Per unit opportunity cost tells you how much of one good you give up for each additional unit of another good you produce. The formula is straightforward: divide the change in the good you’re sacrificing by the change in the good you’re gaining. If moving between two production points means you lose 60 berries to get 3 more rabbits, your per unit opportunity cost of a rabbit is 20 berries.
The Formula
The per unit opportunity cost of Good X, expressed in terms of Good Y, is:
Opportunity cost of each unit of X = (Y₁ − Y₂) ÷ (X₁ − X₂)
Y₁ and Y₂ are the quantities of the good you’re giving up at two different production points. X₁ and X₂ are the quantities of the good you’re gaining at those same two points. The result is always stated in units of the good sacrificed. So if you calculate an opportunity cost of 4 cookies per term paper, the “per term paper” part is the good you’re producing more of, and “4 cookies” is what each additional term paper costs you.
A Step-by-Step Example
Suppose you can either type 3 term papers or bake 12 chocolate chip cookies in one hour. You want the per unit opportunity cost of writing a term paper.
Set up the tradeoff: 3 term papers = 12 cookies. Divide both sides by 3 to isolate one term paper: 1 term paper = 4 cookies. Each term paper you choose to write costs you 4 cookies you could have baked instead.
Now flip it. What’s the per unit opportunity cost of a cookie? Divide both sides of the original equation by 12: 1 cookie = 3/12 = 0.25 term papers. Every cookie costs you one-quarter of a term paper. Notice the two opportunity costs are reciprocals of each other. That relationship always holds and gives you a quick way to check your math.
Reading It Off a Graph
In most economics courses, you’ll calculate per unit opportunity cost from a production possibilities curve (PPC). The PPC plots all the combinations of two goods an economy can produce using its available resources. Pick any two points on the curve, read off their coordinates, and plug them into the formula.
Say Point A on the curve is (2 robots, 100 tons of wheat) and Point B is (5 robots, 40 tons of wheat). The opportunity cost of each additional robot is (100 − 40) ÷ (5 − 2) = 60 ÷ 3 = 20 tons of wheat per robot. You gave up 60 tons of wheat to gain 3 robots, so each robot costs 20 tons.
If the PPC is a straight line, you can use any two points and get the same answer every time, because the slope is constant. The opportunity cost per unit never changes regardless of where you are on the curve.
Constant vs. Increasing Opportunity Cost
A straight-line PPC means constant opportunity cost. Every additional unit of a good costs you the same amount of the other good, no matter how many you’ve already produced. This happens when resources are equally suited to producing either good. Think of a factory that can switch between two products with no loss in efficiency.
A PPC that bows outward from the origin (concave shape) means increasing opportunity cost. The first few units of a good are cheap to produce because you’re using the resources best suited to making that good. As you push for more, you pull in resources that are less and less well-suited, so each additional unit costs more of the other good.
Here’s a concrete example. Suppose your PPC for rabbits and berries has these points along the curve: at 1 rabbit you give up 20 berries, at 2 rabbits you’ve now given up 60 total berries (so the second rabbit cost 40), at 3 rabbits you’ve given up 120 total (the third cost 60), and so on. The per unit opportunity cost rises with each additional rabbit: 20, then 40, then 60, then 80 berries. When you’re working with a bowed-out PPC, the two points you choose matter. You can’t just pick any two endpoints and divide, because the cost per unit changes along the curve. Instead, calculate between adjacent points to find the opportunity cost at that specific range of production.
Using It to Find Comparative Advantage
The most common reason you’ll calculate per unit opportunity cost is to determine comparative advantage between two producers, whether that’s two countries, two companies, or two people. The rule is simple: whoever has the lower per unit opportunity cost of producing a good has the comparative advantage in that good.
Suppose Country A can produce either 50 tons of corn or 25 tons of beef with its resources, and Country B can produce either 30 tons of corn or 10 tons of beef. For Country A, the opportunity cost of 1 ton of beef is 50 ÷ 25 = 2 tons of corn. For Country B, the opportunity cost of 1 ton of beef is 30 ÷ 10 = 3 tons of corn. Country A gives up less corn per ton of beef, so Country A has the comparative advantage in beef.
Now check corn. Country A’s opportunity cost of 1 ton of corn is 25 ÷ 50 = 0.5 tons of beef. Country B’s is 10 ÷ 30 = 0.33 tons of beef. Country B sacrifices less beef per ton of corn, so Country B has the comparative advantage in corn. Both sides benefit by specializing in the good where their per unit opportunity cost is lower and trading for the rest.
Quick Tips for Getting It Right
- Always label your answer. A number without units is meaningless. “20” tells you nothing. “20 tons of wheat per robot” tells you everything.
- Check with the reciprocal. If the opportunity cost of Good X is 4 units of Good Y, the opportunity cost of Good Y should be 1/4 unit of Good X. If those two numbers don’t multiply to 1, something went wrong.
- Watch the direction of change. Y₁ should be the starting quantity and Y₂ the ending quantity after you shift production toward more of Good X. If you mix up which value is which, you’ll get a negative number. Opportunity cost is always expressed as a positive value.
- On a bowed curve, specify the range. Don’t say “the opportunity cost of a rabbit is 40 berries” without noting that this applies when moving from, say, 1 rabbit to 2 rabbits. The cost at a different range of production will be different.