Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes.
What is your question?
Suppose you have a cookie stand, and when you charge $3 per cookie box you sell 200 boxes. But when you raise your price to $4 you only sell 120 boxes.
a. Write an equation for the number of boxes you sell as a function of the price you charge.
b. Denote "B" for number of boxes, and "P" for the price you charge.
c. Assume the function is linear..
To analyze this situation, we can use the concept of demand elasticity. Demand elasticity measures how sensitive the quantity demanded of a product is to changes in its price.
In this case, we can calculate the price elasticity of demand using the midpoint formula:
Price Elasticity of Demand = (Percentage change in quantity demanded) / (Percentage change in price)
Step 1: Calculate the percentage change in quantity demanded:
Change in quantity demanded = 200 - 120 = 80
Percentage change in quantity demanded = (80 / 160) * 100% = 50%
Step 2: Calculate the percentage change in price:
Change in price = $4 - $3 = $1
Percentage change in price = (1 / 3) * 100% = 33.33%
Step 3: Calculate the price elasticity of demand:
Price Elasticity of Demand = (50% / 33.33%) = 1.5
The price elasticity of demand in this case is 1.5, which tells us that the demand for cookies is relatively elastic. This means that a 1% increase in price will result in a 1.5% decrease in quantity demanded. Similarly, a 1% decrease in price will result in a 1.5% increase in quantity demanded.
Therefore, if you want to maximize your revenue, you need to find the price point at which the demand is neither too high nor too low. In this case, it appears that charging $4 per cookie box results in a decrease in quantity demanded, so you could try lowering the price to increase demand.
Keep in mind that this analysis is based on the assumption that there are no other factors affecting demand, such as changes in customer preferences or competition. Conducting market research and experimenting with different prices can provide more accurate insights into determining the optimal price for your cookie stand.