Ben used to sell imported silk ties for $20 each in his store. His sales averaged 30 ties a week. He pays $12 to buy the ties he sells. Ben wondered if he could increase his profit by raising his price to $25. He tried this for a month, but his sales fell to 20 ties a week. How much money did Ben take in at the old price, and what was his profit at the old price? How much income did he receive at the new price, and what was his profit at his new price? Should he keep the new price? Explain how this example demonstrates the law of demand.

Question

Ben used to sell imported silk ties for $20 each in his store. His sales averaged 30 ties a week. He pays $12 to buy the ties he sells. Ben wondered if he could increase his profit by raising his price to $25. He tried this for a month, but his sales fell to 20 ties a week. How much money did Ben take in at the old price, and what was his profit at the old price? How much income did he receive at the new price, and what was his profit at his new price? Should he keep the new price? Explain how this example demonstrates the law of demand.

Is there an equation or formula I could use? I'm not getting this question.

Answer 1

20 * 30 = $600 he took in

(20 - 12) * 30 = $240 profit

25 * 20 = $500 he took in
(25 - 12) * 20 = $260 profit

Answer 2

Yes, there is a formula you can use to solve this problem. Let's break down the steps:

1. Calculate Ben's revenue at the old price:
- Revenue = Price * Quantity
- Price = $20, Quantity = 30 ties per week
- Revenue = $20 * 30 = $600 per week

2. Calculate Ben's profit at the old price:
- Profit = Revenue - Cost
- Revenue = $600 per week, Cost = $12 * 30 ties = $360 per week
- Profit = $600 - $360 = $240 per week

3. Calculate Ben's revenue at the new price:
- Price = $25, Quantity = 20 ties per week
- Revenue = $25 * 20 = $500 per week

4. Calculate Ben's profit at the new price:
- Revenue = $500 per week, Cost = $12 * 20 ties = $240 per week
- Profit = $500 - $240 = $260 per week

Now, let's analyze the results and determine if Ben should keep the new price:

- At the old price, Ben took in $600 per week and had a profit of $240 per week.
- At the new price, Ben took in $500 per week but had a higher profit of $260 per week.

According to these calculations, Ben's profit increased when he raised the price from $20 to $25. However, we should also consider the decrease in sales from 30 ties to 20 ties per week.

This example demonstrates the law of demand, which states that when the price of a product increases, the quantity demanded tends to decrease. In this case, when the price increased to $25, the demand for the ties decreased from 30 ties to 20 ties per week. Although Ben made more profit per tie, the decrease in quantity sold resulted in a smaller overall revenue.

To determine if Ben should keep the new price, he needs to consider other factors such as competitiveness, customer preferences, and potential market demand.