Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C(Q1, Q₂)=Q+3Q where Q₁ and Q₂ represent the output levels of product 1 and product 2. (d) Check the second-order conditions and confirm that the output levels found in (c) are profit-maximizing.
Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by P₁ and P₂. The production cost is C(Q1, Q₂)=Q+3Q where Q₁ and Q₂ represent the output levels of product 1 and product 2. (d) Check the second-order conditions and confirm that the output levels found in (c) are profit-maximizing.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Bartleby Expert Answer for (c):
As firm's objective is Profit Maximization, and in the case of
P = MC
And, as there are 2 products – hence, the Profit Maximizing Condition for the firm is:
P1 = MC1 & P2 = MC2
As we are given the Cost Function as:
C = Q12 + 3Q22
MC1 = ∂C/∂Q1 = 2Q1MC2 = ∂C/∂Q2 = 6Q2
Hence we have:
P1 = MC1 → P1 = 2Q1 → Q1* = P1/2
P2 = MC2 → P2 = 6Q2 → Q2* = P2/6
![1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by \( P_1 \) and \( P_2 \). The production cost is
\[ C(Q_1, Q_2) = Q_1^2 + 3Q_2^2 \]
where \( Q_1 \) and \( Q_2 \) represent the output levels of product 1 and product 2.
(d) Check the second-order conditions and confirm that the output levels found in (c) are profit-maximizing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6274a625-9a74-4008-b392-f1961eea52c4%2Fc615cfaa-0065-43f4-b82e-0eccc7232f27%2Fjs8rzlq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Consider a two-product firm under pure competition. With pure competition, the prices of both commodities will be taken as exogenous, denoted by \( P_1 \) and \( P_2 \). The production cost is
\[ C(Q_1, Q_2) = Q_1^2 + 3Q_2^2 \]
where \( Q_1 \) and \( Q_2 \) represent the output levels of product 1 and product 2.
(d) Check the second-order conditions and confirm that the output levels found in (c) are profit-maximizing.
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