Opportunity Cost

Friedrich von Wieser · 1914 · Wikipedia: Opportunity cost

The cost of any choice is the best alternative you gave up. Spending an hour studying economics means not spending that hour studying calculus. The dollar price of something understates its true cost: you must also count what else you could have done with the money, time, or resources.

The production possibility frontier

The PPF shows all combinations of two goods an economy can produce with its resources. Points on the frontier are efficient: to get more of one, you must give up some of the other. Points inside are wasteful. Points outside are impossible with current resources.

Scheme

; Production Possibility Frontier
; PPF: butter = sqrt(100 - guns^2) (quarter circle, scaled)
; Moving along the frontier: more guns = less butter

(define (ppf guns)
  ; Max 10 guns or 10 butter, concave tradeoff
  (if (> guns 10) 0
    (sqrt (- 100 (* guns guns)))))

(display "Guns  Butter  Opp. cost of 1 more gun")
(newline)
(display "----  ------  -----------------------")
(newline)

(define (show g)
  (let ((b (ppf g))
        (opp (if (= g 0) 0
               (- (ppf (- g 1)) (ppf g)))))
    (display g)
    (display "     ")
    (display (exact->inexact b))
    (display "   ")
    (display (exact->inexact opp))
    (display " butter")
    (newline)))

(show 0)
(show 2)
(show 4)
(show 6)
(show 8)
(show 10)

Increasing opportunity cost

The PPF bows outward because opportunity costs increase. The first gun costs little butter to produce. The last gun costs a lot. Resources are not equally suited to producing both goods: dairy farmers make poor gunsmiths.

Scheme

; Personal opportunity cost: should you study or work?
; Studying: future salary increase of $5000/year
; Working: earn $15/hour now

(define study-hours 4)
(define hourly-wage 15)
(define future-gain-per-hour 5000)  ; annual, per hour of study

; Opportunity cost of studying = wages forgone
(define opp-cost (* study-hours hourly-wage))

; Benefit of studying = future income gain
(define benefit (* study-hours (/ future-gain-per-hour 2000)))
; Assuming 2000 work hours/year, that's $2.50/hour future gain
; Over 40 years: significant

(display "4 hours studying:")
(newline)
(display "  Wages forgone (opp cost): $")
(display opp-cost)
(newline)
(display "  Future gain per year: $")
(display (* study-hours (/ future-gain-per-hour 1)))
(newline)
(display "  Study if future gain > present cost")

Key terms

Term	Meaning
Opportunity cost	Value of the best foregone alternative
PPF	Boundary of producible combinations given fixed resources
Increasing opp. cost	PPF bows outward: each unit costs more than the last

Neighbors

W Opportunity cost
W Production possibility frontier
Calculus Ch.12 — optimization with constraints

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