Elasticity

Alfred Marshall · 1890 · Principles of Economics, Book III

Price elasticity of demand measures how much quantity demanded changes when price changes. Elastic demand (|E| > 1): quantity responds a lot. Inelastic demand (|E| < 1): quantity barely budges. The distinction determines whether raising price increases or decreases total revenue.

Steep vs flat

An inelastic demand curve is steep: price changes, quantity barely moves (insulin, gasoline). An elastic curve is flat: a small price increase sends buyers elsewhere (one brand of cereal).

Scheme

; Price elasticity of demand
; E = (%change in Q) / (%change in P)
; E = (dQ/dP) * (P/Q)

(define (elasticity p1 q1 p2 q2)
  (let ((pct-q (/ (- q2 q1) (* 0.5 (+ q1 q2))))
        (pct-p (/ (- p2 p1) (* 0.5 (+ p1 p2)))))
    (/ pct-q pct-p)))

; Inelastic: insulin
; Price rises 10% ($100 -> $110), quantity drops 2% (1000 -> 980)
(define e-insulin (elasticity 100 1000 110 980))
(display "Insulin elasticity: ")
(display (exact->inexact e-insulin))
(display " (inelastic)")
(newline)

; Elastic: brand of cereal
; Price rises 10% ($4 -> $4.40), quantity drops 30% (500 -> 350)
(define e-cereal (elasticity 4 500 4.40 350))
(display "Cereal elasticity:  ")
(display (exact->inexact e-cereal))
(display " (elastic)")

Revenue implications

Revenue = Price x Quantity. If demand is inelastic, raising price increases revenue (quantity barely drops). If demand is elastic, raising price decreases revenue (too many buyers leave). The revenue-maximizing price is where elasticity equals -1.

Scheme

; Revenue = P * Q
; Inelastic: raise price -> revenue goes UP
; Elastic: raise price -> revenue goes DOWN

(define (revenue p q) (* p q))

; Inelastic good: price $10 -> $12, quantity 100 -> 95
(display "Inelastic good:")
(newline)
(display "  Revenue at $10: ")
(display (revenue 10 100))
(newline)
(display "  Revenue at $12: ")
(display (revenue 12 95))
(display " (UP)")
(newline)
(newline)

; Elastic good: price $10 -> $12, quantity 100 -> 60
(display "Elastic good:")
(newline)
(display "  Revenue at $10: ")
(display (revenue 10 100))
(newline)
(display "  Revenue at $12: ")
(display (revenue 12 60))
(display " (DOWN)")

Key terms

Term	Meaning
Elastic (\|E\| > 1)	Quantity responds more than proportionally to price
Inelastic (\|E\| < 1)	Quantity responds less than proportionally to price
Unit elastic (\|E\| = 1)	Percentage changes are equal; revenue is maximized
Cross elasticity	How demand for one good responds to another good's price

Neighbors

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