ISI 2011 ME2 question 1

[Cermank]

A monopolist sells two products, X and Y . There are three consumers with asymmetric preferences. Each consumer buys either one unit of a product or does not buy the product at all. The per-unit maximum willingness to pay of the consumers is given in the table below.



The monopolist who wants to maximize total payoffs has three alternative marketing strategies: (i) sell each commodity separately and so charge a uniform unit price for each commodity separately (simple monopoly pricing); (ii) offer the two commodities for sale only in a package comprising of one unit of each, and hence charge a price for the whole bundle (pure bundling strategy), and (iii) offer each commodity separately as well as a package of both, that is, offer unit price for each commodity as well as charge a bundle price (mixed bundling strategy). However, the monopolist cannot price discriminate between the consumers. Given the above data, find out the monopolist’s optimal strategy and the corresponding prices of the products.

Any idea how to solve this question? I have no idea how to calculate optimal pricing for a pure and a mixed bundle

[leon]

First check the max revenue generated in the given three cases:

1. Uniform pricing:Revenue is maximised when he sets the unit price to 3 so that consumer 1&2 buy X and consumer 2&3 buy Y. Therefore revenue = 3+3+3+3=12.

2. Pure bundle: Revenue is maiximised when he sets the bundle price to 4. All three consumers 1,2&3 will buy. Therefore revenue= 4+4+4=12

3. Mixed strategy: Revenue is maiximised when he sets the unit prices to 4 and bundle price to 6. Consumer 1&2 will buy X&Y at 4. Consumer 2 will buy the bundle at 6. Therefore revenue=4+4+6=14.

So option 3 is the best strategy.