Complete Question:
Suppose a firm has two types of customers but cannot tell which type of buyer a customer is before a purchase is made. One group of customers has an inverse demand of P = 100 – 10Q, while another group of customers has an inverse demand curve of P = 110 – 22.5Q. If the firm wanted to use a quantity discount pricing scheme, what prices should it set? Assume that the marginal cost of production is constant at $20.
A) The firm could charge $65 per unit for any quantity purchased or $60 per unit if buying 4 or more units.
B) The firm could charge $50 per unit for any quantity purchased or $40 per unit if buying 8 or more units.
C) The firm could charge $25 per unit for any quantity purchased or $20 per unit if buying 2 or more units.
D) The firm could charge $85 per unit for any quantity purchased or $75 per unit if buying 6 or more units.
Answer:
Option A. The firm could charge $65 per unit for any quantity purchased or $60 per unit if buying 4 or more units.
Explanation:
<u>Group One Customers:</u>
We will find the price and quantity by using the following relationship:
Marginal Revenue = Marginal Cost
But the first step would be to calculate marginal revenue.
<u>Step1: Calculate Marginal Revenue</u>
The price and quantity relation of group one customers is given as under:
P = 100 - 10Q
Now we will use total revenue equation which is given as under:
Revenue = Price * Quantity
Here
Price = 100 - 10Q
By putting this in the above equation, we have:
Revenue = (100 - 10Q) * Q
Revenue = 100Q - 10Q^2
Taking derivative on both sides we have:
Marginal Revenue = 100 - 2*10*Q = 100 - 20Q
Now as we know that:
Marginal Revenue = Marginal Cost
Here
Marginal Revenue = 100 - 20Q
Marginal Cost = $20
By putting values, we have:
$100 - 20Q = $20
$100 - $20 = 20Q
Q = $80 / $20 = <u>4 Units</u>
Now putting this value in the price equation we have:
Price = $100 - 10*4 = <u>$60</u>
<u>Group Two Customers:</u>
We will find the price and quantity by using the following relationship:
Marginal Revenue = Marginal Cost
But the first step would be to calculate marginal revenue.
<u>Step1: Calculate Marginal Revenue</u>
The price and quantity relation of group one customers is given as under:
P = 110 – 22.5Q
Now we will use total revenue equation which is given as under:
Revenue = Price * Quantity
Here
Price = 110 - 22.5Q
By putting this in the above equation, we have:
Revenue = (110 - 22.5Q) * Q
Revenue = 110Q - 22.5Q^2
Taking derivative on both sides we have:
Marginal Revenue = 110 - 2*22.5*Q
Marginal Revenue = 110 - 45Q
Now as we know that:
Marginal Revenue = Marginal Cost
Here
Marginal Revenue = 110 - 45Q
Marginal Cost = $20
By putting values, we have:
$110 - 45Q = $20
$110 - $20 = 45Q
Q = $90 / $45 = <u>2 Units</u>
Now putting this value in the price equation we have:
Price = $110 - 22.5*2 = <u>$65</u>
<u></u>
<h2><u>
The data extracted from the above two scenario is as under:</u></h2><h2><u>
For Group 1, Price is $60 and Quantity is 4 Units</u></h2><h2><u>
For Group 2, Price is $65 and Quantity is 2 Units</u></h2><h2><u>
Hence the option A is correct.</u></h2>
