Question

1. Total market demand for pillows in San Francisco is given by P = 125 - 0.5Q. There are 2 suppliers of pillows in the market, who each have a constant marginal cost of $5 per pillow. If the 2 firms collude together and act as a monopolist, they will sell ____________ pillows at a price of $ _______________.

2.  Total market demand for pillows in San Francisco is given by P = 125 - 0.5Q. There are 2 suppliers of pillows in the market, who each have a constant marginal cost of $5 per pillow. If the 2 firms compete against each other in a Cournot duopoly, how many pillows will each firm produce?  



ANSWER BOTH QUESTIONS TO RECEIVE RATING. IF BOTH ARE NOT ANSWERED, NO RATING WILL BE GIVEN. THANKS.

Answer 1

Question 1:

2 firms collude together and act as a monopolist.

A monopoly firm produces at MR = MC
------------

P =125 -0.5Q

=> TR = PQ

=> TR = (125 -0.5Q)Q

=> TR = 125Q - 0.5Q²

---

MR = dTR / dQ

=> MR = 125 - Q

and

MC = 5 (Given)

Set MR =MC
=> 125 - Q = 5

=> Q = 125 - 5

=> Q = 120

and

P = 125 - 0.5Q

=> P = 125 - 0.5(1200

=> P = 125 - 60

=> P = 65

Answer: If the 2 firms collude together and act as a monopolist, they will sell 120 pillows at a price of $65.

-----------------------------------------------------

Question 2: Cournout dupoly:

There are two firms firm 1 and firm 2.

Q₁ is output of firm 1.

Q₂ is output of firm 2.

Q is market output.

So, Q = Q₁ + Q₂

----------------------

Reaction function of firm 1.

Firm 1 maximizes profit at MR₁ = MC₁.

TR₁ = PQ₁

=> TR₁ = (125 - 0.5Q) Q₁

=> TR₁ = (125 - 0.5Q₁ - 0.5Q₂) Q₁

=> TR₁ = (125Q₁ - 0.5Q₁² - 0.5Q₂Q₁)

--

MR₁ = dTR₁ / dQ₁

=> MR₁ = 125 - Q₁ -0.5Q₂

and

MC₁ = 5

Set MR₁ = MC₁

=> 125 - Q₁ - 0.5Q₂ = 5

=> 125 - 5 - 0.5Q₂ = Q₁

=> Q₁ = 120 - 0.5Q₂ ----------------------(firm 1 reaction function) (Eq1)

--------------------------------------------------

Reaction function of firm 2:

Firm 2 maximizes profit at MR₂ = MC₂

TR2 = PQ₂

=> TR₂ = (125 - 0.5Q) Q₂

=> TR₂ = (125 - 0.5Q₁ - 0.5Q₂) Q₂

=> TR₂ = (125Q₂ - 0.5Q₁Q₂ - 0.5Q₂²)

--

MR₂ = dTR₂ / dQ₂

=> MR₂ = 125 - 0.5Q₁ -Q₂

and

MC₂ = 5

Set MR₂ = MC₂

=> 125 - 0.5Q₁ - Q₂ = 5

=> 125 - 5 - 0.5Q₁ = Q₂

=> Q₂ = 120 - 0.5Q₁ ----------------------(firm 2 reaction function) (Eq2)

--------------------------------------------------

Substitute eq(2) in eq(1)

Q₁ = 120 - 0.5Q₂

=> Q₁ = 120 - 0.5(120 - 0.5Q₁)

=> Q₁ = 120 - 60 + 0.25Q₁

=> Q₁ - 0.25Q₁ = 60

=> 0.75Q₁ = 60

=> Q₁ = (60 / 0.75)

=> Q₁ = 80

Put Q₁ = 80 in eq(2)

=> Q₂ = 120 - 0.5Q₁

=> Q₂ = 120 - 0.5(80)

=> Q₂ = 80

---------------------------

Firm 1 will produce 80 pillows (i.e., Q₁ =80)

Firm 2 will produce 80 pillows (i.e., Q₂ =80)