Suppose that there is "dominant" firm with total cost function of c(q) = 100 + 10q + 0.25q². It faces a market demand function (inverse) of p = 100 – 0.5Q, where Q indicates total market supply. This dominant firm has to deal with 10 fringe firms, each of whom behaves perfectly competitively. Each fringe firm has a marginal cost dc(q) function dq • Calculate the supply function of the fringe firms • Using this, calculate the residual demand function of the dominant firm. • Derive the marginal revenue function of the dominant firm. = 20g + 25
Suppose that there is "dominant" firm with total cost function of c(q) = 100 + 10q + 0.25q². It faces a market demand function (inverse) of p = 100 – 0.5Q, where Q indicates total market supply. This dominant firm has to deal with 10 fringe firms, each of whom behaves perfectly competitively. Each fringe firm has a marginal cost dc(q) function dq • Calculate the supply function of the fringe firms • Using this, calculate the residual demand function of the dominant firm. • Derive the marginal revenue function of the dominant firm. = 20g + 25
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![Suppose that there is "dominant" firm with total cost function of
c(q) = 100 + 10g + 0.25q². It faces a market demand function
(inverse) of p = 100 – 0.5Q, where Q indicates total market supply.
This dominant firm has to deal with 10 fringe firms, each of whom
behaves perfectly competitively. Each fringe firm has a marginal cost
dc(q)
= 20q + 25
function
dq
• alculate the supply function of the fringe firms
• Using this, calculate the residual demand function of the dominant firm.
• Derive the marginal revenue function of the dominant firm.
• Find the profit-maximizing price of the dominant firm.
• How much does the competitive fringe supply to the market?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b80beb3-7f20-4cd8-9570-8d0670fcd8d3%2F38408791-53e1-484f-a431-cdf55513f49e%2Fmf4mx1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that there is "dominant" firm with total cost function of
c(q) = 100 + 10g + 0.25q². It faces a market demand function
(inverse) of p = 100 – 0.5Q, where Q indicates total market supply.
This dominant firm has to deal with 10 fringe firms, each of whom
behaves perfectly competitively. Each fringe firm has a marginal cost
dc(q)
= 20q + 25
function
dq
• alculate the supply function of the fringe firms
• Using this, calculate the residual demand function of the dominant firm.
• Derive the marginal revenue function of the dominant firm.
• Find the profit-maximizing price of the dominant firm.
• How much does the competitive fringe supply to the market?
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