Question

The per-unit cost of an item is its average total cost (= total cost/quantity). Suppose that a new smartphone app costs \(100,000 to develop and only \)0.50 per unit to deliver to each smartphone customer. What will be the per-unit cost of the app if it sells 100 units? 1,000 units? 1 million units?

Short answer

• The per-unit cost of the app is $1000.5 if the company sells 100 units.
• The per-unit cost of the app is $100.5 if the company sells 1000 units.
• The per-unit cost of the app is $0.6 if the company sells 1 million units.

Step-by-step solution

Step 1. Calculation of per-unit cost when the company sells 100 units of a smartphone app

The per-unit cost is determined by calculating the average total cost (=total cost/quantity). The cost of developing the smartphone app is $100,000, and the cost of delivering the app to each smartphone customer is $0.50. The total cost of the smartphone app is (development cost + delivery charge x no. of units sold). The number of units sold is 100.

$$\begin{gathered} Per-unit\cos t=\frac{Total\cos t}{Quantitysold} \\ =\frac{Development\cos t+\left(Deliverycharge\times No.ofunitssold\right)}{No.ofunitssold} \\ =\frac{\$100000+\left(\$0.50\times 1000\right)}{1000} \\ =\$100.5 \end{gathered}$$

The per-unit cost of the smartphone app, after 100 units are sold, is $100.5.

Step 3. Calculation of per-unit cost when the company sells 1 million units of smartphone app

The number of units sold is 1 million. By applying the average total cost formula, the per-unit cost of the app is calculated below:

$$\begin{gathered} Per-unit\cos t=\frac{Total\cos t}{Quantitysold} \\ =\frac{Development\cos t+\left(Deliverycharge\times No.ofunitssold\right)}{No.ofunitssold} \\ =\frac{\$100000+\left(\$0.50\times 1000000\right)}{1000000} \\ =\$0.6 \end{gathered}$$

The per-unit cost of the smartphone app, after 1 million units are sold, is $0.6.