businesses ensure they are pricing products above the unit cost to achieve profitability. When unit costs drop, it could be a result of gaining production efficiencies or economies of scale.
Analyzing unit costs can also indicate whether a company is optimally using its resources, and it's particularly essential during financial planning and budget management to align production costs with revenue targets.