Monopoly

• background: Price elasticity of demand

What is a monopoly?

Definition

monopoly: unusual market structure in which a single firm sells a product with no close substitutes

being the only seller → whole market demand = demand curve of monopoly → absence of competition → allows it to pick preferred price (aka market power)

Big Idea

Monopolies arise both naturally and through government protection.

• antitrust laws: regulations crafted by government to counteract actions by firms to reduce competition
  • firms compete → improve quality + decrease price
  • lack of competition → ↑ profits of firms remaining in market at expense of consumers
• even when users pay nothing (e.g. Facebook), users for its dominance with increasing loss of data privacy, addiction, low self-esteem
  • Mark Zuckerberg argues that Facebook competes with videoconferences, parties, telephones, etc. → enlarging the market to make Facebook seem smaller than it really is
• defining whether a firm is a monopoly or not depends on how broadly we define the product/service in question & for antitrust purposes whether that definition is acceptable or not
• a departure from the Perfectly competitive markets we studied previously

New terminology

• price setters/makers: sellers that can set the price of a good
• market power: ability to set the price
• monopoly: one seller of a good or service with no close substitutes

Barriers to entry

Info

barriers to entry: circumstances preventing potential competitors from entering the market

1. legal: arising from government protection
2. natural
   • control of key resources
   • network externalities
   • economies of scale

Legal

• patent: government-granted exclusive right allowing inventors or creators to control use of their inventions for a limited period
• copyright: legal protection granting creators exclusive rights to their original artistic, literary, intellectual works, preventing unauthorised use or reproduction
• government-granted monopoly: when government grants individual or firm permission to be sole supplier of a good or service
  • e.g. AT&T was a government-granted telephone service monopoly from 1913 to 1984
• public monopoly: when the government itself via an agency or corporation is the sole provider of a good or service
  • e.g. postal service, public utilities, gambling outlets
• even without government protection, outsiders might still find it difficult to enter the market or might anticipate it’ll be difficult to compete once inside
  • whether because of cost or technological firm enjoyed by the incumbent

Question

Why would governments create monopolies on one hand, while prevent them on the other?

• todo

Natural

• natural market power: single firm obtains market power through barriers to entry created by the firm itself
• firms can control key resources
  • key resources: essential to produce a good or service
  • e.g. pro sports teams & leagues controlling talent; De Beers’ control of diamond production; Alcoa owning bauxite mines in 1900s → monopolise aluminium market in US at the time
• network externalities: number of consumers ↑ → product value ↑
  • e.g. Facebook, eBay, computer operating systems
    • software developers create apps that run on these computing devices → people use these OSes to get access to those apps (e.g. Procreate and iPad)
  • usually in a cycle

Economies of scale

• natural monopoly: monopoly emerging because it enjoys economics of scale over a very large range of output
  • often the first sellers in the market
  • cost advantages from producing a large output level impede potential competitors from entering the market
• economies of scale: average cost ↓ as quantity ↑
• if a platform’s current/expected users are sufficiently high → difficult for entrant to convince existing users to switch to new platform with far fewer OR new users to sign up… unless they differentiate from the incumbents to achieve critical mass

Important

With constant MC, the MC curve is a flat horizontal line at height c, and ATC starts very high (because of the fixed cost) and slides down toward that line forever without touching it.

• the MC is always below ATC (must intersect, if not ATC will go up)
• AVC is below MC

• large fixed cost of building and maintaining distribution network → at low levels of output, average cost is very high
• adding one customer adds very little to total cost → high levels of output, average cost is lower
• marginal cost is assumed to be constant for simplification
• gap between average total cost and average variable cost shrinks as output increases but will not disappear

Monopoly marginal revenue

• profit maximisation takes into account cost and revenue
• cost is influenced by a firm’s production process
• monopolists & Perfectly competitive markets have the same production & incur the costs of producing

