Marginal Utility

Alfred Marshall · 1890 · Principles of Economics, Book III

The first slice of pizza is great. The fifth is fine. The tenth makes you sick. Diminishing marginal utility: each additional unit of a good provides less additional satisfaction. This is why demand curves slope down: as you have more, you value each extra unit less, so you only buy more if the price drops.

Decreasing bars

Marginal utility falls with each additional unit consumed. Total utility still rises, but slower and slower.

Scheme

; Diminishing marginal utility
; Utility function: U(n) = 20*ln(n+1)
; Marginal utility: MU(n) = U(n) - U(n-1)

(define (utility n)
  (* 20 (log (+ n 1))))

(define (marginal-utility n)
  (- (utility n) (utility (- n 1))))

(display "Unit  Total U   Marginal U")
(newline)
(display "----  -------   ----------")
(newline)

(define (show n)
  (display n)
  (display "     ")
  (display (exact->inexact (utility n)))
  (display "    ")
  (display (exact->inexact (marginal-utility n)))
  (newline))

(show 1)
(show 2)
(show 3)
(show 4)
(show 5)
(show 6)

Consumer surplus

You would pay $10 for the first slice but only $2 for the fifth. If the price is $3, you buy four slices. The difference between what you would have paid and what you actually paid is consumer surplus. It is the area under the demand curve and above the price line.

Scheme

; Consumer surplus: sum of (willingness to pay - price)
; for each unit purchased

(define willingness-to-pay (list 10 8 6 4 2 1))
(define price 3)

; Buy all units where WTP >= price
(define (surplus wtp-list p)
  (if (or (null? wtp-list) (< (car wtp-list) p))
    0
    (+ (- (car wtp-list) p) (surplus (cdr wtp-list) p))))

(define units-bought
  (length (filter (lambda (w) (>= w price)) willingness-to-pay)))

(display "Price: $")
(display price)
(newline)
(display "Units bought: ")
(display units-bought)
(newline)
(display "Consumer surplus: $")
(display (surplus willingness-to-pay price))
(newline)
(display "  ($10-$3) + ($8-$3) + ($6-$3) + ($4-$3) = $")
(display (+ 7 5 3 1))

Key terms

Term	Meaning
Marginal utility	Additional satisfaction from one more unit
Total utility	Cumulative satisfaction from all units consumed
Consumer surplus	Difference between willingness to pay and actual price

Neighbors

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