Cost-Benefit Analysis: Study Guide (Microeconomics 1.5)

What cost-benefit analysis means

Because of scarcity, every choice has a cost. Economists assume that people and firms are rational: they compare the benefits of an option with its costs, and choose the option that leaves them best off. Cost-benefit analysis is simply this comparison done carefully, with every cost counted.

Benefits are measured differently for different decision makers:

• For a consumer, total benefit is the satisfaction, or utility, gained. To compare utility with costs, we often express it in dollars: the most the person would be willing to pay for it.
• For a firm, total benefit is its total revenue: the money it receives from selling its output.

Costs need more care, because the most important costs are often not written on any bill.

Opportunity cost: the next-best alternative

The opportunity cost of a choice is the value of the next-best alternative you give up when you make it.

Nadia has a free Saturday. She can:

Option	Value to Nadia
Work a tutoring shift	$90 (her pay)
Play in a football tournament	$70 (the most she would pay to play)
Visit her cousins	$60 (the most she would pay for the visit)

Nadia chooses the tutoring shift, because it has the highest value. Its opportunity cost is $70, the value of the football tournament. It is not $70 + $60 = $130. She could only have done one of the other two things, so she gives up only the best of them.

Notice the check: a rational choice is one whose benefit ($90) is at least as large as its opportunity cost ($70).

Explicit and implicit costs

The total economic cost of a decision has two parts.

• Explicit costs are payments of money to someone else: fees, wages paid to workers, materials, rent, fuel, interest on a loan.
• Implicit costs are the value of resources you already own and use yourself, measured by what they could have earned in their next-best use. Examples: the wages you give up to run your own business, the rent you could have earned on a building you own, the interest your savings could have earned.

Total economic cost = explicit costs + implicit costs

An accountant usually records only the explicit costs. An economist adds the implicit costs too, because they are real opportunity costs. If you leave them out, a choice can look far better than it is. (You will meet this again in Unit 3, when economic profit is compared with accounting profit.)

Two more rules help you decide what belongs in the cost of a decision:

1. Count only costs that the decision changes. Lunch you would buy whether or not you take a course is not a cost of the course.
2. Ignore money already spent that you cannot get back. It is lost whichever option you choose, so it gives up nothing now. (Economists call this a sunk cost; this is background, and the term is not tested here.)

Total benefit, total cost and net benefit

Net benefit = total benefit − total cost

The optimal choice is the option with the largest total net benefit. Three wrong rules are very common:

• choosing the option with the largest total benefit (it may cost even more);
• choosing the option with the smallest total cost (that is usually “do nothing”);
• choosing any option with a positive net benefit (another option may have a larger one).

Two kinds of decision

Some decisions are about how much: how many batches to bake, how many hours to study, how many kilometres of road to build. These can be broken into small steps. For each extra unit you can ask: does the extra benefit (the marginal benefit) exceed the extra cost (the marginal cost)? If yes, take that step. This marginal approach leads to the same answer as comparing net benefits, and Topic 1.6 develops it.

Other decisions are all or nothing: whether to take a course, accept a job, or build one bridge. Half a bridge gives no benefit, so there are no small steps to compare. These decisions must be judged by comparing total benefit with total cost.

Showing costs and benefits on a graph

Juniper Bakery, a fictional firm, sells every batch of bread it bakes for $60, so its total revenue (its total benefit) rises by $60 per batch. Its total cost includes flour, power and the value of the baker’s own time, an implicit cost. If it bakes nothing, it spends nothing.

To read the best choice from a graph like this, look for the quantity where the total benefit curve is furthest above the total cost curve. Up to that point, each extra batch adds more to revenue than to cost; beyond it, each extra batch adds more to cost than to revenue, so the gap shrinks.

Worked example 1: an all-or-nothing choice with implicit costs

Question. Leila, a student, is deciding whether to spend 8 summer weeks on a full-time robotics course. The course fee is $1,200, materials cost $200 and a bus pass for the course costs $100. If she does not take the course, she will work full time at a café for $450 a week. She values the course at $5,500 (the most she would be willing to pay for what she learns). She has already paid a $50 application fee that she cannot get back. (a) Find her explicit costs, her implicit cost and her total economic cost. (b) Should she take the course? (c) The café raises its offer to $520 a week. Does the decision change?

