Final answer:
To calculate the elasticity of demand for a leather backpack priced at $100, we need to know how quantity demanded changes with price. Without this information or the derivative of the demand function, we cannot accurately determine the elasticity at that price point.
Step-by-step explanation:
The question is asking to determine the elasticity of demand for a leather backpack when the price is set at $100. Demand elasticity measures how sensitive the quantity demanded is to a change in price. To determine the elasticity at this price, we first need to calculate the quantity demanded using the given demand function q = 300 - 2p, where p is the price. Substituting $100 for p gives us q = 300 - 2(100) = 100 units.
Next, we calculate the percentage change in quantity demanded for a small change in price around $100. If the elasticity is greater than 1, demand is elastic at this price point, meaning a one percent decrease in price would result in more than a one percent increase in quantity demanded, leading to an increase in total revenue. Conversely, if the elasticity is less than 1, demand is inelastic, and a price increase would lead to an increase in total revenue.
Unfortunately, the calculation of elasticity at a specific price point requires information about changes in quantity demanded for small changes in price, which is not provided in the question. Normally, the elasticity can be calculated using the formula: Percentage change in quantity demanded divided by percentage change in price. This would involve the derivative of the demand function and further information on changes in prices or quantities.