Unit 1 Topic 1.5

Cost-Benefit Analysis

every curve, every area

3 min readfreeNot practiced

Rosa is deciding how to spend her summer. She could keep her job at a garden center, which pays $4,000, or run her own lawn-care business, which she expects to bring in $6,500 from customers. The business needs a rented mower ($1,200), gas ($300) and flyers ($100). Subtract those and the business looks $4,900 better. But that comparison leaves something out: if she runs the business, she does not get the $4,000 paycheck. Good decisions count every cost, including the ones nobody sends a bill for.

Explicit and implicit costs

An explicit cost is a money payment: rent, wages paid to workers, materials, a mower rental. An implicit cost is the value of something the decision maker gives up without paying anyone: her own time, which could earn a wage elsewhere, or a building or truck she already owns, which could earn rent. Implicit costs are opportunity costs that do not show up as money spent.

The full economic cost of a choice is the sum:

economic cost\text{economic cost}=explicit costs= \text{explicit costs}+implicit costs+ \text{implicit costs}

Explicit costsImplicit costs
What they aremoney paid to othersthe value of your own resources or time given up
Rosa's businessmower $1,200, gas $300, flyers $100garden-center pay $4,000, truck rent forgone $500
Seen on a receipt?yesno, but just as real

Total benefit and net benefit

The total benefit of a choice is everything it gives you. For a consumer, it is the satisfaction of using a good or service, often measured by the most the consumer would pay for it. For a firm, it is the money it takes in from selling its output, its revenue. The net benefit is what is left after the costs:

net benefit\text{net benefit}=total benefit−total cost= \text{total benefit} - \text{total cost}

Worked example: Rosa's summer, every cost counted.

  1. Explicit costs: 1,200+300+1001{,}200 + 300 + 100=1,600= 1{,}600 dollars.
  2. Implicit costs: the job's pay plus the truck rent she gives up, 4,000+500=4,5004{,}000 + 500 = 4{,}500 dollars.
  3. Economic cost: 1,600+4,500=6,1001{,}600 + 4{,}500 = 6{,}100 dollars.
  4. Net benefit: 6,500−6,100=4006{,}500 - 6{,}100 = 400 dollars. The business is still worth running, but by $400, not $4,900.
  5. If the job paid $5,000, implicit costs would be $5,500, economic cost $7,100, and net benefit 6,500−7,100=−6006{,}500 - 7{,}100 = -600 dollars: the job would be the better choice.

The common slip is subtracting only the explicit costs, which makes almost any business look like a good idea.

The best choice has the largest net benefit

A bar chart of total benefit and cost for 0 to 5 guitar lessons a month at $25 a lesson; net benefit is largest, $45, at 3 lessons. Invented data.
Figure 1. Total benefit keeps rising with more lessons, but net benefit peaks at 3 lessons. Invented data for practice. LevlPrep original diagram.

When you can choose how much of something to do, compare the net benefit at each amount. Jamal values guitar lessons at $50 for one a month, $90 for two, $120 for three, $140 for four and $150 for five; each lesson costs $25. His net benefits are $25, $40, $45, $40 and $25. He should take 3 lessons, where net benefit is largest, even though 5 lessons would give the most total benefit. Going from 3 to 5 lessons adds $30 of benefit but $50 of cost. Chasing the largest total benefit, rather than the largest net benefit, is the trap.

Costs and benefits change the answer. If lessons fell to $15, net benefits would be $35, $60, $75, $80 and $75, and 4 lessons would become the best choice.

All-or-nothing choices and how-much choices

Some decisions are all or nothing: run the business or not, build the playground or the skate park. For these, compare the net benefit of each whole option. Others are about how much: how many lessons, how many hours, how many units to make. For those, the totals work, but it is often quicker to ask whether one more unit adds more benefit than cost. The next topic builds that habit, which runs through the rest of the course.

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