acalculator

How much is the marginal benefit?

Enter the total benefit at a starting quantity and at a new quantity. The marginal benefit calculator divides the change in total benefit by the change in quantity. Add a marginal cost to see whether one more unit is worth it.

Your numbers

Marginal benefit
10

From a quantity of 2 to 3, total benefit changes by 10: a marginal benefit of 10 per unit.

Change in total benefit
10
Change in quantity
1

Marginal benefit: 10. From a quantity of 2 to 3, total benefit changes by 10: a marginal benefit of 10 per unit.

The results are estimates for information only. They are not financial, tax, or legal advice. Check the numbers with your lender or a qualified professional before you decide. Terms of use

How to calculate

Computes marginal benefit, the change in total benefit divided by the change in quantity, and compares it with marginal cost to say whether one more unit is worth it.

Example with the default inputs (Starting quantity 2, Total benefit at the start 32, New quantity 3, Total benefit at the new quantity 42): From a quantity of 2 to 3, total benefit changes by 10: a marginal benefit of 10 per unit.

Method: Marginal benefit = (TB₂ − TB₁) ÷ (Q₂ − Q₁), where TB is total benefit at quantity Q. With a marginal cost MC: do more when MB > MC, do less when MB < MC, and stop where MB = MC.

  • Total benefit is in one unit throughout, such as dollars of willingness to pay or points.
  • Over more than one unit, the result is the average marginal benefit of each extra unit in that range.
  • Arithmetic is exact on the typed decimals; results show up to 6 decimals (6 significant figures below 0.0001 in size).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Starting quantity 2, Total benefit at the start 32, New quantity 3, Total benefit at the new quantity 42 gives Marginal benefit 10, Change in total benefit 10, Change in quantity 1.Source: Principles of Economics v2.0 (Saylor Academy open textbook, CC BY-NC-SA 3.0), 6.1 The Logic of Maximizing Behavior (marginal benefit is the amount by which an additional unit of an activity increases its total benefit; Laurie Phan’s economics study: total benefit 18, 32 and 42 points after 1, 2 and 3 hours, 50 after 5; marginal benefits 18, 14 and 10 points; net benefit is largest where marginal benefit equals marginal cost). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s09-01-the-logic-of-maximizing-behavi.html: 42 − 32 = 10 points
  2. Starting quantity 1, Total benefit at the start 18, New quantity 2, Total benefit at the new quantity 32 gives Marginal benefit 14.Source: Principles of Economics v2.0 (Saylor Academy open textbook, CC BY-NC-SA 3.0), 6.1 The Logic of Maximizing Behavior (marginal benefit is the amount by which an additional unit of an activity increases its total benefit; Laurie Phan’s economics study: total benefit 18, 32 and 42 points after 1, 2 and 3 hours, 50 after 5; marginal benefits 18, 14 and 10 points; net benefit is largest where marginal benefit equals marginal cost). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s09-01-the-logic-of-maximizing-behavi.html: 32 − 18 = 14 points
  3. Starting quantity 3, Total benefit at the start 42, New quantity 5, Total benefit at the new quantity 50, Marginal cost of each extra unit 6 gives Marginal benefit 4, Marginal benefit − marginal cost -2, Marginal decision rule Do less: each extra unit costs more than the benefit it adds..Source: Principles of Economics v2.0 (Saylor Academy open textbook, CC BY-NC-SA 3.0), 6.1 The Logic of Maximizing Behavior (marginal benefit is the amount by which an additional unit of an activity increases its total benefit; Laurie Phan’s economics study: total benefit 18, 32 and 42 points after 1, 2 and 3 hours, 50 after 5; marginal benefits 18, 14 and 10 points; net benefit is largest where marginal benefit equals marginal cost). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s09-01-the-logic-of-maximizing-behavi.html
  4. Starting quantity 1.5, Total benefit at the start 12.25, New quantity 4, Total benefit at the new quantity 20.5, Marginal cost of each extra unit 3.3 gives Marginal benefit 3.3, Marginal benefit − marginal cost 0, Marginal decision rule Stop here: marginal benefit equals marginal cost, where net benefit is largest..Source: Principles of Economics v2.0 (Saylor Academy open textbook, CC BY-NC-SA 3.0), 6.1 The Logic of Maximizing Behavior (marginal benefit is the amount by which an additional unit of an activity increases its total benefit; Laurie Phan’s economics study: total benefit 18, 32 and 42 points after 1, 2 and 3 hours, 50 after 5; marginal benefits 18, 14 and 10 points; net benefit is largest where marginal benefit equals marginal cost). https://saylordotorg.github.io/text_principles-of-economics-v2.0/s09-01-the-logic-of-maximizing-behavi.html

