Question
Sometimes the unit price on two sizes of the same product will be the same. When this is the case, how will different kinds of discounts affect the total unit prices of each size?
Answers
GPT-4o mini
When the unit price of two different sizes of the same product is the same, applying discounts can affect their total prices differently depending on the type of discount offered. Here are a few scenarios:
1. **Percentage Discount**: If both sizes receive the same percentage discount, the unit price remains the same after the discount is applied since the percentage is applied to the original unit price. For example, if both sizes are $10 and have a 20% discount, they will each become $8, and the unit prices will remain identical.
2. **Fixed Amount Discount**: If a fixed dollar amount discount is applied, the effect on the total price will depend on the size and price of each product. For instance, if a small size is priced at $5 and receives a $2 discount, its new price will be $3, leading to a new unit price of $3. If a larger size is $10 and also receives a $2 discount, its new price will be $8. The unit prices will now differ; the smaller size will have a lower unit price compared to the larger size since the discount will have a relatively more significant impact on the smaller priced item.
3. **Buy One Get One Free (BOGO)**: This discount type can also affect perceived unit prices differently. For instance, if a small size costs $4 and a large size costs $8, a BOGO on the large size (buy one for $8, get one free) makes the effective unit price $4 per unit, while a BOGO on the small size would make its effective unit price $2 per unit when you account for the free one.
4. **Tiered Discounts**: If tiered discounts apply (for example, the price decreases after buying a certain quantity), the effective unit prices may differ depending on how many units are purchased of each size. As the quantity increases, the larger size might offer a better unit price with increased purchasing.
In conclusion, while the initial unit prices may be the same, the application of different types of discounts can lead to different total prices and potentially different effective unit prices for the two sizes of the product, depending on the structure of the discount applied.
1. **Percentage Discount**: If both sizes receive the same percentage discount, the unit price remains the same after the discount is applied since the percentage is applied to the original unit price. For example, if both sizes are $10 and have a 20% discount, they will each become $8, and the unit prices will remain identical.
2. **Fixed Amount Discount**: If a fixed dollar amount discount is applied, the effect on the total price will depend on the size and price of each product. For instance, if a small size is priced at $5 and receives a $2 discount, its new price will be $3, leading to a new unit price of $3. If a larger size is $10 and also receives a $2 discount, its new price will be $8. The unit prices will now differ; the smaller size will have a lower unit price compared to the larger size since the discount will have a relatively more significant impact on the smaller priced item.
3. **Buy One Get One Free (BOGO)**: This discount type can also affect perceived unit prices differently. For instance, if a small size costs $4 and a large size costs $8, a BOGO on the large size (buy one for $8, get one free) makes the effective unit price $4 per unit, while a BOGO on the small size would make its effective unit price $2 per unit when you account for the free one.
4. **Tiered Discounts**: If tiered discounts apply (for example, the price decreases after buying a certain quantity), the effective unit prices may differ depending on how many units are purchased of each size. As the quantity increases, the larger size might offer a better unit price with increased purchasing.
In conclusion, while the initial unit prices may be the same, the application of different types of discounts can lead to different total prices and potentially different effective unit prices for the two sizes of the product, depending on the structure of the discount applied.