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Suppose the market demand curve is given by100 2P Q  . If one Cournot duopolist produces1 10Q  ,the residual demand curve faced by the other Cournot duopolist isA) P = 90 – 2Q2.B) P = 80 – 2Q2.C) Q2 = 80 – P.D) Q2 = 80 – 2P

Question

Suppose the market demand curve is given by100 2P Q  . If one Cournot duopolist produces1 10Q  ,the residual demand curve faced by the other Cournot duopolist isA) P = 90 – 2Q2.B) P = 80 – 2Q2.C) Q2 = 80 – P.D) Q2 = 80 – 2P

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Solution

The Cournot model is a model of competition among firms in an oligopoly where firms decide on a quantity to produce independently and simultaneously. In this case, we have a duopoly, meaning there are two firms in the market.

The market demand curve is given by Q = 100 - 2P. This is the total quantity demanded in the market for a given price.

If one Cournot duopolist (let's call this Firm 1) produces Q1 = 10, this means that the quantity produced by this firm is 10 units.

The residual demand curve faced by the other Cournot duopolist (Firm 2) is the market demand curve minus the quantity produced by Firm 1. This is because the quantity that Firm 2 can sell is the total quantity demanded in the market minus the quantity already being supplied by Firm 1.

So, the residual demand curve faced by Firm 2 is Q2 = Q - Q1 = (100 - 2P) - 10 = 90 - 2P.

Rearranging this equation to solve for P gives us P = 45 - Q2/2.

So, the correct answer is not listed among the options you provided. The correct residual demand curve faced by the other Cournot duopolist is P = 45 - Q2/2.

This problem has been solved

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