Munisa bakes cakes to order in Samarkand. For a year she charged 10 dollars a cake and sold about 30 cakes a week, which brought in 300 dollars. When the price of flour and butter rose, she wondered whether she should raise her own price, and by how much.
She had kept careful records. Over several months of small changes, she noticed a pattern: for every dollar she raised the price, she sold one cake fewer each week. At 11 dollars she sold 29 cakes; at 12 dollars, 28.
She made a small table on the back of an order form. At 10 dollars, 30 cakes bring in 300 dollars. At 20 dollars, 20 cakes bring in 400 dollars. At 30 dollars, only 10 cakes sell, and the revenue falls back to 300 dollars.
The table surprised her. Prices of 10 dollars and 30 dollars bring in exactly the same money, one by selling many cheap cakes and the other by selling a few expensive ones. The price that brought in the most money was 20 dollars, exactly halfway between them. Her son, who was studying for a business exam, explained why: the revenue rises and then falls in a symmetrical curve, so its highest point always sits midway between two prices that give the same result.
Munisa did not jump straight to 20 dollars. She raised the price to 16 dollars first, to see whether her regular customers would stay. They did, and revenue rose to 384 dollars a week. A month later she moved to 20, and the pattern held.
Better still, she now baked 20 cakes a week instead of 30, so her costs fell while her revenue rose.