One of our colleagues has been enjoying a well-earned break in Spain. He has particularly liked sitting in the sun with a cold pint, and his usual watering hole charged a very reasonable €4 for the drink. In fact, just about everywhere priced a pint at €4 or €4.50.
One day he walked along the coast and found a bar for a couple of beers to build up his strength for the walk back. The taste was slightly spoiled by the charge of €5.50, and the glass was, shall we say, not overfilled.
So he only had one, and set off on his walk back.
Now, he is a curious chap, and it occurred to him that the bar that he had just visited had probably lost money by having higher prices. Had the pint been €4 as in many other places he would have bought two, but as it was he only bought one. The bar had made more profit on the one pint with its higher price, but would two lots of a lower margin been better.
So, at what wholesale price would the profit be the same on one pint at €5.50 and two pints at €4?
And is it likely that the bar was losing money with its higher prices?
We need to solve 5.5 - x = 2 (4 - x) and a little rearrangement gives x = 2.5. So at a buy-in price of €2.50 one pint at €5.50 makes €3, and two pints at €4 make €1.50 each, so €3 again.
Now, most bars have a 100% mark up, so the €4 bar is likely to be buying at €2. So at a buy-in price of €2 one pint at €5.50 makes €3.50, but two pints at €4 make €2 each, so €4.
It would appear that the expensive bar could be missing out.