(a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts as a monopolist and sets output where MR = MC)? Hint: The first firm’s inverse demand is P = 400−(Q1 +Q2), but since Q2 = 0 we can write this as P = 400−Q1 and so MR = 400 − 2Q1. Mathematically this problem is the same as a monopoly problem. What quantity will firm 1 choose? What price will it charge? What are the producer surplus and profit? (b) Now suppose instead that the second firm produces exactly 100 units, and that the first firm anticipates this. The total output is the first firm’s output, Q1, plus 100, so substituting Q1 + 100 for QT in the inverse demand implies that P = 300 − Q1. That is if firm 1 produces Q1 it expects the price to be 300−Q1. This implies that MR = 300−Q2. How much will firm 1 produce (set MR = MC)? What price will clear the market given the total output Q1 + Q2? What are the producer surplus and profit? (c) Explain intuitively why neither firm wants to change their production if each is producing 100 (Q1 = Q2 = 100)?
Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. One simple way to depict rivalry in a duopoly (2 firms) is the Cournot model. This model is reasonable in agricultural markets where firms choose production (plantings) in advance and the market price is determined later after the crop is harvested. In the Cournot model, we imagine that the two firms simultaneously choose their production or quantity and that demand (market clearing) determines the price given each firms’ quantity.
(a) Suppose (hypothetically) that the second firm produces 0 units, and the first firm anticipates this, so the first firm is the only seller. How much will the first firm produce (in this case the first firm acts as a monopolist and sets output where MR = MC)?
Hint: The first firm’s inverse demand is P = 400−(Q1 +Q2), but since Q2 = 0 we can write this as P = 400−Q1 and so MR = 400 − 2Q1. Mathematically this problem is the same as a
(b) Now suppose instead that the second firm produces exactly 100 units, and that the first firm anticipates this. The total output is the first firm’s output, Q1, plus 100, so substituting Q1 + 100 for QT in the inverse demand implies that P = 300 − Q1. That is if firm 1 produces Q1 it expects the price to be 300−Q1. This implies that MR = 300−Q2. How much will firm 1 produce (set MR = MC)? What price will clear the market given the total output Q1 + Q2? What are the producer surplus and profit?
(c) Explain intuitively why neither firm wants to change their production if each is producing 100 (Q1 = Q2 = 100)?
(you are explaining why Q1 = Q2 = 100 is a Cournot-Nash equilibrium).
(d) Calculate the total producer surplus (both firms) and
(e) Intuitively, why is the
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