The Antigen Bundle Pricing Problem

Background:
Combination vaccines have become the preferred type of vaccine for immunizing children in high and middle income countries. However, these new vaccines are prohibitive in price to most developing countries, causing them to rely on older less-expensive vaccines. This product divergence decreases economies of scale for the purchase of vaccines and eliminates the financial incentive for manufacturers to maintain production of less-expensive vaccines, or even to develop new vaccines for diseases affecting developing countries.

Objectives:
To establish a combination vaccine pricing strategy to satisfy countries' antigen demand at the lowest possible price, while providing a positive profit for the vaccine producers.

Methods:
Combination vaccines are treated as bundles of antigens that can be priced as a single item. Such bundles are used to formulate an optimization problem that determines the combination vaccine allocation between vaccine producers and different countries, under a price discrimination agreement.

Results:
The optimization problem results in a mixed integer non-linear programming problem that maximizes the total social surplus, measured as the societal benefit resulting from adding the aggregated manufacturing profits and the aggregated customer surplus.

Conclusions:
For any given allocation of combination vaccines, there could be a set of prices at which vaccine producers and countries can commit without sacrificing coverage, nor the economic benefit for both parties.