How to price discriminate when the two types are not differentiable?

Starting Point

Die Hard Fans: the conventional pricing MC=0, set MR=MC.

Die hard fans: set single fee, F, to sell ALL matches?

Ticket Prices Information

  • Coventry City offer season tickets which allow die-hard fans to attend all 23 home matches in a season
  • But what about fair-weather fans?
    • Also offer price per match?
    • Season ticket is approx £506, for 23 matches – average of £22 per match
    • What price can be charged per match?
      • Not less than £22
      • But what about more than £22?

Die hard fans: what if price were £22?

Self-selection constraint for die-hard fans

All consumers aim to maximise consumer surplus. So, to sell season tickets to die-hard fans: consumer surplus with season ticket must exceed (or be at least as high as) consumer surplus without season ticket.

Die hard fans if match-day price is £22: offer season ticket at fee just smaller than yellow + green area

Self-selection constraint for fair-weather fans

To sell per-match tickets to fair-weather fans: consumer surplus must be positive, and greater than consumer surplus with season ticket

Might be worth NOT selling per-match tickets at all – depends on profit that could be earned from fair-weather fans, relative to profit given up from die-hard fans.

Ticket Pricing with Self-selection Constraints

Increasing the match-day price per ticket:

  • increases the price that can be charged for the season ticket from die-hard fans
  • increases surplus from fair-weather fans, for a given demand
  • but reduces demand from fair-weather fans

Ultimately, this all adds up to the effect on marginal revenue, MR

  • with MC=0, increase price up to point at which MR=0!

Two-part Tariff

A two-part tariff is a pricing strategy where customers are charged two distinct components: a fixed entry fee and a variable usage fee. This pricing method is commonly used by firms with market power to maximize their profits and capture consumer surplus.

Structure

  • Fixed Component (Entry Fee):
The entry fee is a one-time or recurring fixed payment that grants access to the product or service. This could be in the form of:
    • Membership fees
    • Access charges
    • Initial setup costs
    • Enrollment fees
  • Variable Component (Usage Fee):
The usage fee is charged per unit of consumption, typically set at or near the marginal cost of production

Example

This is an example of a two-part tariff: Fixed fee (F) plus price per unit (p): choose combination of F and p to maximise TOTAL profit.

In the general case, offer two pricing options:

Option High Fixed price = FH, price per unit = pH Option Low Fixed price = FL, price per unit = pL

In the Coventry example, set p_H=0 and F_L=0.

Monopoly vs Two-part Tarrif