Suppose a firm has two types of customers but cannot tell which type of buyer the customer is before a purchase is made. If the firm wanted to use quantity discounting, it should charge per unit for any quantity purchased or .

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.

Option A. The firm could charge $65 per unit for any quantity purchased or $60 per unit if buying 4 or more units.

Explanation:

Group One Customers:

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.

Step1: Calculate Marginal Revenue

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  = 4 Units

Now putting this value in the price equation we have:

Price = $100 - 10*4 = $60

Group Two Customers:

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.

Step1: Calculate Marginal Revenue

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  = 2 Units

Now putting this value in the price equation we have:

Price = $110 - 22.5*2 = $65

reducing the scale of the market for a new product.