3. 20 points compete to share the market. Aardvark and Bambi have identical tech

Question

3. 20 points compete to share the market. Aardvark and Bambi have identical technologies, and the marginal cost and average cost of production for each is S25. Demand for dolls is described by P = 85-40. Aardvark and Bambi are the only manufacturers of dolls, and they a. (5 points) What are the marginal revenue functions for Aardvark and Bambi? b. (10 points) for full credit Find the optimal quantity produced by each firm. Show your work c. (5 points) What is the profit earned by each firm at that production level?

Explanation / Answer

This is an example of Cournot duopoly:

Q = q1 + q2

Quantity produced by Aardvark = q1

Quantity produced by Bambi = q2

Revenue (Aardvark) = Pq1 = q1 x (85 - 4(q1 + q2))

MR (Aardvark) = dR/dq1 = 85 - 8q1 -4q2

Similarly, MR (Bambi) = 85 - 8q2 - 4q1

b)

Profit would be maximized by both firms where: MR1 = MR2 = MC = 25

Setting marginal revenues = MC, we get:

8q1 + 4q2 = 60

8q2 + 4q1 = 60

Solve these equations to get:

q1 = q2 = 5 units

c) Profit earned by each firm = P x q - 25 x q

P = 85 - 4 x 10 = $45

Profit = 20 x 5 = $100

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