Question

1. You operate in an Imperfectly Competitive market where demand for you product is given by: P= 100 - 0.05Q. What Price output combination would maximize your profit?

2. What would happen to your answer in #1 if entry made consumers more senstitive to your price and your demand changed to: P = 100 - 0.1Q?

Answer 1

Solution :-

(1) :-

an Imperfectly Competitive market

demand for product is given by:

P = 100 - 0.05Q

Total revenue is given by :-

Total Revenue = Price x Quantity

TR = P x Q

= ( 100 - 0.05Q) x Q ........( P = 100 - 0.05Q)

TR = 100Q - 0.05Q^2

Now, differentiate TR with respect to Q

dTR/dQ = 100 - 0.1Q

So,

MR = 100 - 0.1Q

Hence, in imperfect competitive market, profit maximizing condition will be :-

MR = MC

100 - 0.1Q = MC

100 - MC = 0.1Q

Q = ( 100 - MC)/0.1

Q = 100/0.1 - MC/0.1

[ Q = 1000 - 10MC]....... profit maximizing quantity

Now,

Demand function P = 100 - 0.05Q

Put [ Q = 1000 - 10MC ] in demand function

P = 100 - 0.05 x ( 1000 - 10MC)

P = 100 - 50 + 0.5MC

[ P = 50 + 0.5MC ]........profit maximizing price

So, Price output combination maximizing your profit would be Q = 1000 - 10MC and

P = 50 + 0.5MC.

(2) :-

if entry made consumers more senstitive to your price and

your demand changed to:

P = 100 - 0.1Q

Then, new total Revenue is given by

TR = P x Q

= ( 100 - 0.1Q) x Q......( P = 100 - 0.1Q)

TR = 100Q - 0.1Q^2

Now, differentiate TR with respect to Q

dTR/dQ = 100 - 0.2Q

MR = 100 - 0.2Q

Thus, New profit maximizing condition :-

MR = MC

100 - 0.2Q = MC

100 - MC = 0.2Q

Q = ( 100 - MC)/0.2

[ Q = 500 - 5MC ]....... profit maximizing quantity

New demand function:-

P = 100 - 0.1Q

Put [ Q = 500 - 5MC ] in new demand function

P = 100 - 0.1 x ( 500 - 5MC)

P = 100 - 50 + 0.5MC

[ P = 50 + 0.5MC ] ..... profit maximizing price

Thus, New price output combination maximizing profit would be Q = 500 - 5MC

and Price P = 50 + 0.5MC.

So, if entry made consumers more sensitive to your price, then the quantity demand (Q) at each price would reduce by half.