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# Revenue Maximization Problem With Price Discrimination

IP.com Disclosure Number: IPCOM000004779D
Original Publication Date: 2001-May-17
Included in the Prior Art Database: 2001-May-17
Document File: 5 page(s) / 275K

Motorola

## Related People

Suresh Kalyanasundaram: AUTHOR

## Abstract

Revenue Maximization Problem With Price Discrimination

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Revenue Maximization Problem with Price Discrimination

Suresh Kalyanasundaram

1 Single-link Revenue Maximization with Price Discrimination

In this work, we rst formulate the single-link revenue maximization problem with price discrimination when users express the benet they obtain corresponding to dierentamounts of resource allocation by means of a utility function. We then presenta numerical example that illustrates that, using price discrimination, the network can obtain a higher revenue when compared to the case without price discrimination. Finally,we extend the single-link formulation to the case of multiple links.

Utility functions quantify the value that a user or an application attaches to all possible resource allocation amounts. Welet U i x i denote the utility function of user i ,where x i refers to the amount of throughput resource and U i x i to the utility obtained from that allocation. In a public network, the service provider is interested in maximizing revenue and wishes to determine the prices per unit bandwidth to charge dierent users such that revenue is maximized.

We assume that the network has knowledge of the utility functions of users. The network uses this knowledge of the utility functions of users to determine the demand curveofeachuser. Let M denote the number of users of the system, and let C be the capacityof the channel. The network operator's problem is to determine a vector of prices p 1 ;p 2 ;::: ;p M such that it is the optimal solution to the following problem.

maximize

M i=1 p i D i p i (1)

[p 1 ;p 2 ;:::;p M

P

P

subject to

M i=1 D i p i C:

Note that p i is the price per unit bandwidth that user i is charged. Also observe that if price dis- crimination were not allowed, then the network can only determine a single price per unit bandwidth instead of dierent prices for dierent users. In the problem in Eq. (1), D i p i refers to the quantity demanded by user i at price p i . The term D i p i is called the demand function of user i . The above optimization problem states that the system operator will set the price per unit bandwidth for each user such that it will maximize its revenue subject to the constraint that the aggregate demand at that set of prices is less than the channel capacity. The product of p i and D i p i is the revenue obtained from user i , which when summed over all users yields the total revenue.

Wenow describe how the demand curve of a user is obtained from its utility function. At a given price p ,we wish to nd out the quantity demanded by a user whose utility function is given by U x ). By F( p we denote the set of all feasible demands that the user can make given that the price per

1

unit bandwidth is p . Among the set of all feasible demands, the user will make that demand which maximizes its \consumer surplus." Note that by making a demand of x , the u...