Final answer:
To increase the quantity sold of coffee by 50 percent with an elasticity of demand of 5, the seller must reduce the price by 10 percent from $2 to $1.80.
Step-by-step explanation:
If the elasticity of demand is 5, and the price of a cup of coffee is $2, we can use the concept of elasticity to find out how much the seller would need to reduce the price to increase the quantity sold by 50 percent. Elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price. In this case, the quantity demanded needs to increase by 50 percent. Since we know the elasticity (E) is 5, we can rearrange the formula to solve for the percentage change in price (P).
E = (% change in quantity demanded) / (% change in price)
5 = (50) / (% change in price)
% change in price = 50 / 5
% change in price = 10
Thus, the seller would need to reduce the price by 10 percent to increase the quantity sold by 50 percent. If the current price is $2, a 10 percent reduction would be $0.20, so the new price should be $2 - $0.20 = $1.80.