Lesson 3 of 12 · 6 min
Marginal cost and revenue
NCERT §6.2
Kavya already makes 100 boxes a week. Before taking an order for one more, she wants to know what that extra box will cost her and what it will bring in.
The lesson in notes
In short
In economics the word marginal means a rate of change. Marginal cost MC is dC/dx, the instantaneous rate of change of total cost C with the number of items x.
Marginal revenue MR is dR/dx, where R(x) is the total revenue from selling x units. It approximates the extra money earned by selling one more unit.
Worked example: C(x) = 0.005x³ − 0.02x² + 30x + 5000 gives MC = 0.015x² − 0.04x + 30. At x = 3 this is 0.135 − 0.12 + 30 = 30.015, about ₹30.02.
Worked example: R(x) = 3x² + 36x + 5 gives MR = 6x + 36, which is 66 at x = 5.
Profit is P = R − C, and marginal profit is MR − MC. Profit is largest where MR = MC and P″ < 0.
Worked example: items sold at a price of 5 − x/100 each, with total cost x/5 + 500, give P = 24x/5 − x²/100 − 500. P′ = 24/5 − x/50 = 0 at x = 240, and P″ = −1/50 < 0, so 240 items maximise profit.