The two most familiar pricing models in practice have only one parameter: linear pricing (a constant price per item), and subscription or bundling (one price for the entire bundle).
a) Pure Bundling
Bundling has recently received substantial attention for information goods [BB99, CS99]. The price schedule is:
Profit is
where 
, the lowest 
that will
subscribe. For lower , the value of the bundle of N items
( 
) is not enough to cover the price of the bundle. 
is
defined by 
.
Taking the derivative of profit with respect to 
and setting it equal to zero
yields the profit-maximizing bundle price of 
, 
. Profit equals 
. Consumer
surplus and social welfare are 
and 
respectively.
b) Linear Pricing
An alternative one-parameter model is linear pricing. Consumers pay 
for
each item they choose to receive. Thus, the price schedule is:
Facing this marginal price of , each person will choose their optimal
number of articles ( 
) so that 
. Then,
. Profit to the monopolist is:
Maximizing profit yields 
. Consumer surplus and
social welfare under linear pricing are
and respectively.
Profit equals , which is the same as for
pure bundling. However not all pricing schemes of the same
complexity yield the same profit. For example, if were
uniformly distributed between 
and 
(where 
) then pure bundling would attain higher
profit than linear pricing, since the area under the curve will be
reduced for linear pricing, but not for pure bundling.