Price discrimination and profit

A post last week dealt with price discrimination in the car insurance market. See You could be paying higher insurance premiums than someone with the same driving history, car and background because of price optimization.

Charging different prices to different groups of customers based on their ability and willingness to pay (a discount) is price discrimination. Buyers with a lower price elasticity of demand will be charged a higher price.

If the firm were to charge the same price to each group, they would actually make less profit since they would end up violating the rule which says "choose Q so that marginal revenue (MR) = marginal cost (MC)."

Suppose a firm has two groups of customers, A and B, shown below. Group A's demand is generally less elastic. The blue line is demand. Green is MR. The flat line is both MC and ATC (average total cost). Having ATC = MC is not realistic but it simplifies the explanation.

The darker red lines just show us how to find P and Q for each group. Profit is Q*(P - ATC).




Now group B


Group A profit) 8*(24 - 8) =128

Group B profit) 12*(20 - 8) = 144

Total profit = 128 + 144 = 272

What if they charge both groups 22?

Group A profit) 9*(22 - 8) =126  (at Q = 9, MR does not equal MC)

Group B profit) 10*(22 - 8) = 140 (at Q = 10, MR does not equal MC)

Total profit = 126 + 140 = 266

So there is less profit (266) if they charge the same price to each group than if the price discriminate (272).

Economist Robert P. Murphy gives an example of how there is nothing wrong with price discrimination:

"the granting of special pricing for certain groups need not harm the groups paying full freight.

For example, if a movie theater in a small town were barred from giving child, student, and senior discounts — and instead had to charge one ticket price for all customers — it might not be able to stay in business. It would hardly help the middle-aged adults to have a "fair" pricing policy with no theater in town. This example shows the pitfalls in thinking about "the cost" of providing a seat in a movie theater and deriving the "fair" price that a theater ought to charge all customers."

See The Economics of Coupons and Other Price Cuts

Also see Price Discrimination by Tejvan Pettinger. A key passage is:

"Price discrimination will enable some firms to stay in business who otherwise would have made a loss. For example price discrimination is important for train companies who offer different prices for peak and off-peak. Without price discrimination, they may go out of business or be unable to provide off-peak services."