Question

Assume a monopolist with marginal cost of 0 is selling to two types of agents whose demand function is given by qA= 10−p, qB= 8−p. The monopolist is not allowed to price discriminate between the two agents. But he designs one package consisting of 10 units and another one consisting of 8 units.What is the highest price the monopolist can charge for the bigger package so that it is still bought by some agents?

(a)p= 32   (b)p= 48   (c)p= 50    (d)p= 34

Answer is D

Answer 1

First Agent demand function, qA=10-P

Inverse Demand Function, P= 10- qA

Since it is monopoly, MR = 10 - 2qA (doubling the slope)

We know, MC = 0

Now we can get the optimum quantity by equating MC and MR

MR = MC

10 - 2qA = 0

=> 2qA = 10

=> qA = 5

Now putting the quantity in demand function we can get the maximum price he can charge from first agent

P = 10 - qA

=> P = 10 - 5

=> P = 5

Now he can charge from the package of 10 quantity, 10 X 5 = 50(without consideration of 2nd Agent)

Now,

2nd Agent Demand Function, qB= 8 - P

Inverse demand function, P = 8 - qB

MR = 8 - 2qB

Optimum Quantity => MR = MC

=> 8 - 2qB = 0

=> 2qB = 8

=> qB = 4

Maximum Price he can charge from the 2nd agent -

P = 8 - qB

=> P = 8 - 4

=> P= 4

And the maximum price he can charge from the package of 8 quantity is 8 X 4 = 32

Now if you look at the both package prices then the package with quantity 8 can be bought at price 32. but the package of same product having 10 quantity can be bought at price 50. Additional  charge is 18(no one will by because additional 2 number of quantity bear price 9 each). now the options with price 50 is no more valued because no one will buy it. Price 48 is also much more higher(additional 16, no one will by because additional 2 number of quantity bear price 8 each). He can charge only price 34 as per the options given in the question, because the customer will be willing to give the extra price 2 as they will get additional 2 number of quantity at a lower price.