Cost–Benefit Analysis & Sunk Costs

You’ll be able to

Apply the marginal decision rule to a table of marginal benefits and costs
Explain why sunk costs must be excluded from a forward-looking decision
Distinguish marginal from average and total quantities

Every optimization in the course is this one rule

Continue an activity while marginal benefit exceeds marginal cost, and stop where MB = MC. That rule becomes MR = MC for the profit-maximizing firm, MRP = wage for the hiring decision, and MSB = MSC for the socially optimal quantity. They are not four rules; they are one rule with different labels on the axes.

The optimum

MB > MC → do more · MB = MC → optimal · MB < MC → do less

The optimum is where marginal quantities meet, never where total benefit peaks or average cost bottoms out.

Sunk costs are identical under every option

A sunk cost has been incurred and cannot be recovered. Because the decision rule compares additional benefit with additional cost, and a sunk cost is the same whatever you choose, it cannot distinguish the options and must be ignored. In Unit 3 this becomes the shut-down rule: a firm losing money should keep producing in the short run if it covers variable cost, because fixed cost is sunk and will be paid either way.

Marginal, average and total

Total is the running sum, average is total divided by quantity, and marginal is the change from one more unit — the difference between consecutive totals. Marginal can fall while average still rises, and total keeps growing as long as marginal is positive. When a table gives totals, write the marginal column immediately: it is almost always what the question needs.

Worked example

A firm can undertake projects with marginal benefits of $90, $70, $50 and $30. Each costs $45. How many should it undertake, and what is the total surplus?

1.Project 1: $90 > $45 — undertake. Surplus $45.
2.Project 2: $70 > $45 — undertake. Surplus $25.
3.Project 3: $50 > $45 — undertake. Surplus $5.
4.Project 4: $30 < $45 — reject; it would reduce surplus by $15.
5.Total surplus = $45 + $25 + $5.

Answer: Three projects, for a surplus of $75. The fourth would still raise total benefit — by $30 — but by less than it raises cost, which is what makes it the wrong choice.

Watch out

Maximizing total benefit is not the objective. Total benefit rises well past the point where extra units cost more than they are worth. Stop at MB = MC.

Checkpoint

A firm has already spent $50,000 on a project that cannot be recovered. Deciding whether to continue, it should consider:

Checkpoint

Total cost rises from $340 at 8 units to $375 at 9 units. The marginal cost of the ninth unit is:

Checkpoint

At the current quantity, marginal benefit is $20 and marginal cost is $35. To improve the outcome the actor should:

On the exam

When a table of totals appears, compute the marginal column in the margin before reading the question. Nearly every quantitative decision item is answered from it.

Answer the 3 checkpoints as you read.