Question

You own a hot dog stand that you set up outside the student union every day at lunch time. Currently, you are selling hot dogs for a price of $3, and you sell 30 hot dogs a day (point A on the diagram). You are considering cutting the price to $2. The graph shows two possible increases in the quantity sold as a result of your price cut. Use the information in the graph (new quantities are given on the horizontal axis) to calculate the price elasticity between these two prices on each of the demand curves. Use the midpoint formula to calculate the price elasticities. On the demand curve containing the points "A" and "B", the price elasticity of demand for a price cut from $3 to $2 is ___ (Hint: Include the negative sign and enter your response rounded to two decimal places.) On the demand curve containing the points " A " and "C", the price elasticity of demand for a price cut from $3 to $2 is ___ (Hint: include the negative sign and enter your response rounded to two decimal places.)

Answer 1

The price elasticity of demand is calculated using the midpoint formula, considering the percentage change in quantity demanded and the percentage change in price. By inputting the new quantity sold at the reduced price along with the original quantity and price, the price elasticity of demand is obtained after computing and dividing these percentage changes.

Step-by-step explanation:

The question pertains to calculating the price elasticity of demand using the midpoint formula when considering a price change for hot dogs sold at a stand. The midpoint formula is used to calculate the elasticity between two given points on a demand curve, which is the percentage change in quantity demanded divided by the percentage change in price. To find price elasticity, we start by computing the percentage change in quantity and price separately, then divide the results as dictated by the midpoint formula.

Using the data given in the hypothetical scenario: Let's say the new quantity of hot dogs sold after dropping the price to $2 is provided. We will assume quantities B and C to represent the new quantities sold at the $2 price. For each quantity, we must apply the percentage changes in quantity and price:

Percentage change in quantity demanded= [(new quantity - original quantity) / ((new quantity + original quantity) / 2)] × 100

Percentage change in price= [(new price - original price) / ((new price + original price) / 2)] × 100

Finally, the price elasticity of demand is calculated by dividing the percentage change in quantity by the percentage change in price:

Price Elasticity of Demand = (Percentage change in quantity demanded) / (Percentage change in price)