Question

Suppose you are the manager of a theatre company. You have identified two groups of customers. Group 1 has a demand given by Q 1 = 100 - 4P and Group 2 has a demand given by Q 2 = 120 -2P. You are currently charging the same price - 40 euros - to both groups. To maximize revenue, you should charge a price of

25 euros to group 1 and 60 euros to group 2

12.50 euros to group 1 and 30 euros to group 2

50 euros to group 1 and 20 euros to group 2

12.50 euros to group 1 and 50 euros to group 2

which one is correct?

Answer 1

Answer : correct option is :

12.50 euros to group 1 and 30 euros to group 2.

Explanation :

Given :

as a manager of theatre ,

Suppose you have two groups of constomer :

Group 1 has demand = Q1 = 100 - 4P

And group 2 has demand = Q2 = 120 - 2P

You as manager currently charging the same price to both of them i.e 40 euros

Let find out the maximum revenue , you should charge a price of ?

Solution :

1) your revenue for group 1 customer is :

R = p(100 - 4P)

In order to maximize this revenue , we take derivatives and get :

R' = 100 - 8P.

So the best price at maximum revenue for group 1 customer =

P = 100 ÷ 8 = 12.50 euros

2) your revenue for the customer 2 is :

R = p( 120 - 2P )

In order to maximize revenue , we take derivatives and get :

R' = 120 - 4P

So the best price at maximum revenue for group to constomer is :

P = 120 ÷4 = 30.euros