Elasticity measures how sensitive customers are to price changes. If a small price increase causes a large drop in sales, demand is elastic. If sales barely change, demand is inelastic.  

Imagine you run a music studio charging $120 per lesson with 9 clients, generating $1,080 in revenue. If you raise the price to $200 and only 5 clients remain, revenue becomes $1,000. Despite serving fewer clients, your studio nearly maintains its revenue while potentially reducing service costs. If the cost per client is $100, total costs drop from $900 to $500, and profit increases from $180 to $500. 

To calculate the price elasticity of demand, divide the percentage change in quantity demanded by the percentage change in price. Horowitz was speaking with a business owner who asked how to calculate the percentage change in price. Was the $80 price increase in this example a 66.7% increase ($80/$120) when comparing it to the original price, or a 40% increase ($80/$200) when comparing it to the new price? Horowitz responded that to find the percentage change, they should compare it to the original price. However, to avoid this confusion, economists usually use the midpoint by taking the average of the $200 and $120, which is $160, so the price increases by 50% ($80/$160).  

In this case, using the midpoint, the price increased by 50%, while the number of clients dropped by 57.14% ((9-5)/(9+5)/2), resulting in an elasticity of approximately −1.14. Since the absolute value is greater than 1, demand is considered elastic, meaning customers are relatively responsive to price changes.  

Elasticity mainly depends on how easily your customers can switch to alternatives. If your service is unique, demand may be less sensitive to price. But if substitutes are easy to find, even a small price hike could drive customers away. These factors determine how much quantity demanded will fall when prices rise. 

Your customers’ income also matters. In the U.S., the top 20% of households earn over half of all income. That means a small segment of clients may be willing to pay much more if you offer something they value. Many businesses ask: What do my highest-paying clients want beyond the basics? Can I design premium services to meet those needs? 

The concept of elasticity helps firms make informed pricing and output decisions. Policymakers use it to forecast future tax revenues, the effects of raising minimum wages, and how innovations in production affect profits in various industries.