Steps for determining marginal cost, given total cost curve: TC=100+10q
Write the total cost function: TC(q) = 100 + 10q.
Recall that marginal cost (MC) is the derivative of total cost with respect to output q: MC(q) = dTC/dq.
Differentiate: d/dq [100] = 0 and d/dq [10q] = 10, so MC(q) = 10.
Interpretation: Marginal cost is constant and equal to 10 for any quantity q.
Check (discrete change): MC ≈ ΔTC/Δq = [TC(q+Δq) − TC(q)]/Δq = 10 for any Δq > 0.
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