Three firms in a single industry are the only source, in a given airshed, of emissions of a uniformly mixed pollutant, say, CO₂. Their emissions levels are currently ₁ = 300, ₂200, and e3 100, where the subscript denotes firms. The environmental regulator has decided that emissions should be reduced by half, to E=300. The firms' abatement cost functions are given by C₁ (a₁) = 0.1a, C₂(a₂) = 0.2a2, and C3 (a3) = 0.3a²3 respectively. (It is assumed that these functions describe the firms' entire cost structure, including the cost of producing the optimal level of output given e;.) Enforcement costs - oro zoro and there is no uncertainty
Three firms in a single industry are the only source, in a given airshed, of emissions of a uniformly mixed pollutant, say, CO₂. Their emissions levels are currently ₁ = 300, ₂200, and e3 100, where the subscript denotes firms. The environmental regulator has decided that emissions should be reduced by half, to E=300. The firms' abatement cost functions are given by C₁ (a₁) = 0.1a, C₂(a₂) = 0.2a2, and C3 (a3) = 0.3a²3 respectively. (It is assumed that these functions describe the firms' entire cost structure, including the cost of producing the optimal level of output given e;.) Enforcement costs - oro zoro and there is no uncertainty
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Three firms in a single industry are the only source, in a given airshed, of emissions of
a uniformly mixed pollutant, say, CO₂. Their emissions levels are currently e₁ = 300,
e2 =
200, and e3 100, where the subscript denotes firms. The environmental regulator
has decided that emissions should be reduced by half, to E=300. The firms' abatement
cost functions are given by C₁ (a₁) = 0.1a₁, C₂(a₂) = 0.2a2, and C3 (a3) = 0.3a²3
respectively. (It is assumed that these functions describe the firms' entire cost structure,
including the cost of producing the optimal level of output given e;.) Enforcement costs
are zero and there is no uncertainty.
Suppose the regulator decide to employ a Command-and-Control scheme, requiring
that each firm reduce its emissions in proportion to ej. Calculate the aggregate cost
of abatement and each firm's emissions level.
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'0.1×1502+0.2×1002+0.3×502' mean is
'0.1×1502+0.2×1002+0.3×502 = 2250 + 2000 + 750' or
'0.1×150×2+0.2×100×2+0.3×50×2 = 30 + 40 + 30' ?
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