nous products. In many markets, products produced by competing firms are not perfect but imperfect substitutes. We consider such a case here. There are in total N firms, each producing a unique variety which are imperfect substitutes to each other. Since they are different, each variety i with i=1,2,..., N, has a price p₁. Let the symmetric inverse demand of each variety be Pi(gi, Q-i) = abgi – oQ-is where Q = 9; is the total output produced by all firms other than firm i. Parameters a, b, and o are all strictly positive. The parameter a is the price when no firms supply to the market. The parameter b measures how sensitive p; is to a change of firm i's own supply, while o measures such sensitivity to other firms' total supply. Notice that in a Cournot model, we would have b = o. An assumption o [-b/(N-1), b] is imposed to ensure the problem is well-defined (this assumption is only for completeness of the problem and is irrelevant for your derivation). Each firm has a constant marginal cost c> 0. We assume that firms compete by choosing quantities, just like in a standard Cournot model with homogenous products. d. e. f. g. Find the symmetric equilibrium price p* for each variety. How does q* change when N increases? Explain why. How does q* change when o increases? Explain why. Suppose o is instead of a negative value. How does q* change when N increases? Explain why.
nous products. In many markets, products produced by competing firms are not perfect but imperfect substitutes. We consider such a case here. There are in total N firms, each producing a unique variety which are imperfect substitutes to each other. Since they are different, each variety i with i=1,2,..., N, has a price p₁. Let the symmetric inverse demand of each variety be Pi(gi, Q-i) = abgi – oQ-is where Q = 9; is the total output produced by all firms other than firm i. Parameters a, b, and o are all strictly positive. The parameter a is the price when no firms supply to the market. The parameter b measures how sensitive p; is to a change of firm i's own supply, while o measures such sensitivity to other firms' total supply. Notice that in a Cournot model, we would have b = o. An assumption o [-b/(N-1), b] is imposed to ensure the problem is well-defined (this assumption is only for completeness of the problem and is irrelevant for your derivation). Each firm has a constant marginal cost c> 0. We assume that firms compete by choosing quantities, just like in a standard Cournot model with homogenous products. d. e. f. g. Find the symmetric equilibrium price p* for each variety. How does q* change when N increases? Explain why. How does q* change when o increases? Explain why. Suppose o is instead of a negative value. How does q* change when N increases? Explain why.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Our discussion of Cournot in the lecture focused on the case with homoge-
nous products. In many markets, products produced by competing firms
are not perfect but imperfect substitutes. We consider such a case here.
There are in total N firms, each producing a unique variety which are
imperfect substitutes to each other. Since they are different, each variety
i with i = 1, 2, ..., N, has a price pi. Let the symmetric inverse demand of
each variety be
Pi(gi, Q-i) = a - bqi - oQ-i,
-i
where Q_₁ = [q; is the total output produced by all firms other than firm
i. Parameters a, b, and o are all strictly positive. The parameter a is the
price when no firms supply to the market. The parameter b measures how
sensitive p; is to a change of firm i's own supply, while o measures such
sensitivity to other firms' total supply. Notice that in a Cournot model, we
would have b = o. An assumption o € [-b/(N-1), b] is imposed to ensure
the problem is well-defined (this assumption is only for completeness of the
problem and is irrelevant for your derivation).
Each firm has a constant marginal cost c> 0. We assume that firms
compete by choosing quantities, just like in a standard Cournot model with
homogenous products.
d.
e.
f.
g.
Find the symmetric equilibrium price p* for each variety.
How does q* change when N increases? Explain why.
How does q* change when o increases? Explain why.
Suppose o is instead of a negative value. How does q* change
when N increases? Explain why.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a4decfa-c86a-4508-ad17-cd6b643e587a%2F86c1357a-f3af-4b73-a80e-9c986672ecf1%2Fbwgi1n6_processed.png&w=3840&q=75)
Transcribed Image Text:Our discussion of Cournot in the lecture focused on the case with homoge-
nous products. In many markets, products produced by competing firms
are not perfect but imperfect substitutes. We consider such a case here.
There are in total N firms, each producing a unique variety which are
imperfect substitutes to each other. Since they are different, each variety
i with i = 1, 2, ..., N, has a price pi. Let the symmetric inverse demand of
each variety be
Pi(gi, Q-i) = a - bqi - oQ-i,
-i
where Q_₁ = [q; is the total output produced by all firms other than firm
i. Parameters a, b, and o are all strictly positive. The parameter a is the
price when no firms supply to the market. The parameter b measures how
sensitive p; is to a change of firm i's own supply, while o measures such
sensitivity to other firms' total supply. Notice that in a Cournot model, we
would have b = o. An assumption o € [-b/(N-1), b] is imposed to ensure
the problem is well-defined (this assumption is only for completeness of the
problem and is irrelevant for your derivation).
Each firm has a constant marginal cost c> 0. We assume that firms
compete by choosing quantities, just like in a standard Cournot model with
homogenous products.
d.
e.
f.
g.
Find the symmetric equilibrium price p* for each variety.
How does q* change when N increases? Explain why.
How does q* change when o increases? Explain why.
Suppose o is instead of a negative value. How does q* change
when N increases? Explain why.
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