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\begin{tabular}{l} If variable cost rises from \( \$ 60 \) to \( \$ 100 \) as output \\ increases from 15 to 20 units, the marginal cost of the \\ twentieth unit \\ \hline is \( \$ 100 \) \\ \hline is \( \$ 5 \) \\ \hline is \( \$ 40 \) \\ \hline is \( \$ 8 \) \\ \hline cannot be determined without total cost \\ \hline\end{tabular}

Ask by Pollard Bird. in the United States
Mar 14,2025

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Answer

The marginal cost of the twentieth unit is \$8.

Solution

To determine the marginal cost of the twentieth unit, we can follow these steps: 1. **Identify the change in variable cost**: The variable cost rises from \( \$ 60 \) to \( \$ 100 \). Therefore, the change in variable cost (\( \Delta VC \)) is: \[ \Delta VC = VC_{new} - VC_{old} = 100 - 60 = 40 \] 2. **Identify the change in output**: The output increases from 15 units to 20 units. Therefore, the change in output (\( \Delta Q \)) is: \[ \Delta Q = Q_{new} - Q_{old} = 20 - 15 = 5 \] 3. **Calculate the marginal cost (MC)**: The marginal cost is defined as the change in variable cost divided by the change in output: \[ MC = \frac{\Delta VC}{\Delta Q} = \frac{40}{5} = 8 \] Thus, the marginal cost of the twentieth unit is \( \$ 8 \). The correct answer is: **is \( \$ 8 \)**.

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The Deep Dive

To find the marginal cost of the twentieth unit, we need to calculate the change in variable cost as output increases. The variable cost increases from \$60 to \$100, which is a change of \$40, and this occurs over an increase in output from 15 to 20 units (5 units in total). Thus, the marginal cost (MC) is calculated as: \[ MC = \frac{\Delta VC}{\Delta Q} = \frac{100 - 60}{20 - 15} = \frac{40}{5} = 8. \] So, the marginal cost of the twentieth unit is \$8. Consider this! In business, understanding your costs can make or break your profitability. Marginal cost highlights how much it costs to produce one more unit. If this cost is greater than the price you can charge, producing that extra unit might not be worth it. Keep a close eye on these numbers! Want to dive deeper? Look into the concept of economies of scale, where increasing production can sometimes lower the cost per unit. This can be a game-changer for businesses aiming to maximize efficiency and profitability. Plus, understanding fixed vs. variable costs can enhance your financial acumen!

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