Marginal Cost Example

Business Calculus · Axiom Academy

Finding and interpreting the marginal cost function Problem: Electronics Manufacturer A company manufactures headphones. Their total cost function (in dollars) for producing x units is: Find the marginal cost function Calculate the marginal cost at x = 100, 200, and 300 units Marginal cost is the derivative of the total cost function: Apply the power rule to each term: Let's evaluate MC(x) = 15 + 0.02x at three production levels: At 100 units: The 101st headphone costs approximately 17 to produce At 200 units: The 201st headphone costs approximately 19 to produce At 300 units: The 301st headphone costs approximately 21 to produce Why is Marginal Cost Increasing? As production increases, each additional unit becomes more expensive. This could be due to: Equipment running less efficiently at high capacity Need for more expensive raw materials Diminishing returns as facilities become crowded Suppose the company sells each headphone for 20 . Where should they stop producing? Set MC = Price: 15 + 0.02x = 20 Solving: 0.02x = 5 , so x = 250 The company should produce 250 headphones to maximize profit at this price point. You've seen how marginal cost analysis helps businesses make production decisions. Based on the example above, which approach is correct?

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