Question

You sell Apples and Banana. You are considering selling them together and separately. You have three types of buyers, Banana lovers, fruit lovers and Apple lovers. The maximum price that buyers are willing to pay is given below

Maximum price each buyer is willing to pay

Apple

Banana

Banana lovers

$50

$40

Fruit Lovers

$75

$30

Apple Lovers

$100

$10

The cost function for Apple is given by the following cost function

C(Q) = 20 + 10Q

The cost function for Banana is given by the following cost function

C(Q) = 26.5+5Q

What is the profit maximizing price for Apple? Banana? What will be your company’s profits?
Can you come up with a pricing that can do better than profits shown in part 1? When you use this pricing, what price should it charge to maximize profit and how much profit can you expect to earn?

Answer 1

Apples and Banana

a) Profit maximizing prices:

i) For Apple = $100

ii) For Banana = $40

b) Profits equal revenue minus costs:

i) For Apple = $100Q - (20 + 10Q) = $60Q

ii) For Banana = $40 - (26.5 + 5Q) = $8.50Q

c) To maximize profit, the price to charge is $100 for Apples and $40 for Banana.

d) I would expect to earn a profit of $68.50 for a set of apple and banana.

Step-by-step explanation:

To maximize profit, Apple and Banana will be sold separately.

But, selling them together, the best profit maximizing prices will be $100 for Apples and $10 for Banana.

At this combined price, the banana still makes a contribution of $5 per unit towards offsetting the fixed cost of $26.50