6_4(i). Consider an industry with n identical firms in which the ith firm's total cost functions is: +9n. C₁=aq+bqQ, where Q=9₁ +92 + Derive the industry's supply function.
6_4(i). Consider an industry with n identical firms in which the ith firm's total cost functions is: +9n. C₁=aq+bqQ, where Q=9₁ +92 + Derive the industry's supply function.
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![**Question Q06_4(iii) on Cost and Supply Functions**
Consider an industry with \( n \) identical firms in which the \( i \)-th firm's total cost function is:
\[ C_i = aq_i^2 + bq_iQ, \]
where \( Q = q_1 + q_2 + \cdots + q_n \).
**Objective**: Derive the industry's supply function.
This question requires an understanding of cost functions and supply functions in the context of microeconomics. Given the total cost function for an individual firm and the aggregate quantity produced by the industry, the task is to derive the rule or function that describes how the industry's total supply responds to changes in market conditions. This typically involves mathematical derivation and should be based on the given cost structure. Please refer to your course materials on cost functions and supply derivation for detailed methodologies and steps.
To approach this problem, consider the following steps:
1. Differentiate the given cost function with respect to \( q_i \) to find the marginal cost for the \( i \)-th firm.
2. Utilize the marginal cost in combination with the market equilibrium condition where marginal cost equals market price to derive the supply function.
3. Aggregate the individual supply functions to form the industry supply function.
**Note**: There is no graphical or diagrammatic information provided within this text. However, it would be beneficial to visualize the problem using supply and cost curves for better conceptual understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2F26e92ecc-332b-49cf-a2aa-abe3dc9929a2%2Ftcksubv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question Q06_4(iii) on Cost and Supply Functions**
Consider an industry with \( n \) identical firms in which the \( i \)-th firm's total cost function is:
\[ C_i = aq_i^2 + bq_iQ, \]
where \( Q = q_1 + q_2 + \cdots + q_n \).
**Objective**: Derive the industry's supply function.
This question requires an understanding of cost functions and supply functions in the context of microeconomics. Given the total cost function for an individual firm and the aggregate quantity produced by the industry, the task is to derive the rule or function that describes how the industry's total supply responds to changes in market conditions. This typically involves mathematical derivation and should be based on the given cost structure. Please refer to your course materials on cost functions and supply derivation for detailed methodologies and steps.
To approach this problem, consider the following steps:
1. Differentiate the given cost function with respect to \( q_i \) to find the marginal cost for the \( i \)-th firm.
2. Utilize the marginal cost in combination with the market equilibrium condition where marginal cost equals market price to derive the supply function.
3. Aggregate the individual supply functions to form the industry supply function.
**Note**: There is no graphical or diagrammatic information provided within this text. However, it would be beneficial to visualize the problem using supply and cost curves for better conceptual understanding.
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