The Upstream Nukem Co. uses a technology that produces pollutants as a by-product. The companydumps these pollutants into Radiant River. The only way that Nukem can reduce pollution is by cuttingoutput. Nukem's profits, expressed as a function of the amount x (in tons) of pollutants per day, isIIN (x) = 80x - 5x²The pollution adversely affects the performance of Downstream Glowing Fisheries. Glowing's profit,as a function of the quantity of pollution, is given byIIG(x) = K - 5x²where K is a constant relating to all factors other than pollution.(i) If there are no restraints on pollution and no negotiations between the two companies, how muchpollution will Nukem produce per day? x =.108ОС42(ii) What is the socially optimal quantity of pollution? x* =15со ст3O 2 Suppose Nukem has the right to continue to pollute, but Glowing can pay it a constant price per ton toreduce pollution. This price will be determined through (competitive) market negotiations between thetwo companies. Negotiation is costless. Let the price be represented by P per ton. Note that if thepost-negotiation quantity of pollution is x < ☎, then Glowing pays p(x − x) to Nukem.-(iii) Write down Glowing's profit as a function of x for an arbitrary price P. Find the quantity (p)of pollution that is optimal for Glowing under the new scheme. This is Glowing's "demand" forpollution.GO 1-0.1pO 0.5p(p)0.1p - 10.1pO 0.1p²N(iv) Write down Nukem's new profit function, and find the level of pollution (p). This is Nukem's"supply" of pollution.6 -0.1p2 -0.1pO 4 -0.1p8 -0.1pO 10-0.1p(v) If the two firm's transact as perfect competitors, find the equilibrium price p* for pollutionreduction. p*:=O 50O 302040(vi) What is the total gain in social surplus across the two firms from the transaction?1040O 90250O 160

The Upstream Nukem Co. uses a technology that produces pollutants as a by-product. The company dumps these pollutants into Radiant River. The only way that Nukem can reduce pollution is by cutting output. Nukem's profits, expressed as a function of the amount x (in tons) of pollutants per day, is IIN (x) : 80x – 5x2 = The pollution adversely affects the performance of Downstream Glowing Fisheries. Glowing's profit, as a function of the quantity of pollution, is given by IIG(x) = K - 5x² where K is a constant relating to all factors other than pollution.

The Upstream Nukem Co. uses a technology that produces pollutants as a by-product. The company dumps these pollutants into Radiant River. The only way that Nukem can reduce pollution is by cutting output. Nukem's profits, expressed as a function of the amount x (in tons) of pollutants per day, is IIN (x) : 80x – 5x2 = The pollution adversely affects the performance of Downstream Glowing Fisheries. Glowing's profit, as a function of the quantity of pollution, is given by IIG(x) = K - 5x² where K is a constant relating to all factors other than pollution.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A: Answer to the question is as follows:

Question

The Upstream Nukem Co. uses a technology that produces pollutants as a by-product. The company
dumps these pollutants into Radiant River. The only way that Nukem can reduce pollution is by cutting
output. Nukem's profits, expressed as a function of the amount x (in tons) of pollutants per day, is
IIN (x) = 80x - 5x²
The pollution adversely affects the performance of Downstream Glowing Fisheries. Glowing's profit,
as a function of the quantity of pollution, is given by
IIG(x) = K - 5x²
where K is a constant relating to all factors other than pollution.
(i) If there are no restraints on pollution and no negotiations between the two companies, how much
pollution will Nukem produce per day? x =.
10
8
ОС
4
2
(ii) What is the socially optimal quantity of pollution? x* =
1
5
со ст
3
O 2

Suppose Nukem has the right to continue to pollute, but Glowing can pay it a constant price per ton to
reduce pollution. This price will be determined through (competitive) market negotiations between the
two companies. Negotiation is costless. Let the price be represented by P per ton. Note that if the
post-negotiation quantity of pollution is x < ☎, then Glowing pays p(x − x) to Nukem.
-
(iii) Write down Glowing's profit as a function of x for an arbitrary price P. Find the quantity (p)
of pollution that is optimal for Glowing under the new scheme. This is Glowing's "demand" for
pollution.
G
O 1-0.1p
O 0.5p
(p)
0.1p - 1
0.1p
O 0.1p²
N
(iv) Write down Nukem's new profit function, and find the level of pollution (p). This is Nukem's
"supply" of pollution.
6 -0.1p
2 -0.1p
O 4 -0.1p
8 -0.1p
O 10-0.1p
(v) If the two firm's transact as perfect competitors, find the equilibrium price p* for pollution
reduction. p*:
=
O 50
O 30
20
40
(vi) What is the total gain in social surplus across the two firms from the transaction?
10
40
O 90
250
O 160

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Step 4: Find the optimal x(g) when glowing pays to Nukem

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