Opportunity cost (OC) is the value of the next best alternative forgone when choosing to produce more of one good. It measures the trade-off between two goods.
Linear PPC (production possibility curve) implies constant OC when moving along the curve.
Example given for linear OC: if the OC of producing an additional pair of shoes is 1.33 rolls of sushi, then the OC of producing an additional roll of sushi is 3/4 of a pair of shoes, and these are reciprocals when measured for the same two points. In symbols:
OC_{ ext{shoes}} = rac{4}{3} ext{ rolls of sushi per shoe}
OC_{ ext{sushi}} = rac{3}{4} ext{ shoes per sushi}
And OC{ ext{shoes}} = rac{1}{OC{ ext{sushi}}} for the same two points, with units reciprocals.
The reciprocal relationship holds for the same two points even in a nonlinear case, but there is a caveat: if you compare different pairs of points, the reciprocals may not hold.
If the OC of producing an additional roll of sushi is 3/4 of a pair of shoes, then the OC of producing an additional pair of shoes is 4/3 rolls of sushi, illustrating the reciprocal property for the same two points.
Important caveat: when you move to nonlinear OC (nonlinear PPC), the OC values change along the curve; the reciprocals still apply when you stay on the same pair of points, but not necessarily across different point pairs.
Question: Is constant OC only for linear? No. The constant-OC property is tied to a linear (straight-line) PPC. For nonlinear (bowed-out) PPC, OC is not constant.
In nonlinear cases, OC between two fixed points remains reciprocal, but as you move to different pairs of points, the OC values can differ dramatically.
Linear vs Bowed-Out Production Possibility Curves (PPC)
Linear PPC: OC is constant in both directions (constant trade-off regardless of where you are on the curve).
Bowed-out PPC: OC is increasing in both directions (as you move down and to the right, producing more of one good becomes increasingly costly in terms of the other good).
The left-hand side and right-hand side are often erased to create space for new examples, showing how the shape changes the OC dynamics.
Bowed-out example setup (pizza and books):
Horizontal axis: slices of pizza
Vertical axis: number of books
Points A, B, C: A = (10 pizza, 9 books), B = (20 pizza, 8 books), C = (30 pizza, 5 books)
Calculations for OCP (opportunity cost of producing one more unit of pizza, OC_P):
From A to B: you gain 10 pizza and give up 1 book → OC_{P}(A o B) = rac{1 ext{ book}}{10 ext{ pizza}} = 0.1 ext{ books per pizza}
From B to C: you gain 10 pizza and give up 3 books → OC_{P}(B o C) = rac{3 ext{ books}}{10 ext{ pizza}} = 0.3 ext{ books per pizza}
Observation: OC_P increases from 0.1 to 0.3 books per pizza as pizza production increases, illustrating increasing OC along a bow-out.
Calculations for OCB (opportunity cost of producing one more unit of books, OC_B):
From C to B: you gain 3 books and give up 10 pizzas → $$OC_{B}(C o B) = rac{10 ext{ pizzas}}{3 ext{ books}} \