How it works

  • Change in total benefit = TB₂ − TB₁
  • Change in quantity = Q₂ − Q₁
  • Marginal benefit = (TB₂ − TB₁) ÷ (Q₂ − Q₁)

With a marginal cost (MC) of each extra unit:

  • Marginal benefit − marginal cost = MB − MC
  • Marginal decision rule: when MB > MC the page says "Do more: each extra unit adds more benefit than it costs."; when MB < MC, "Do less: each extra unit costs more than the benefit it adds."; when they are equal, "Stop here: marginal benefit equals marginal cost, where net benefit is largest."

Rules:

  • Quantities are 0 or more. Total benefits and the marginal cost may be negative. Each is at most 1 quadrillion in size.
  • The two quantities must differ; otherwise there is no answer.
  • A result too large to show as a number gives no answer. So does a result that is not 0 but too small to show as a number.
  • The arithmetic is exact on the decimals you type, and the comparison with marginal cost uses the exact marginal benefit. Results show up to 6 decimals (6 significant figures below 0.0001 in size), rounded half away from 0.

Assumptions

  • Both total benefits are measured the same way: dollars someone would pay, points, or any other single unit.
  • Over a change of more than one unit, the result is the average marginal benefit of each extra unit in that range.

Worked examples by hand

Laurie Phan's third hour. From 2 to 3 hours of study, total benefit goes from 32 to 42 points: MB = (42 − 32) ÷ (3 − 2) = 10 points.

Her second hour. From 1 to 2 hours: MB = (32 − 18) ÷ 1 = 14 points.

Hours 4 and 5, against a cost. From 3 to 5 hours: MB = (50 − 42) ÷ (5 − 3) = 4 points an hour. With a marginal cost of 6 points an hour, MB − MC = −2: "Do less".

Decimals, at the best point. From 1.5 to 4 units, total benefit goes from 12.25 to 20.5: MB = 8.25 ÷ 2.5 = 3.3. With MC = 3.3, MB − MC = 0: "Stop here".

Other questions people ask

What is marginal benefit?

Marginal benefit is the extra benefit from one more unit of a good or an activity: the amount by which total benefit rises when the quantity goes up by one. It usually falls as you have more, because the first units meet the most urgent wants.

How do I calculate marginal benefit?

Subtract the starting total benefit from the new total benefit, and divide by the change in quantity. A student who expects 32 points from 2 hours of study and 42 points from 3 hours gains (42 − 32) ÷ (3 − 2) = 10 points from the third hour.

How does marginal benefit relate to marginal cost?

Compare them. If the marginal benefit of one more unit is above its marginal cost, doing more adds to net benefit; if it is below, doing less does. Net benefit is largest where marginal benefit equals marginal cost: the marginal decision rule.

What if the quantity changes by more than one unit?

The calculator divides by the whole change, so the result is the average marginal benefit of each extra unit in the range. Going from 3 to 5 hours adds 8 points, or 4 points an hour.

What units does marginal benefit use?

The units of total benefit per unit of quantity. Benefit is often measured in dollars, as the most someone would pay; it can be any measure, such as exam points or hours saved, as long as both totals use the same one.

Can marginal benefit be negative?

Yes. When one more unit makes you worse off, such as a meal too many, total benefit falls and the marginal benefit is below zero.