Suppose a firm has two types of customers but cannot tell which type of buyer a

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 - 100, while another group of customers has an inverse demand curve of P = 110 - 22.50. 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. The firm could charge S65 per unit for any quantity purchased or S60 per unit if buying 4 or more units. The firm could charge $50 per unit for any quantity purchased or S40 per unit if buying 8 or more units. The firm could charge $25 per unit for any quantity purchased or $20 per unit if buying 2 or more units. The firm could charge $85 per unit for any quantity purchased or $75 per unit if buying 6 or more units.

Explanation / Answer

The correct option is A

Group one customers

P = 100 - 10Q

Revenue = Price X quantity

R = (100 - 10Q)Q

R = 100Q - 10Q2

Marginal revenue = 100 - 20Q

Quantity to be sold is found by equating marginal revenue & marginal cost

100 - 20Q = $ 20

Q = 4 units

price = 100 - 10Q

Price = $ 60

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Another group of customers

P = 110 - 22.5Q

Revenue = (110 - 22.5Q) Q

Marginal revenue = 110 - 45 Q

MR = MC

110 - 45 Q = $ 20

Q = 2 units

price = 110 - 22.5 X2

Price = $ 65

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