Computing Elasticity

Business Calculus · Axiom Academy

Step-by-step calculation of price elasticity of demand Problem: Streaming Service Pricing A streaming service has found that demand for subscriptions follows: where x is thousands of subscribers and p is price in dollars Find: The elasticity of demand when the price is 15/month First, we need to find how many subscribers there are at 15: 40,000 subscribers at 15/month We need to find how quantity changes with price. Starting from p = 25 - 0.25x : Differentiate with respect to p: For every 1 increase in price, demand drops by 4,000 The point elasticity formula is: Substitute our values (p = 15, x = 40, dx/dp = -4): A 1% increase in price causes a 1.5% decrease in quantity demanded . Since |E| > 1, demand is elastic at this price point. With elastic demand, the streaming service should consider lowering prices . The increase in subscribers would more than offset the lower price per subscriber, increasing total revenue. Current: 40,000 subscribers × 15 = 600,000/month If price drops 10% to 13.50: ~46,000 subs × 13.50 = 621,000/month Revenue increases despite lower price! You can now calculate and interpret price elasticity of demand. Based on the example above, which approach is correct?

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