find the uniform price if there is two customers: Type A who will only pay 10.00 dollars for a single unit of the good, and Type B who will only pay 8.00 dollars for a single unit of goods. There is 100 customers of Type A and 50 of the customers of Type B.
Well, in order to find the uniform price that satisfies both Type A and Type B customers, let's see if we can come up with something that appeases both of their wallets.
Since Type A customers are willing to pay $10.00 per unit and there are 100 of them, we can imagine a scenario where they are chanting "10! 10! 10!"
On the other hand, Type B customers are a little more frugal and are only willing to pay $8.00 per unit. We can imagine them sitting in a circle, singing "8! 8! 8!"
Now, here comes the tricky part. We need to find a price that keeps both Type A and Type B customers happy. So, let's take a moment to think about what we can offer to keep both groups satisfied.
How about this: we'll charge $8.00 per unit, so the Type B customers will be overjoyed, and then we'll kindly inform the Type A customers that we're running a special promotion today and they can have the goods for $10.00 per unit. This way, we can make everyone feel like they got a great deal, even though deep down, we know what the price actually was.
So, the uniform price that works for both Type A and Type B customers is $8.00 per unit. Remember, it's all about making everyone laugh, or at least smile.
To find the uniform price, we need to determine the price that satisfies both Type A and Type B customers.
Let's assume the uniform price is "x" dollars for a single unit of the good.
For the Type A customers, the price they are willing to pay is $10.00. Since there are 100 Type A customers, the total revenue from Type A customers is given by:
Total revenue from Type A = 100 customers * $10.00 per unit
For the Type B customers, the price they are willing to pay is $8.00. Since there are 50 Type B customers, the total revenue from Type B customers is given by:
Total revenue from Type B = 50 customers * $8.00 per unit
To find the uniform price, the total revenue from Type A must equal the total revenue from Type B. Therefore:
100 customers * $10.00 per unit = 50 customers * $8.00 per unit
Simplifying the equation:
1000 = 400 + 50x
600 = 50x
Dividing both sides by 50:
12 = x
Therefore, the uniform price would be $12.00 per unit of goods.
To find the uniform price, we need to determine the price that satisfies both Type A and Type B customers. The price should be acceptable for both types of customers so that they are willing to purchase the goods.
First, we need to calculate the total revenue from Type A customers. Type A customers are willing to pay $10.00 for a single unit of the good, and there are 100 of them. Therefore, the total revenue from Type A customers is:
Total revenue from Type A = $10.00 * 100 = $1000.00
Next, let's calculate the total revenue from Type B customers. Type B customers are willing to pay $8.00 for a single unit of the good, and there are 50 of them. So, the total revenue from Type B customers is:
Total revenue from Type B = $8.00 * 50 = $400.00
Now, we want to find a uniform price that can satisfy both types of customers. To do this, we need to find a price that will result in the same total revenue as the sum of the individual revenues from Type A and Type B customers.
Let's assume that the uniform price is P dollars.
Total revenue from Type A customers at the uniform price = P * 100
Total revenue from Type B customers at the uniform price = P * 50
To find the uniform price, we set the total revenue from the two types of customers equal to the sum of the individual revenues:
P * 100 + P * 50 = $1000.00 + $400.00
Simplifying this equation:
150P = $1400.00
Dividing both sides by 150:
P = $1400.00 / 150
P ≈ $9.33 (rounded to two decimal places)
Therefore, the uniform price, which satisfies both Type A and Type B customers, is approximately $9.33.