Download Notes on second-degree price discrimination

NOTES ON PRICE DISCRIMINATION BY SELF-SELECTION – SECOND
DEGREE PRICE DISCRIMINATION
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Assume two types of consumer with different demands for good; Type A has low
demand and Type B has high demand.
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Producer wants to sell at a lower price to Type A consumers and a higher price to
Type B consumers. However, consumers are not readily identifiable, except by
their purchasing behaviour. Challenge for producer is to develop two pricequantity packages that will be designed so that consumers self-select the package
intended for them. If successful, this will increase the profit of the producer
beyond what could be earned with a single package covering both consumer
types.
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Producer will offer two packages: each consists of a take-it-or-leave-it offer of a
particular quantity of the good at a particular price: high price and high quantity
for Type B consumers and low price and low quantity for the Type A consumers.
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Necessary condition for attracting Type B consumers to the more expensive
package is to give them at least as much consumer surplus as they could get by
purchasing the “Type A” package.
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The profit-maximizing set of price-quantity packages will be one that gives Type
A consumers less than they would be willing to purchase at the price charged, in
order to charge more to Type B consumers.
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This model can be interpreted as a price-quality model instead, with demand
curves for two quality levels by different consumer types. In this case, the profitmaximizing set of price-quality packages will be one that gives Type A
consumers a lower quality than they would have been willing to purchase, in
order to create enough “distance” between the Type A and Type B packages.
This would be called quality discrimination instead of price discrimination.
Example (note that these are individual demand curves, so if there are 100 of each type of
consumer, the market demand is 100 times larger than each of these equations):
Type A demand: P = 10 - .02Q
Type B demand: P = 10 - .01Q
MC = AC = 0 (for simplicity)
There are 100 of each type of consumer.
Producer wants to design two take-it-or-leave-it packages of price and quantity.
First try: Sell the maximum quantity the consumer will purchase, at a price equal to all
the area under the individual consumer’s demand curve. For Type B consumers this
means a quantity of 1000 and a price of (10 x 1000)/2 = $5,000. For Type A consumers,
this means a quantity of 500 at a price of (10 x 500)/2 = $2,500. Because there are 100
of each type of consumer, and because there are zero costs, profit is expected, by the
producer, to be 100 x $5,000 + 100 x $2,500 = $750,000. However, this design of the
price-quantity packages is flawed. If Type B consumers purchase the Type A package of
500 units at a price of $2,500, they will get consumer surplus of [(10 – 5) x 500]/2 + (5 x
500) - $2,500 = $1,250. If they purchase the Type B package, they will get consumer
surplus of zero. So, with this package design, they will prefer to purchase the Type A
package. Actual profit will end up being 200 x $2,500 = $500,000.
Second try: Sell the maximum quantity each consumer is willing to purchase, but lower
the Type B price so that the consumer surplus from purchasing the Type B package is at
least as good as what it would be if the Type B consumer purchased the Type A package.
For Type A consumers, this means a quantity of 500 at a price of $2,500 (same as above).
For Type B consumers, this means a quantity of 1000 at a price of $5,000 - $1,250 =
$3,750 (i.e., leaving Type B consumers a consumer surplus of $1,250). Consumers will
now self-select into two groups, with the Type A consumers paying a low price for a low
quantity and Type B consumers paying a high price for a high quantity. Profit for the
producer will be (100 x $1,250) + (100 x $3,750) = $625,000.
Third try: Reduce the quantity (and the corresponding price) for the Type A consumers
(making this package also less attractive for the Type B consumers). Charge more for the
Type B package than above but still leave the Type B consumer with the same consumer
surplus as he would have gotten from consuming the Type A package (because the Type
A package is now smaller, this is a smaller amount of consumer surplus than before). As
an example, make the Type A package include a quantity of 333.33, rather than 500. We
can calculate the area under the Type B consumer’s demand curve up to this quantity as
[(10 – 3.33) x 333.33]/2 + (3.33 x 333.33) = $2,222. The price-quantity package offered
will be a price of $2,222 for a quantity of 333.33. Type B consumers, if they chose this
Type A package would get consumer surplus of [(10 – 6.66) x 333.33]/2 + (6.66 x
333.33) - $2,222 = $555.50. The Type B package would be designed to give this amount
of consumer surplus. Therefore, the Type B package would offer a quantity of 1000, at a
price of $5,000 - $555.50 = $4444.50. Each type of consumer would be willing to
choose the package intended for them. Total profit for the producer would be (100 x
$2,222) + (100 x $4444.50) = $666,650. As you can see, this design of the two packages
delivers increased profits for the producer.
Note that this example could readily be interpreted in terms of quality and price. Simply
assume that each consumer chooses only one of the products and that Q reflects a varying
level of quality. Type B consumers are willing to consume a higher quality, while Type
A consumers are willing only to consume a lower quality. The producer designs pricequality packages to try to maximize profit through consumer self-selection.