Monopoly and Competition

Adam Smith · 1776 · Wikipedia: Monopoly

In perfect competition, many firms sell identical products at the market price. No single firm can influence the price: they are price takers. A monopoly is the opposite: one firm controls the entire market and sets the price. The monopolist restricts output below the competitive level, charges more, and creates deadweight loss.

Perfect competition: price takers

Under perfect competition, the firm faces a horizontal demand curve at the market price. It produces where marginal cost equals price. Economic profit is zero in the long run because entry drives price down to average cost.

Scheme

; Perfect competition: firm is a price taker
; Produce where marginal cost = price

(define market-price 20)

; Marginal cost increases with quantity
(define (marginal-cost q) (+ 5 (* 0.5 q)))

; Find optimal quantity: MC = P
(define (find-competitive-q price)
  (let loop ((q 1))
    (if (>= (marginal-cost q) price) q
        (loop (+ q 1)))))

(define comp-q (find-competitive-q market-price))
(display "Market price: $") (display market-price) (newline)
(display "Competitive quantity: ") (display comp-q) (newline)
(display "MC at that quantity: $") (display (marginal-cost comp-q)) (newline)

; Total revenue and cost
(define revenue (* market-price comp-q))
(define total-cost
  (let loop ((q 1) (tc 0))
    (if (> q comp-q) tc
        (loop (+ q 1) (+ tc (marginal-cost q))))))

(display "Revenue: $") (display revenue) (newline)
(display "Total cost: $") (display total-cost) (newline)
(display "Profit: $") (display (- revenue total-cost))

Monopoly: price setter

The monopolist faces the entire market demand curve. To sell more, it must lower the price on all units. It produces where marginal revenue equals marginal cost, which is less than the competitive quantity. The result: higher price, lower quantity, and a deadweight loss triangle.

Scheme

; Monopoly vs competition
; Demand: P = 100 - Q
; MC = 10 + 0.5Q

(define (demand q) (- 100 q))
(define (marginal-revenue q) (- 100 (* 2 q)))  ; MR has twice the slope
(define (marginal-cost q) (+ 10 (* 0.5 q)))

; Monopoly: MR = MC -> 100 - 2Q = 10 + 0.5Q -> Q = 36
(define (find-q mr-or-d mc)
  (let loop ((q 1))
    (if (>= (mc q) (mr-or-d q)) q
        (loop (+ q 1)))))

(define monopoly-q (find-q marginal-revenue marginal-cost))
(define monopoly-p (demand monopoly-q))
(display "Monopoly: Q=") (display monopoly-q)
(display ", P=$") (display monopoly-p) (newline)

; Competition: P = MC -> 100 - Q = 10 + 0.5Q -> Q = 60
(define comp-q (find-q demand marginal-cost))
(define comp-p (demand comp-q))
(display "Competition: Q=") (display comp-q)
(display ", P=$") (display comp-p) (newline)

; Deadweight loss (triangle area)
(define dwl (* 0.5 (- comp-q monopoly-q) (- monopoly-p comp-p)))
(display "Deadweight loss: $") (display dwl)

Natural monopoly

Some industries have such high fixed costs and low marginal costs that a single firm can serve the entire market more cheaply than two or more. Utilities, railroads, broadband infrastructure. Breaking up a natural monopoly raises costs. The solution is usually regulation: let the monopoly exist but control its pricing.

Scheme

; Natural monopoly: high fixed cost, low marginal cost
; Average cost falls over the relevant range

(define fixed-cost 1000)
(define marginal-cost 2)

(define (total-cost q) (+ fixed-cost (* marginal-cost q)))
(define (average-cost q) (/ (total-cost q) q))

(display "Average cost at different scales:") (newline)
(for-each
  (lambda (q)
    (display "  Q=") (display q)
    (display ": AC=$") (display (exact->inexact (average-cost q)))
    (newline))
  '(10 50 100 500 1000))

; Two firms splitting the market
(define (two-firm-ac q)
  (/ (+ fixed-cost (* marginal-cost (/ q 2))) (/ q 2)))

(display "One firm at Q=500: AC=$")
(display (exact->inexact (average-cost 500))) (newline)
(display "Two firms at Q=250 each: AC=$")
(display (exact->inexact (two-firm-ac 500)))
(newline)
(display "Natural monopoly: one firm is cheaper")

Key concepts

Structure	Price	Efficiency
Perfect competition	P = MC (price taker)	Efficient, zero economic profit
Monopoly	MR = MC, P > MC (price setter)	Deadweight loss, positive profit
Natural monopoly	Regulated pricing	One firm cheapest, but needs oversight

Neighbors

Foundations (Wikipedia)

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