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? 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

Ans)- Imperfectly competitive market

given market demand: P= 100 - 0.05Q

Total revenue (TR) = Price * quantity

TR = P*Q

Put P = 100 - 0.05Q from demand function

TR = (100 - 0.05Q)Q

TR = 100Q - 0.05Q²

Differenciate w.r.t. Q

dTR/dQ = 100 - 0.1Q

MR = 100 - 0.1Q

hence, Profit maximising condition in Imperfect competitive market

MR = MC

[100 - 0.1Q = MC]

0.1Q = 100 - MC

Q = (100-MC)/0.1

Q = 100/0.1 - MC/0.1

[Q = 1000 - 10MC] --------------profit maximising quantity

put Q = 1000 - 10 MC in demand function

P = 100-0.05(1000-10MC)

P = 100 - 50 + 0.5MC

[P = 50 + 0.5MC]---------------------------------profit maximising quantity

Hence, profit maximising combination of output and price would be: Q = 1000-10MC and P = 50+0.5MC.

Now, if consumer more sensitive to your price

i.e. new demand function: P = 100 - 0.1Q

then New TR = P*Q

TR = (100-0.1Q)Q

TR = 100Q - 0.1Q²

MR = 100 - 0.2Q ( by diffentiating TR w.r.t. Q)

hence new profit maximising condition will be-

MR = MC

[100 - 0.2Q = MC]

0.2Q = 100-MC

Q = 100/0.2 - MC/0.2

[Q= 500 - 5MC]------------------------------------profit maximising quantity

put Q= 500- 5MC in new demand function

P = 100- 0.1(500 - 5MC)

P = 100 -50 + 0.5 MC

[P=50 + 0.5MC]-------------------------------------profit maximising price

Hence,the new profit maximising combination of output and price would be: Q = 500 - 5MC and P = 50+0.5MC

Result:

If Consumer made more senstitive to your price,then the quantity demand (Q) at each price would reduce by half.