opportunity-cost-pairs

Opportunity Cost Concepts

  • 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:
    • OCextshoes=43extrollsofsushipershoeOC_{ ext{shoes}} = \frac{4}{3} ext{ rolls of sushi per shoe}
    • OCextsushi=34extshoespersushiOC_{ ext{sushi}} = \frac{3}{4} ext{ shoes per sushi}
    • And OC<em>extshoes=1OC</em>extsushiOC<em>{ ext{shoes}} = \frac{1}{OC</em>{ 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 → OCP(AoB)=1extbook10extpizza=0.1extbooksperpizzaOC_{P}(A o B) = \frac{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 → OCP(BoC)=3extbooks10extpizza=0.3extbooksperpizzaOC_{P}(B o C) = \frac{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}} \