Question1: A homogeneous products duopoly faces a market demand function given b

Question

Question1: A homogeneous products duopoly faces a market demand function given by Q = 40-4P, where Q = Q1 + Q2. Both firms have a constant marginal cost MC-2 1. Suppose the two firms set their quantities simultaneously by guessing the other firm's quantity choice. Derive the equation of each firm's reaction curve and then graph these curves. 2. What is the Cournot equilibrium quantity and price in this market for each firm? 3. What would the equilibrium price in this market be if it were perfectly competitive? 4. What is the Bertrand equilibrium price in this market?

Explanation / Answer

1) we have Q = 40 - 4P

or P = 10-0.25(Q1 + Q2)

Firm 1 total revenue = 10Q1 - 0.25Q12 - 0.25Q1Q2

firm 1 marginal revenue = 10-0.5Q1-0.25Q2

now put MR=MC, and solve for Q1 to get firm 1 reaction curve.

10-0.5Q1 -0.25Q2 = 2

Q1 = 16-0.5Q2 ( firm 1 reaction curve. )

now Firm 2 total revenue = 10Q2 - 0.25Q22-0.25Q1Q2

firm 2 marginal revenue = 10-0.5Q2-0.25Q1

now put MR=MC, and solve for Q2 to get firm 2 reaction curve.

10-0.5Q2-0.25Q1 = 2

Q2 = 16-0.5Q1 ( firm 2 reaction curve.)

2) for cournot equilbruim quantity and price, we have to find Q1 and Q2.

so , Q1 = 16-0.5(16-0.5Q1)

Q1 = 16-8+0.25Q1

0.75Q1 = 8

Q1 = 10.7  

Q2 = 16-0.5(10.7)

Q2 = 16-5.35 =10.6

market equilbruim quantity and price is

Q = 10.7 +10.6 = 21.3

P = 10-0.25(21.3)

P = 10 -5.325

P =$4.7

3) Equilbruim price would be determine by equating MR=MC

P =10-0.25Q

MR = 10-0.5Q and MC =2

10-0.5Q = 2

Q = 16

P = 10-4 = $6

so, market equilbruim price is $6

4)please uplaod it again. its against chegg policy

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