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\begin{tabular}{l} 8) Alicia is currently spending \( \$ 6,000 \) per week on total variable costs \\ to produce 500 hats. To produce 505 hats per week she would have to \\ spend \( \$ 6,100 \) per week. The marginal cost per hat is _- \\ \hline OA) \( \$ 6,100 \) \\ OB) \( \$ 100 \) \\ OC) \( \$ 20 \) \\ OD) \( \$ 5 \)\end{tabular}

Ask by Knight John. in the United States
Mar 15,2025

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The marginal cost per hat is \$20.

Solución

To find the marginal cost per hat, we can use the following formula: \[ \text{Marginal Cost} = \frac{\text{Change in Total Cost}}{\text{Change in Quantity}} \] ### Step 1: Identify the known values - Current total variable cost for 500 hats: \( \$6,000 \) - Total variable cost for 505 hats: \( \$6,100 \) - Change in total cost: \( 6,100 - 6,000 = 100 \) - Change in quantity: \( 505 - 500 = 5 \) ### Step 2: Calculate the marginal cost Now we can substitute the values into the formula: \[ \text{Marginal Cost} = \frac{100}{5} \] ### Step 3: Perform the calculation Calculating the above expression gives: \[ \text{Marginal Cost} = 20 \] ### Conclusion The marginal cost per hat is \( \$20 \). Thus, the correct answer is **OC) \( \$20 \)**.

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The Deep Dive

To find the marginal cost per hat, we first determine the change in total costs and the change in quantity produced. Alicia's costs increase from \( \$ 6,000 \) to \( \$ 6,100 \) when she increases production from 500 hats to 505 hats. This means the total cost increases by \( \$ 100 \) for producing 5 additional hats. The marginal cost is calculated as: \[ \text{Marginal Cost} = \frac{\text{Change in Total Cost}}{\text{Change in Quantity}} = \frac{100}{5} = 20 \] So, the marginal cost per hat is \( \$ 20 \). Therefore, the answer is OC) \( \$ 20 \).

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