Perfectly competitive firms vs monopolists

• perfectly competitive firms are price takers who can only take given prices, but sell any output they wish at this price → influences revenue
  • selling more doesn't lower market price; selling less does not increase market price
  • it only needs to consider what output maximises its profit given P\*
• monopolists have to decide how much to sell AND at what price
  • a monopolist looking to ↑ sales must ↓ price; ↑ price means ↓ sales
  • might have a lot of market power, but is still constrained by [[Law of Demand]]
• both market demand curves are downward sloping
  • perfectly competitive firm’s demand curve is horizontal at market price → must sell at same price as everyone else BUT can sell whatever
  • monopolist must lower price to sell more (using Claritin e.g.)
    • price effect: charge $1lesson200unitsitcoul{d}^{\prime }vesoldatoriginalprice\to revenuedecreasesby$200
    • quantity effect: sell 200 more units at $4each\to increaserevenueby$800
• overall effect on total revenue depends on whether price or quantity effect is larger

Finding marginal revenue for monopolists

• market demand curve is in inverse

---

1. find slope $\frac{△P}{△Q}=\frac{-1}{200}=-\frac{1}{200}$
2. Inverse market demand: $P=\text{choke price}-\text{slope}=6-\frac{1}{200}{Q}_d$
3. Invert: $Q_d=1200-200P$
   • $-200$ is the slope

---

• total revenue is maximised where demand is unit elastic (in this e.g. at $3)
• midpoint: price is 1/2 of choke price and quantity is 1/2 of freebie quantity
  • above midpoint, demand is elastic
    • when prices decrease → total revenue increases → marginal revenue is positive
  • below midpoint, demand is inelastic
    • when prices continue to decrease → TR drops → marginal revenue is negative

Linear demand curves

• the marginal revenue curve is also linear
• shares the same y-intercept as the demand curve, and
• is twice as steep

Monopoly Q* and P*

Purpose

to determine the profit-maximising condition, the monopolist’s optimal quantity and price practices uniform pricing.

• the monopolist can sell to more buyers and increase profits further by selling to different buyers at different prices (why they don’t is covered later)

1. Find $Q\ast$: Where $MR=MC$
2. Find $P\ast$: Price where $Q_d=Q\ast$
   • go UP to the demand curve; don’t take MC 😭
3. Find total profit.
   • 

Claritin class example (ref. slides)

• blockbuster drug: generates $1b in revenue per calendar year

Can answer algebraically, without graph, assuming MC & FC & demand curve (ALWAYS LINEAR) is given.

1. Finding $Q\ast$

$$\begin{array}{rl}{\text{Q}}_d& =1200-200P\\ \text{P}& =6-\frac{1}{200}{Q}_d\\ \text{MR}& =6-\frac{2}{200}Q\\ & \\ Q\ast \text{is where}& \text{MR}=\text{MC}\\ \text{MC}& =1\\ 1& =6-\frac{2}{200}Q\ast \\ 2Q\ast & =1000\\ Q\ast & =500\end{array}$$

• multiply MR by 2 because it’s [[#^a088f9|twice as steep]]
• they share the same $y$-intercept

2. Finding $P\ast$

$$\begin{array}{rl}P\ast & =6-\frac{1}{200}Q\ast \\ & =6-\frac{1}{200}(500)\\ & =\$3.50\end{array}$$

3. Finding total profit

Important

When MC is constant, $\text{MC}=\text{AVC}$.

$$\begin{array}{rl}\text{MC}& =1\\ \text{FC}& =10\text{million}\\ \text{TR}& =Q\ast \times P\ast \\ & =500\times 3.50\\ & =1750\text{million}\\ \text{TC}& =Q\ast \times MC+FC\\ & =500\times 1+10\\ & =510\text{million}\\ \pi & =TR-TC\\ & =1240\text{million}\\ & =1.24\text{billion}\end{array}$$

Price discrimination

Price discrimination

Price discrimination

Info

Only looking at examples to show how they capture more consumer surplus to turn into producer surplus (& profit). We will not derive the profit-maximising price discrimination scheme.

