Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand

Question

Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost?

2. Consider question 1 again but assume that Joe’s and Rebecca’s firms compete in prices rather than in quantities. Consumers perceive the ready-mix concrete produced by the two firms as identical products. Find the Nash equilibrium prices when the two firms set their prices simultaneously.

Explanation / Answer

Given,

Qd= 10000-100P

TR= 10000P- 100P2

MR= 10000-200P

MR=MC

10000-200P=25

10000-200P=25

9975/200=P= 49.875

Equilibrium price= 50 (rounding of)

Equilibrium output= 10000-5000= 5000

Profit= TR-TC

TR= 500000-250000

= 250000

TC= 25x5000=125000

Profit= 125000

They both earn= 62500 each

2) we have,

P>MC

Hence firms are at abnormal profits and will continue producing. There are increasing returns to scale.

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