Question

Given the total cost and total fixed cost data of table 1 , calculate the total variable cost incurred at each level of output. $$ \begin{aligned} &\text { Table } 1\\\ &\begin{array}{|l|l|l|} \hline \text { Quantity Produced } & \text { Total fixed cost } & \text { Total cost } \\ \hline 1 & \$ 1000 & \$ 1500 \\ \hline 2 & 1000 & 1950 \\ \hline 3 & 1000 & 2350 \\ \hline 4 & 1000 & 2700 \\ \hline 5 & 1000 & 3000 \\ \hline 6 & 1000 & 3300 \\ \hline 7 & 1000 & 3650 \\ \hline 8 & 1000 & 4000 \\ \hline 9 & 1000 & 4400 \\ \hline 10 & 1000 & 4900 \\ \hline \end{array} \end{aligned} $$

Short answer

The Total Variable Costs (TVC) for each level of output are as follows: \( \$500, \$950, \$1350, \$1700, \$2000, \$2300, \$2650, \$3000, \$3400, \$3900 \).

Step-by-step solution

Create a column for Total Variable Cost (TVC) in Table 1

First, let's extend Table 1 to include a new column for Total Variable Cost (TVC). The extended table should look like this: $$ \begin{aligned} &\text { Table } 1\\\ &\begin{array}{|l|l|l|l|} \hline \text { Quantity Produced } & \text { Total fixed cost } & \text { Total cost } & \text { Total variable cost (TVC) }\\\ \hline 1 & \$ 1000 & \$ 1500 & \\ \hline 2 & 1000 & 1950 & \\ \hline 3 & 1000 & 2350 & \\ \hline 4 & 1000 & 2700 & \\ \hline 5 & 1000 & 3000 & \\ \hline 6 & 1000 & 3300 & \\ \hline 7 & 1000 & 3650 & \\ \hline 8 & 1000 & 4000 & \\ \hline 9 & 1000 & 4400 & \\ \hline 10 & 1000 & 4900 & \\ \hline \end{array} \end{aligned} $$

Calculate the Total Variable Cost for each level of Output

Now, we will calculate the Total Variable Cost (TVC) for each level of output by subtracting the Total Fixed Cost from the Total Cost using the formula: TVC = Total Cost - Total Fixed Cost. The calculations for each level of output are as follows: 1. TVC = \$1500 - \$1000 = \$500 2. TVC = \$1950 - \$1000 = \$950 3. TVC = \$2350 - \$1000 = \$1350 4. TVC = \$2700 - \$1000 = \$1700 5. TVC = \$3000 - \$1000 = \$2000 6. TVC = \$3300 - \$1000 = \$2300 7. TVC = \$3650 - \$1000 = \$2650 8. TVC = \$4000 - \$1000 = \$3000 9. TVC = \$4400 - \$1000 = \$3400 10. TVC = \$4900 - \$1000 = \$3900

Fill in the TVC values in Table 1

Finally, we will fill in the calculated Total Variable Costs (TVC) in the newly created column in Table 1: $$ \begin{aligned} &\text { Table } 1\\\ &\begin{array}{|l|l|l|l|} \hline \text { Quantity Produced } & \text { Total fixed cost } & \text { Total cost } & \text { Total variable cost (TVC) }\\\ \hline 1 & \$ 1000 & \$ 1500 & \$ 500\\ \hline 2 & 1000 & 1950 & \$ 950 \\ \hline 3 & 1000 & 2350 & \$ 1350 \\ \hline 4 & 1000 & 2700 & \$ 1700 \\ \hline 5 & 1000 & 3000 & \$ 2000 \\ \hline 6 & 1000 & 3300 & \$ 2300 \\ \hline 7 & 1000 & 3650 & \$ 2650 \\ \hline 8 & 1000 & 4000 & \$ 3000 \\ \hline 9 & 1000 & 4400 & \$ 3400 \\ \hline 10 & 1000 & 4900 & \$ 3900 \\ \hline \end{array} \end{aligned} $$ Now, we have the Total Variable Cost (TVC) for each level of output in Table 1.

Key concepts

Total Fixed Cost

Total Fixed Costs (TFC) are expenses that do not change with the level of output produced by a business. These costs are 'fixed' over a specified period and are not affected by fluctuations in production levels. Examples of fixed costs include rent, salaries of full-time employees, insurance, and loan payments.

In the provided exercise, the total fixed cost is given as $1000 across all levels of output from one unit to ten units. This shows a typical characteristic of fixed costs - they remain constant regardless of the quantity produced. Understanding total fixed costs is vital for businesses as it helps in determining the pricing strategy, budgeting, and forecasting profits.

Total Cost

Total Cost (TC) in economics refers to the sum of all costs incurred by a business to produce a certain level of output. It includes both fixed and variable costs. The formula to calculate Total Cost is TC = TFC + TVC, where TFC represents Total Fixed Costs, and TVC denotes Total Variable Costs.

In our exercise, we consider total costs at various levels of production, which help us understand how costs accumulate as more units are produced. By analyzing total costs in relation to the number of goods produced, businesses can make informed decisions regarding production levels, cost control, and pricing strategies.

Cost Calculation in Economics

Cost calculation in economics is a fundamental concept involving the analysis and summing up of different types of costs within business operations. It assists in decision-making and strategic planning. To calculate Total Variable Costs (TVC), we use the formula TVC = TC - TFC. Variable costs change with the level of production, such as raw materials and hourly wages.

The exercise provided exemplifies cost calculation by determining the TVC at different levels of output. Accurate cost calculation ensures effective pricing models and helps to identify the break-even point, where the total revenues equal total costs, leading to no profit or loss. Understanding how total fixed costs, total variable costs, and total costs interact provides a complete picture of a business's financial health and operational efficiency.