Definition

Price discrimination: charging different customers different prices for the same product or service, when there are no or minimal cost differences

• objective: charge higher price to those wtih higher willingness to pay (higher elastic demand); lower price to those with lower WTP

• examples:
  • different prices for the same-class plane ticket for the same flight
    • intertemporal purchase: plane tickets are more expensive closer to the date
    • people who are willing to wait and buy last-minute → higher WTP (esp. for emergency)
  • student & senior citizen discounts in restaurants, movie theatres
  • paperbacks and hardcovers have a negligible cost difference
    • people who buy hardcovers are a different demographic from the paperbacks
• lower price → higher elasticity → higher quantity sold → ultimately more revenue

Conditions required for price discrimination to be viable

1. Firm must have market power
2. Firm must have ability to sort customers
   • WTP can be tied to a personal or demographic characteristic
   • sometimes can be hidden → data, online purchases/surveillance and past history is useful here
3. Firm must be able to prevent resale
   • arbitrage: buying an asset in one market at a lower price and immediately selling it in another market at a higher price to make a risk-free profit
   • firms don't want this to happen

First-degree: Perfect price discrimination

• each consumer is charged the maximum she’s willing to pay for each unit bought
• enables you to capture the additional producer surplus other than the actual
• when something that was expensive becomes cheaper → consumers don't view it as benevolent; it’s profit-maximisation, and they’re just trying to grab all the consumer surplus
• e.g. buying a car, auction sites, two-part tariffs

2-part tariff

• 2-part tariff: fixed fee $F$ to participate in the transaction + unit price $p$
  • paying for entry into a place + paying for a good or service within the place you’ve already paid for
  • e.g. $20togetintotheamusementpark,and$1 per ride; country clubs + “pay as you use”/F&B; clubs’ cover charges + price per drink
  • consumer total spend is $F+p\times q$
• the usage fee of $1resultsin$PS = $0$; PS comes from access fee
  • producer surplus: total revenue - total variable cost
  • to find the producer surplus from the access fee, calculate the areas of the triangles/rectangles
    • in this case, the consumer spends \20 + $1 \times 20 = $40$
• copy down

Block price

• block pricing: bundling the total charge and quantity in a package
• e.g. park entrance includes card entitling buyer to specific number of rides at no additional cost
• equivalent block pricing of amusement park example above is $40 payment resulting in entry to park + 1 token/ride
• entire consumer surplus remains extracted

Second-degree: indirect price discrimination

• second-degree: indirect price discrimination
• according to characteristics of purchase; buyer’s choice reveals her type
• e.g. coupons, quantity discounts

Third-degree: Group pricing

• third-degree: group pricing
  • based on identity of buyer (via observable & verifiable characteristics)
  • all buyers within a group have a common identity and pay the same unit price
  • e.g. senior-citizen discounts, ladies’ night, student discounts

Example

• monopoly drug producer sells in only 2 countries at different demand curves
• working it out algebraically (see Monopoly Class Slides.pdf > page=30) results in country 2 having a higher demand curve → country 2 has a higher price than country 1

If you can’t do uniform pricing

• when you have to apply uniform pricing, try to pick in between the two markets to compromise; OR charge for one market and the others just have to follow
  • look at the lower choke price; to cater to both, it MUST be below the lower choke price

flowchart LR
A(uniform price) --> B(sell only to Country 2)
A --> C(sell to both → price must be less than $6<br><i>we can aggregate</i>)

sell only to country 2

$$\begin{array}{rl}\text{P*}& =500\\ {\text{Q}}_{\text{T}}\ast & =4\\ \text{PS}& =(\text{P}-\text{average unit cost}){\text{Q}}_{\text{T}}\\ & =\$16\end{array}$$

• $\text{average unit cost}=\text{MC}=1$

sell to both countries

$$\begin{array}{rl}{\text{Q}}_{\text{T}}& =21-3p\\ p& =7-\frac{1}{3}\text{Q}\\ \text{MR}& =7-\frac{2}{3}\text{Q}\\ 7-\frac{2}{3}\text{Q}& =1\\ 6& =\frac{2}{3}\text{Q}\\ \text{Q*}=9& ;\text{P*}=4.00\\ \text{producer surplus}& =(\text{P}-\text{AVC})\text{Q*}\\ & =(4-1)9\\ & =\$27\end{array}$$Link to original

Market power

• can you raise prices $1 tomorrow and still have customers?
  • yes: have market power
  • no: you’re a price-taker
• demand curve slopes down (not flat) → some buyers stick around even at a higher price
• note-take later