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Price discrimination strategies

September 27, 2011

Sometimes you can divide a firm’s potential customers into different groups, with different demand elasticities. A clothes shop for instance might find that its customers who have jobs, have a relatively inelastic demand whilst students (who are keen on clothes but short on cash) have a much more elastic demand, ie they are much more willing to buy clothes in greater quantities when the price drops.

Consider now a firm that has two customer groups, call them ’employed’ and ‘students’. It can produce at a constant marginal cost of 10.

The demand function for ’employed’ is Q_{emp}=63-0.5P
The demand function for ‘students’ is Q_{stu}=200-2P

If it set a uniform price based on the demand function for ’employed’ then the inverse demand function for ’employed’ would be P=126-2Q_{emp} so TR=PQ=126Q-2Q_{emp}^2 \Rightarrow MR = \frac{d(TR)}{dQ}=126 - 4Q_{emp}.

When MR = MC, 10 = 126 - 4Q_{emp} \Rightarrow Q=29

Subbing that back into the inverse demand function, P=126-2(29)=68

So the firm would sell at a price of 68. It would sell a quantity of 29 to the ’employed’ market and at that price it would sell Q_{stu}=200-2(68) = 64 a quantity of 64 to the ‘student’ market.

Total sales would be 93 and at a price of 68 each that gives total revenue of 6324. With a cost of 10 per unit, total cost (assuming no fixed cost here) would be 930 so total profit would be 5394.

However, its possible to increase that profit, if you can set a separate price for students. If we want to find the profit maximising price for students, we would have an inverse demand function of P=100-0.5Q_{stu} so TR=100Q-0.5Q_{stu}^2 \Rightarrow MR = 100-Q_{stu}.

When MR = MC, 10 = 100-Q_{stu} \Rightarrow Q=90
Subbing that back into the inverse demand function, P=100-0.5(90) = 55

So for the ‘student’ market the profit-maximising price would be 55.

If we sell to the ’employed’ market at a price of 68, and offer a student discount to sell to the ‘student’ market at a price of 55, then our total revenues will be (68 x 29)+(55 x 90) = 6922. Total cost would be (10 x 29)+(10 x 90) = 1190. So total profit will be 5732.

We have increased total profit by being able to sell at a lower price to the student market, simply because their demand was more elastic, so by reducing the price for students from 68 to 55, we profited by the large increase in output of sales to students from 64 to 90.

Of course this strategy does not work if we can’t identify who the students are. If people from the ’employed’ market start being able to pass themselves off as students then our strategy falls down!

So in order to use a price discrimination strategy, you generally have to have three things:
1. You need to have some form of market power.
2. You need to have consumer groups with different sensitivities to price (different elasticities of demand) and you need to be able to identify them.
3. You need to be able to prevent or limit resales (its no good if students can buy up a large stock of your goods at the lower price, then sell them on to ’employed’ customers!)

Price discrimination strategies are all around us. Different ticket pricing on trains for instance, where you pay a higher price for travelling on ‘peak hours’ than you do at other times of the day, is basically a way of identifying which consumers have relatively inelastic demand (commuters who need to get the train to go to work in the morning) and charging them higher prices, while charging a lower price to customers who are travelling for other reasons, and may have other alternative forms of transport (car, bus etc) and so need to be enticed on to the train with a lower price.

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