Diminishing Returns

David Ricardo · 1817 · Principles, Ch. 2 · Also: Wikipedia

Adding more of one input while holding others fixed eventually yields less and less additional output. The first worker on a farm adds a lot. The tenth adds less. The hundredth might add almost nothing. The curve of total output bends and flattens.

The bending curve

Total output rises, but each additional unit of input contributes less. The slope of the total output curve decreases. This is what "diminishing marginal product" looks like.

Scheme

; Diminishing returns: output = sqrt(input) * scale
; Each additional worker produces less additional output

(define (total-output workers)
  (* 10 (sqrt workers)))

(define (marginal-product n)
  (- (total-output n) (total-output (- n 1))))

(display "Workers  Total   Marginal")
(newline)
(display "-------  -----   --------")
(newline)

(define (show-row n)
  (display n)
  (display "        ")
  (display (exact->inexact (total-output n)))
  (display "   ")
  (display (exact->inexact (marginal-product n)))
  (newline))

(show-row 1)
(show-row 2)
(show-row 4)
(show-row 9)
(show-row 16)
(show-row 25)

Why it happens

Fixed factors become bottlenecks. More workers share the same land, the same tools, the same factory floor. Coordination costs rise. Each worker has less capital to work with. Ricardo saw this first in agriculture: more labor on the same land yields diminishing harvests.

Scheme

; Fixed capital, variable labor
; Output = min(workers, machines) * productivity
; When workers exceed machines, extras add less

(define machines 5)
(define productivity 10)

(define (output workers)
  ; Each machine needs one worker to operate fully.
  ; Extra workers help but at reduced rate.
  (let ((full (min workers machines))
        (extra (max 0 (- workers machines))))
    (* productivity (+ full (* 0.2 extra)))))

(display "Workers  Output  Marginal")
(newline)
(let loop ((n 1) (prev 0))
  (when (<= n 10)
    (let ((out (output n)))
      (display n)
      (display "        ")
      (display (exact->inexact out))
      (display "    ")
      (display (exact->inexact (- out prev)))
      (newline)
      (loop (+ n 1) out))))

Key terms

Term	Meaning
Diminishing returns	Each additional unit of input produces less additional output
Marginal product	The extra output from one more unit of input
Fixed factor	An input held constant while others vary

Neighbors

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