How much must each of the companies reduce their emissions by (in tonnes) for the policy to be cost-effective? Explain and show how you arrive at the answer.

Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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Two different companies, A and B, can reduce their emissions of hazardous substances to the following marginal costs (measured in
SEK per tonne of reduced emissions).

MACa =10 + 50Sa       MACb = 5 + 70Sb

where Sa and Sb, respectively, represent A's and B's emission reductions
 
Assume that in the absence of any government policy, Company A will emit 38 tonnes while Company B will emit 26 tonnes. The state now wants to achieve a reduction in emissions by a total of 30 tonnes, ie. Sa + Sb = 30.
 
a) How much must each of the companies reduce their emissions by (in tonnes) for the policy to be cost-effective? Explain and show how you arrive at the answer.
 
b) If the state decides that the total emission reduction is to be achieved by means of a system with transferable emission rights, how high would the price of an emission right (equivalent to one tonne) be? Ignore here the possible problems with market power that can arise with only two players in the market.
 
c) The regulated authority is considering whether the emission rights should be auctioned or distributed free of charge (so-called
‘Grandfathering’). Will this choice affect: (i) the proportion of total emissions that are reduced; and / or (ii) the price of allowances? Be sure to motivate your answers.
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