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 thefirst firm anticipates this, so the first firm is the only seller. How much willthe first firm produce (in this case the first firm acts like a monopolist andsets 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 is 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’soutput, Q1, plus 100, so substituting Q1 + 100 for QT ot in the inversedemand implies that P = 300 − Q1. That is, if firm 1 produces Q1 itexpects the price to be 300−Q1. This implies that MR = 300−Q2. Howmuch will firm 1 produce (set MR = MC)? What price will clear themarket given the total output Q1 + Q2? What is the producer surplusand profit? (c) Explain intuitively why neither firm wants to change their production ifeach is producing 100 (Q1 = Q2 = 100)? Note that your are explainingwhy Q1 = Q2 = 100 is a Cournot-Nash equilibrium). (d) Calculate the total producer surplus (both firms) and consumer surplusin part (a) and (b). Why is consumer surplus higher with 2 firms thanwith one firm? (e) Intuitively, why is the dead weight loss smaller with two firms than withonly one firm?
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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 like 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 is 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 ot 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 is the producer surplus
and profit?
(c) Explain intuitively why neither firm wants to change their production if
each is producing 100 (Q1 = Q2 = 100)?
Note that your are explaining
why Q1 = Q2 = 100 is a Cournot-Nash equilibrium).
(d) Calculate the total producer surplus (both firms) and consumer surplus
in part (a) and (b). Why is consumer surplus higher with 2 firms than
with one firm?
(e) Intuitively, why is the dead weight loss smaller with two firms than with
only one firm?
