Question

The WipeOut Ski Company manufactures skis for beginners. Fixed costs are \(\$ 30 .\) Fill in Table 7.16 for total cost, average variable cost, average total cost, and marginal cost. $$\begin{array}{llllccc} \hline \text { Quantity } & \begin{array}{l} \text { Variable } \\ \text { cost } \end{array} & \begin{array}{l} \text { Fixed } \\ \text { cost } \end{array} & \begin{array}{l} \text { Total } \\ \text { cost } \end{array} & \begin{array}{c} \text { Average Variable } \\ \text { cost } \end{array} & \begin{array}{c} \text { Average Total } \\ \text { cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 & 0 & \$ 30 & & & & \\ \hline 1 & \$ 10 & \$ 30 & & & & \\ \hline 2 & \$ 25 & \$ 30 & & & & \\ \hline 3 & \$ 45 & \$ 30 & & & & \\ \hline 4 & \$ 70 & \$ 30 & & & & \\ \hline 5 & \$ 100 & \$ 30 & & & & \\ \hline 6 & \$ 135 & \$ 30 & & & & \\ \hline \end{array}$$

Short answer

The completed table is: $$\begin{array}{llllccc} \hline \text { Quantity } & \text { Variable cost } & \text { Fixed cost } & \text { Total cost } & \text { Average Variable cost } & \text { Average Total cost } & \text { Marginal cost } \\ \hline 0 & 0 & \$ 30 & \$ 30 & - & - & - \\ \hline 1 & \$ 10 & \$ 30 & \$ 40 & \$ 10 & \$ 40 & \$ 10 \\ \hline 2 & \$ 25 & \$ 30 & \$ 55 & \$ 12.50 & \$ 27.50 & \$ 15 \\ \hline 3 & \$ 45 & \$ 30 & \$ 75 & \$ 15 & \$ 25 & \$ 20 \\ \hline 4 & \$ 70 & \$ 30 & \$ 100 & \$ 17.50 & \$ 25 & \$ 25 \\ \hline 5 & \$ 100 & \$ 30 & \$ 130 & \$ 20 & \$ 26 & \$ 30 \\ \hline 6 & \$ 135 & \$ 30 & \$ 165 & \$ 22.50 & \$ 27.50 & \$ 35 \\ \hline \end{array}$$

Step-by-step solution

Calculate Total Cost (TC) for each quantity

Add Fixed Cost (FC) to Variable Cost (VC) for each quantity to find the Total Cost (TC): TC = FC + VC For example, for the first row with quantity 1: TC = \(30 + \)10 = $40

Calculate Average Variable Cost (AVC) for each quantity

Divide the Variable Cost (VC) by quantity (Q) to find the Average Variable Cost (AVC): AVC = VC / Q For example, for the first row with quantity 1: AVC = \(10 / 1 = \)10

Calculate Average Total Cost (ATC) for each quantity

Divide the Total Cost (TC) by the quantity (Q) to find the Average Total Cost (ATC): ATC = TC / Q For example, for the first row with quantity 1: ATC = \(40 / 1 = \)40

Calculate Marginal Cost (MC) for each quantity

The Marginal Cost (MC) is the increase in the Total Cost (TC) when producing one additional unit. To find MC, subtract the previous total cost from the current total cost: MC = TC_current - TC_previous For example, for the second row with quantity 2: MC = \(55 - \)40 = $15 The table with all the values calculated is: $$\begin{array}{llllccc} \hline \text { Quantity } & \begin{array}{l} \text { Variable } \\ \text { cost } \end{array} & \begin{array}{l} \text { Fixed } \\ \text { cost } \end{array} & \begin{array}{l} \text { Total } \\ \text { cost } \end{array} & \begin{array}{c} \text { Average Variable } \\ \text { cost } \end{array} & \begin{array}{c} \text { Average Total } \\ \text { cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { cost } \end{array} \\ \hline 0 & 0 & \$ 30 & \$ 30 & - & - & - \\ \hline 1 & \$ 10 & \$ 30 & \$ 40 & \$ 10 & \$ 40 & \$ 10 \\ \hline 2 & \$ 25 & \$ 30 & \$ 55 & \$ 12.50 & \$ 27.50 & \$ 15 \\ \hline 3 & \$ 45 & \$ 30 & \$ 75 & \$ 15 & \$ 25 & \$ 20 \\ \hline 4 & \$ 70 & \$ 30 & \$ 100 & \$ 17.50 & \$ 25 & \$ 25 \\ \hline 5 & \$ 100 & \$ 30 & \$ 130 & \$ 20 & \$ 26 & \$ 30 \\ \hline 6 & \$ 135 & \$ 30 & \$ 165 & \$ 22.50 & \$ 27.50 & \$ 35 \\ \hline \end{array}$$

Key concepts

Total Cost Calculation

Understanding how total costs are calculated in economics is fundamental for any business, including a company like WipeOut Ski Company. Total cost is simply the sum of all costs a company incurs to produce a given level of output. It consists of fixed costs, which do not vary with the output level, and variable costs, which do. In our exercise case, the fixed cost is \(\$30\) and does not change regardless of the number of skis produced.

To calculate the total cost (TC), we add the fixed cost (FC) to the variable cost (VC) for each quantity of output produced. For instance, if the company produces one pair of skis with a variable cost of \(\$10\), the total cost would be calculated as:\[TC = FC + VC = \$30 + \$10 = \$40\].

This straightforward formula is applied at each level of production to determine the total cost for different quantities, aiding in pricing strategies and financial planning for the company.

Average Variable Cost

Next, we delve into the concept of average variable cost (AVC), which is essential for businesses to understand the cost per unit of varying expenses related to production. In the case of WipeOut Ski Company, the variable costs would include materials, labor, and any other costs that increase with each additional ski produced.

To find the AVC, we divide the total variable cost by the quantity of goods produced. For example, if the variable cost for producing one ski is \(\$10\), the AVC is also \(\$10\), as it's the cost of producing that one ski:
\[AVC = \frac{VC}{Q} = \frac{\$10}{1} = \$10\].

This calculation is performed for each quantity level, allowing the company to understand how efficiency changes as production scales up.

Average Total Cost

Average total cost (ATC) is a crucial indicator for businesses to evaluate the per-unit cost of all expenses—both fixed and variable. The ATC helps in determining the breakeven price point for each product.

Similar to our earlier calculations, ATC is obtained by dividing the total cost by the quantity of output. For our ski company with its first ski sold, the ATC would be calculated like this:\[ATC = \frac{TC}{Q} = \frac{\$40}{1} = \$40\].

As output increases, the impact of the fixed cost diminishes, potentially leading to a decrease in the ATC, demonstrating economies of scale. It's an important metric for management decisions, pricing, and financial analysis.

Marginal Cost

Lastly, marginal cost (MC) is a term used frequently in economics, referring to the change in the total cost when an additional unit is produced. It is a measure of the cost of producing one more unit of a good.

In practice, MC is calculated by taking the difference between the total cost of producing 'n' units and 'n-1' units. For example, if producing two skis costs \(\$55\) in total and producing one ski costs \(\$40\), the MC for producing the second ski is:\[MC = TC_{current} - TC_{previous} = \$55 - \$40 = \$15\].

Determining the marginal cost is vital for understanding the implications of scaling up production and can assist in making informed production and pricing decisions. This concept is pivotal when a company must decide whether increasing production is beneficial or not in the long run.