(a)

1. Explicit costs = fee + materials + bus pass = 1,200 + 200 + 100 = $1,500.
2. Implicit cost = café wages given up = 450 × 8 = $3,600. No money leaves her pocket, but she loses income she would otherwise have earned.
3. The $50 application fee is gone whatever she decides, so it is not a cost of this decision.
4. Total economic cost = 1,500 + 3,600 = $5,100.

(b) Net benefit = 5,500 − 5,100 = +$400. The benefit exceeds the total economic cost, so taking the course is the rational choice.

(c) Implicit cost = 520 × 8 = $4,160. Total economic cost = 1,500 + 4,160 = $5,660. Net benefit = 5,500 − 5,660 = −$160. Now she should take the café job instead.

Check and interpretation. Counting only explicit costs, the course would always look like a $4,000 gain (5,500 − 1,500), and Leila could not see why a better wage offer should matter. The implicit cost is what makes the decision depend on her alternative. She is exactly indifferent at a weekly wage of (5,500 − 1,500) ÷ 8 = $500.

Worked example 2: a “how much” choice for a firm

Question. Use Juniper Bakery’s data (Figure 1). The price is $60 per batch.

Batches per day	0	1	2	3	4	5	6
Total revenue ($)	0	60	120	180	240	300	360
Total cost ($)	0	25	55	95	145	210	290

(a) Calculate net benefit for each quantity and find the best number of batches. (b) Show that comparing the extra revenue and extra cost of each batch gives the same answer. (c) Why is 6 batches, with the largest total revenue, not the best choice? (d) The price falls to $45 per batch. Costs do not change. Find the new best quantity.

(a) Net benefit = total revenue − total cost:

Batches	0	1	2	3	4	5	6
Net benefit ($)	0	35	65	85	95	90	70

The largest net benefit is $95, at 4 batches per day.

(b) Each batch adds $60 of revenue. The extra cost of each batch is the change in total cost: 25, 30, 40, 50, 65, 80. Batches 1 to 4 each add more revenue than cost (the 4th adds $60 and costs $50), so bake them. The 5th adds $60 but costs $65, so net benefit would fall by $5. Stop at 4: the same answer.

(c) At 6 batches total revenue is $360, but total cost is $290, leaving only $70. The 5th and 6th batches each cost more to make than they bring in.

(d) New total revenue: 0, 45, 90, 135, 180, 225, 270. New net benefit: 0, 20, 35, 40, 35, 15, −20. The best quantity falls to 3 batches, with net benefit $40. Marginal check: the 3rd batch adds $45 and costs $40 (do it); the 4th adds $45 but costs $50 (do not).

Interpretation. A “how much” decision can be solved two ways: compare total net benefits, or take one step at a time while marginal benefit is at least marginal cost. Both give the same quantity. When the benefit of each unit falls, the best quantity falls too.

Common misconceptions

• “Opportunity cost is the value of all the options I did not choose.” It is the value of the next-best option only, because you could have done just one of them.
• “An implicit cost is not a real cost because I pay nothing.” Using your own time, money or property gives up what it could have earned. That is a cost.
• “Choose the option with the largest total benefit.” Choose the largest net benefit. In Worked example 2, the largest total revenue (6 batches) gives a smaller net benefit than 4 batches.
• “If net benefit is positive, go ahead.” Positive is not enough when there are other options. At $60, 6 batches have a positive net benefit, but 4 batches have a larger one.
• “Money I have already spent should affect my choice.” Spending you cannot recover is lost whichever option you choose. Leila’s $50 application fee does not change her decision.
• “Every decision can be made by comparing marginal benefit and marginal cost.” Only decisions that can be split into steps. All-or-nothing choices must compare totals.
• “Total benefit for a firm is its profit.” Total benefit for a firm is its total revenue. Net benefit (revenue minus all costs) is the profit idea.

Where this leads

Cost-benefit analysis builds on the opportunity cost ideas from the PPC and from comparative advantage and trade (Topic 1.4). Next, Topic 1.6: Marginal Analysis and Consumer Choice develops the “how much” approach: marginal benefit, marginal cost and how consumers use their income to get the most utility. Test yourself now with the practice questions, then use the revision notes and the checklist to consolidate.