Marginal Cost

Business Calculus · Axiom Academy

The cost of producing one more unit - the derivative in action The Central Question in Business Every business faces a crucial question: "Should we produce one more unit?" To answer this, we need to know: How much does it cost to make that extra unit? This is called the marginal cost . Total cost divided by total quantity Tells you cost per unit on average Cost of producing the next unit Tells you cost of one more unit right now If C(q) is the total cost function, where q is the quantity produced, then the marginal cost is: This represents the instantaneous rate of change of cost with respect to quantity. Interpretation: MC(q) tells you approximately how much your total cost increases when you produce one more unit beyond q units. A company's total cost function for producing widgets is: where q is the number of widgets and C(q) is in dollars. Find the marginal cost function and evaluate it at q = 100. Notice how the marginal cost curve: Decreases at first - due to efficiencies of scale (learning curve, bulk discounts) Then increases - as production reaches capacity (overtime, equipment strain, diminishing returns) The minimum point often represents the most efficient production level Marginal cost is essential for making optimal business decisions: If selling one more unit brings in 10 (marginal revenue) and costs 5 (marginal cost), you should produce it! Profit rule: Produce if MR > MC

This is the written version of the interactive lesson above. See the full Business Calculus course.