Price Discrimination Overheads

Price discrimination is the selling of two varieties of a product to two different buyers at different net prices, where the net price is the price paid by the buyer, adjusted for any cost of product differentiation Price discrimination occurs when a firm charges different prices to different customers for reasons other than differences in production costs

Requirements for Price Discrimination There must be a downwards sloping demand curve for the firm's output The firm must be able to raise price without losing all its customers

The firm must be able to identify consumers who are willing to pay more for the product The firm must know who will pay the higher price Auctions Airlines

The firm must be able to prevent low-price customers from reselling to high-price customers Arbitrage is the purchase of products at a low price in order sell them at a high price

Ways to identify customers long term relationships age sex type of job other commonly bought items place of residence insurance agent jeweler doctor

Prevention of Arbitrage Customer specific products haircuts house plans dental filling gall bladder operation

Use of product predicated on specific characteristics student discount card senior citizen discount air travel with weekend stay summer use of condominium at ski resort

Product is hard to resell because of distance or transactions costs purchase of feeder cattle purchase of corn silage purchase of custom made shoes

First-degree (perfect) price discrimination A firm practices first-degree or perfect price discrimination Specifically, perfect price discrimination involves the seller charging a different price for each unit of the good in such a way that the price charged for each unit is equal to the maximum willingness to pay for that unit if it is able to charge the maximum price each consumer is willing to pay for each unit sold

Example of Grandpa Jones 5 Spoker D tractors Marginal value of zero to Grandpa Jones 2 identical interested buyers

Tractors Price First$16,000 Second$12,000 Third $8,000 Fourth $6,000 Fifth $4,000 Value (demand) schedule for each buyer

$ Tractors Price and Demand

Price(Demand) Total Revenue > $16,00000 $12,000336,000 $16,000232,000 $12,000448,000 $8,000540,000 $8,000648,000 $6,000742,000 $6,000848,000 $4,000936,000 $16,000116,000 Uniform pricing $4, ,000

To sell all 5 tractors the uniform price must be $8,000 Total revenue = $40,000

Can Grandpa Jones do better? How about $12,000 a piece for 4 tractors? Total revenue = $48,000

Grandpa Jones ends up with a tractor of no value to him An individual willing to pay $8,000 for a tractor is shut out of the market But revenue is higher than when selling all 5 at a uniform price of $8,000

First Degree Price Discrimination Charge the maximum price each consumer is willing to pay for each unit sold

Sell the first tractor for $16,000 First Degree Price Discrimination Sell the second tractor for $16,000 Sell the third tractor for $12,000 Sell the fourth tractor for $12,000 Sell the fifth tractor for $8,000 Total Revenue = $64,000

How does Grandpa Jones do it? Offer a bundle of two tractors for $28,000 Each consumer will buy one bundle Total revenue is $56,000 $48,000 < $56,000 < $64,000

Offer a bundle of two tractors for $28,000 Even better With an option to bid on a third Each consumer will buy one bundle The auction for the remaining tractor will yield $8,000 Total revenue = $64,000 Or an option to buy a third for $8,000

Either one guy buys or the other guy buys and Grandpa Jones is left with two tractors Offer a three unit bundle for $36,000 Offer a two unit bundle for $28,000 Either one guy buys or the other guy buys and Grandpa Jones is left with no tractors Total profit = $64,000 Another way

Offer a bundle of five tractors for $46,000 Why not offer all five units One buyer will purchase all five of them All the tractors are gone and Grandpa Jones’s profits are only $46,000

But first buyer can then sell two tractors for $28,000 to the other buyer First buyer has profits of $18,000 Total profits are $64,000 But poor Grandpa only gets $46,000 of them

A simple example of discriminating monopolist p = Q Q = /2p Cost = MC = $4.00

Uniform pricing first

TR MR MC Profit Q Price UNFUNF Cost Exact

Revenue Profit Max for Uniform Price Monopolist Output $ Price MR MC PUPU QUQU Cost Profit

Results Uniform Price Monopolist Q = 4 TR = 48 TC = 16 Profit = 32

Now consider a price discriminating monopolist Each unit receives a different price

MC TRMRProfit Q Price Cost Exact DSCDSC DSC

Profit Max for Discriminating Monopolist Output $ Price MR PUPU QUQU MC

Profit Max for Discriminating Monopolist Output $ Price PUPU QUQU MC

Q = 8 TR = 88 TC = 32 Profit = 56 Discriminating Monopolist Uniform Price Monopolist Q = 4 TR = 48 TC = 16 Profit = 32 Results

Monopoly and Competition The perfectly discriminating monopolist will produce the same amount as a competitive industry with the same cost structure

Consumers much prefer competition They pay much less for the same quantity

Competitive Equilibrium Output $ Price MC Cost/ Revenue

Non-integer quantities (sales) If the monopolist can charge for and sell partial quantities, then the maximum that can be charged is the total area under the demand curve to the left of a given quantity

Profit Max for Discriminating Monopolist Output $ Price MC Cost Profit

Discriminating Monopolist Q = 8 TR = 88 TC = 32 Profit = 56 Perfectly Discriminating Monopolist Q = 8 TR = 96 TC = 32 Profit = 64 Results

Segregating Markets Identify Consumers Prevent Arbitrage Airline Example

Number of Round-trip Tickets $ Demand MR MC H E Revenue Cost Profit Uniform Price Monopoly Total Profit = $1200

Number of Round-trip Tickets $ Demand MR MC H E Charge $160 for No Restriction Ticket Profit Gain Total Profit = $1600 AC Revenue Cost

Number of Round-trip Tickets $ Demand MR MC H Charge $100 for Student Tickets P > MC

Number of Round-trip Tickets $ Demand MC Charge $100 for Student Tickets P > MC

Number of Round-trip Tickets $ Demand MC Charge $100 for Student Tickets P > MC

Number of Round-trip Tickets $ Demand Charge $100 for Student Tickets MC Additional Cost Additional Revenue

Number of Round-trip Tickets $ Demand H Charge $100 for Student Tickets MC Additional Cost Additional Profit

Number of Round-trip Tickets $ Demand H Overall Gain from Price Discrimination Gain MC

The End

MC TRMRProfit Q Price Cost Exact DSCDSC DSC

TR MRProfit MRTRMRProfit Q Price UNFUNF CostMC UNF DSCDSC DSC

Number of Round-trip Tickets $ F E H G