Question

You are the manager of a local sporting goods store and recently purchased a shipment of 60 sets of skis and ski bindings at a total cost of $25,000 (your wholesale supplier would not let you purchase the skis and bindings separately, nor would it let you purchase fewer than 60 sets). The community in which your store is located consists of many different types of skiers, ranging from advanced to beginners. From experience, you know that different skiers value skis and bindings differently. However, you cannot profitably price discriminate because you cannot prevent resale. There are about 20 advanced skiers who value skis at $400 and ski bindings at $275; 20 intermediate skiers who value skis at $300 and ski bindings at $400; and 20 beginning skiers who value skis at $200 and ski bindings at $350. What is your maximum revenue if you charge a separate price for skis and bindings? $ What is your maximum revenue if you sell skis and bindings as a bundle? $

Answer 1

We have 60 skis and the demand for skis is: 20 people(Advanced) willing to pay upto 400$, 20 people(Intermediates) willing to pay upto 300$ and 20 people(beginners) willing to pay upto 200$

The maximum revenue for skis in this case will be either by pricing it at 300 so that 40 people buy it (advanced and intermediates) or pricing it at 200 so that 60 people buy it (All 3 groups), in both cases the revenue will be 200*60=300*40=12000$ (If you price it at 400$, only advanced will buy it and revenue will be 8000$)

So revenue from skis sold seperately = 12000$

Similarly for ski bindings we have 20 people(Advanced) willing to pay upto 275$, 20 people(Intermediates) willing to pay upto 400$ and 20 people(beginners) willing to pay upto 350$

Revenue from a price of 400=400*20 (Only intermediates will buy) 8000$

Revenue from a price of 350 = 350*40= 14000$ (intermediates and beginners will buy)

Revenue from a price of 275 = 275*60 = 16,500$ (All 3 groups will buy)

Thus max revenue from ski bindings sold seperately = 16,500$

Total max revenue if both are sold seperately = 16,500+12,000$= 28,500$

Now, for bundle

we have 20 people(Advanced) willing to pay upto 400+275=675$, 20 people(Intermediates) willing to pay upto 400+300=700$ and 20 people(beginners) willing to pay upto 200+350=550$

In this case, we get the max revenue from selling the bundle at 550 so that all 60 buyers buy it(Since 550*60>675*40 and 550*60>700*20). The max revenue 550*60=33000$

Therefore the max revenue from selling as a bundle is 33,000$

Hope it helps. Do ask for any clarifications if required.