Question

Aardvark and Bambi are the only manufacturers of dolls, and they compete to share the market. Aardvark and Bambi have identical technologies, and the marginal cost and average cost of production for each is $30. Demand for dolls is described by P = 60 - 5Q.

A) What are the marginal revenue functions for Aardvark and Bambi?  

B) Find the optimal level of production for each firm. Show your work for full credit.

C) What is the profit earned by each firm at that production level?

D) Suppose Aardvark and Bambi decide to collude to increase their profit. How much would they produce together? Show your work for full credit.

E) If such collusion were legal, why would such an agreement be unstable? Explain briefly.

Answer 1

A) P=60-5q1-5q2

TR1= 60q1- 5q1² -5q1q2

MR1 ( Aardvark) = 60- 10q1- 5q2

MR2 (Bambi)= 60-5q1-10q2

2) the optimal level of production for both firm is the level of output where MR= MC

MR1=MC1

60-10q1-5q2= 30

-10q1= 30-60+5q2

q1= 3-0.5q2

MR2=MC2

60-10q2-5q1=30

q2= 3-0.5q1

Put q2 in Aadvark optimal level of output funcufun.

q1= 3-0.5(3-0.5q1)

q1= 3- 1.5+0.25q1

0.75q1= 1.5

q1=2

q2= 3-0.5(2)

q2= 2

So both firm optimal level of output is 2 units.

C) profit earned by each firm= TR-TC

Profit = (2*40)-(30*2)= 80-60

Profit= $20 .

Since each firms have identical cost and have same optimal level of output. TherfoThe both firms profit is $20.

D) when they collude. Thier cost become one cost and facing only demand curve P= 60-5q

MR= 60-10q and MC= 30

60-10q=30

Q= 3

So they will produce only 3 units of output.