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

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