The inverse demand function for a furniture firm is P(x) = 15- X while the firm total cost is TC(x) = 3X. Now, let's assume that for every X produced by the firm causes a pollution to the environment in the function of e(x) = 2X i) ii) Calculate the price, quantity, and profit if the firm does not incur the cost of pollution. Now let's assume that the firm decides to internalize the cost of pollution. Calculate the new price, quantity, and profit when the pollution has been internalized.
The inverse demand function for a furniture firm is P(x) = 15- X while the firm total cost is TC(x) = 3X. Now, let's assume that for every X produced by the firm causes a pollution to the environment in the function of e(x) = 2X i) ii) Calculate the price, quantity, and profit if the firm does not incur the cost of pollution. Now let's assume that the firm decides to internalize the cost of pollution. Calculate the new price, quantity, and profit when the pollution has been internalized.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![The inverse demand function for a furniture firm is P(x) = 15- X while the firm total cost
is TC(x) = 3X. Now, let's assume that for every X produced by the firm causes a pollution
to the environment in the function of e(x) = 2x
i)
Calculate the price, quantity, and profit if the firm does not incur the cost of
pollution.
ii)
The final payoff for firm 1 and firm 2 in a compensation mechanism as a result of
externalities caused by the firm 1 is following:
π₁ = max px -c (x) - t₂x - (t₁-t₂)²
i)
ii)
Now let's assume that the firm decides to internalize the cost of pollution. Calculate
the new price, quantity, and profit when the pollution has been internalized.
iii)
iv)
T₂ = t₂x-e(x) - (t₂-t₁)²
Obtain firm 1 First Order Condition (FOC) with respect to x-good.
Obtain firm 1 First Order Condition (FOC) with respect to t₁ and derive optimal
solution for t₁.
Obtain firm 2 First Order Condition (FOC) with respect to x-good.
From (iii), show that p = c'(x) + e'(x) using information you obtained in (i) and (ii).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa6ea8983-163c-46c9-8622-fe71cfe1e0e8%2F8fb3ee2a-93ea-4fb0-8d15-9b01621acd23%2Fzfvy93m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The inverse demand function for a furniture firm is P(x) = 15- X while the firm total cost
is TC(x) = 3X. Now, let's assume that for every X produced by the firm causes a pollution
to the environment in the function of e(x) = 2x
i)
Calculate the price, quantity, and profit if the firm does not incur the cost of
pollution.
ii)
The final payoff for firm 1 and firm 2 in a compensation mechanism as a result of
externalities caused by the firm 1 is following:
π₁ = max px -c (x) - t₂x - (t₁-t₂)²
i)
ii)
Now let's assume that the firm decides to internalize the cost of pollution. Calculate
the new price, quantity, and profit when the pollution has been internalized.
iii)
iv)
T₂ = t₂x-e(x) - (t₂-t₁)²
Obtain firm 1 First Order Condition (FOC) with respect to x-good.
Obtain firm 1 First Order Condition (FOC) with respect to t₁ and derive optimal
solution for t₁.
Obtain firm 2 First Order Condition (FOC) with respect to x-good.
From (iii), show that p = c'(x) + e'(x) using information you obtained in (i) and (ii).
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