Question

The table below indicates the willingness to pay for CDs by various types of buyers. There are N buyers of each type. Costs are $2.50 per CD. Find prices and profits when the seller offers the products (i) individually. (ii) as a bundle. (iii) individually and as a bundle (i.e. uses mixed bundling).

CDs	Romantic	Neoclassical	Tchaikovsky lover	Sophisticate
Berlioz/Tchaikovsky	$8	$6	$9	$2
Bartok/Stravinsky	$6	$6	$2	$9

Answer 1

Lets first rewrite the table in terms of profit. For that we need to reduce 2.5 from each person's reservation price since that is our cost. This gets us the table below.

Now lets examine the three strategies.

i. Individually- For first CD combination, lets call it BT, there are 4 profit options. 5.5, 3.5, 6.5 and -.5. If we select 5.5, Romantic (lets call R) will buy, Neoclassical (lets call them N) will not buy. Tchaikovsky Lover (lets call them T) will also buy. Sophisticate (lets call them S) will, of course, not buy. So total profit for BT in this case would be 5.5*2=11. If we keep the price 3.5, RNT will buy, giving us profit of 3.5*3=10.5. If we keep the price 6.5, only T will buy and profit will be 6.5. So keeping price of BT at 5.5 will give us highest profit of 11. The price of BT here would be 5.5+2.5=8.
For BS, similar calculation will tell us that keeping price at 3.5 is best option as R and N will buy, giving us profit of 7. The price for BS would be 3.5+2.5=6.

So total profit when selling individually is 11+7=18.

ii. Bundling- Here we will need to bundle both BT and BS. The combined reservation profit will be the total of both BT and BS for each individual. So, the combined profit in case of R,N,T and S are 9,7,6 and 6, respectively. If we do calculations similar as in part i, it is clear that keeping the bundled profit at 6 will make sure that all 4 buy, giving us a total profit of 6*4=24. Any other combined price will give us lesser profit. The price of the bundle would be 6+2.5*2 (since we are selling 2 CDs in the bundle)=11.

iii. Mixed- In mixed strategy we can sell both bundled and individual. The most profitable strategy here would be to keep the bundled price at 7-selling to both R and N. Then we will sell BT at 6.5, which T will buy and will sell BS at 6.5, which S would buy. This gives us a total profit of 7*2+6.5*2=14+13=27. This is the highest! The price of the bundle here would be 7+2.5*2=12. Price of both BT and BS is 6.5+2.5=9.