Case Study Answers of Negative Externality in Consumption

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Briefing for the government of Autarka
Subject : The issue of pollution in the coastline water of Autarka
Prepared by:
Core Message …

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1
Briefing for the government of Autarka
Subject : The issue of pollution in the coastline water of Autarka
Prepared by:
Core Message
This brief is to address the pollution problem of the coastline water in the nation of
Autarka and the possible solution. The scientific community lobbies to impose a tax on the
soft drinks producers to reduce the overproduction of the soft drinks. Tax on producers will
reduce the quantity sold in the market and reduce pollution. Thus, the proposed tax should be
implemented.
Recommendation
The government should implement the proposed tax policy that is to tax the soft drink
producers by $1/bottle.
Key information
In the Autarka na tion, the problem of rubbish accumulation in the coastline waters is
rising which is impacting marine life in a negative way. There are two producers of soft drinks
in this nation namely Bubbles PLC and Carbon. The consumers of these soft drinks exert a
ne gative externality in consumpt ion . A negative externality in consumption arises because
they produce rubbish (used bottles) by consuming soft drinks but do not compensate for the
loss to the marine population. In this case, the producers of soft drinks are overproducing, that
is, the equilibrium output (or used bottles of soft drinks) is higher than the socially optimum
level. To reduce the rubbish accumulation near the coastline, the scientific community wants
the government to raise the tax rate on soft d rink producers to $1/bottle. Though the
consumers are creating the pollution as they are relatively difficult to locate and tax and thus
the tax is required to be imposed on the producers. Hence, the proposed tax policy should be
implemented.
The proposed tax will raise the price of soft drinks which will push the quantity traded
in the market down. If this policy is implemented by the government there will be different
impacts on different economic entities. The tax burden will be divided into consumers and
producers based on the elasticity of demand and supply. The consumers have to pay more
which will reduce their benefits . The producers will receive less and thus their profit also
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reduces. However, the government receives tax payments. The net effect o n social welfare can
be understood by looking at the following diagram:
Fig: Market for soft drinks in Autarka
Source: Author’s formulation
MSB and MSC are marginal social benefit and cost, M PB and MPC are marginal
private benefit and cost. Due to the pollution , the environmental welfare loss was area ESG
which is gone after the imposition of tax. Equilibrium Q (65000) falls to Q* (25000) (socially
desirable ). AES is the area of deadweight loss to the society. The area ESG can‘t be calculated
as the ma gnitude of externality is not known. As the scientific community argues that raising
the tax to $1/bottle would help to solve the problem it is assumed that the length of AS and
EG are the same. Thus the loss of area ASE is offset by the gain of area ESG a nd thus the
policy implementation is justified ( Pindyck, and Rubinfeld 2020 ).
Financial Implications
Consumers ’ benefit falls to BAP b ($18000) from BEP and producers’ welfare falls to
OSP s from PEO as a result of the tax. The length P bPs shows the tax amount ($1) and thus area
AES is the area of deadweight loss ($20,000) to the society . The government revenue is area
PbASP s ($25000) . The net welfar e of the society will be positi ve if the area AES is greater
than or equal to the area SEG a nd the implementation of this policy will be justified (Besanko,
and Braeutigam 2020) .
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The cost function of Bubbles PLC (B) is:
Or,
And, the cost function of Carbon Corp (C) is:
Where , and are the total cost and quantity produced by the i-th firm .
i= B, C.
The market demand function is given as:
To find the profit function of the firms, the equation for revenue from selling the output in the
market is to be determined :
And
The profit function of B and C are:
And,
Both the firms try to maximize their profit given the market demand, their cost structure and
the output decisions of the other firm . The profit maximization condition of firm B is: B B Q AC TC *  B B Q TC 15.3 C C Q TC 30.3 i TC iQ ) ( 00001.0 6.3 ,
00001.0 6.3
C B Q Q P or
Q P
  
  C B B B B
B B
Q Q Q Q TR or
Q P TR
00001.0 00001.0 6.3 ,
*
2  
 C B C C C Q Q Q Q TR 00001.0 00001.0 6.3 2   i Q Q Q Q or
Q Q Q Q Q
C B B B B
B C B B B B
…….. ………. 00001.0 00001.0 45.0 ,
15.3 00001.0 00001.0 6.3
2
2
   
     ii Q Q Q Q or
Q Q Q Q Q
C B C C B
B C B C B B
…….. ………. 00001.0 00001.0 30.0 ,
30.3 00001.0 00001.0 6.3
2
2
   
    
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According to the first -order condition of profit -maximization, the left -hand side of the above
equati on should be zero. Hence,
Equation 1 is the best response function of Bubbles PLC.
Similarly,
According to the first -order condition of profit -maximization, the left -hand side of the above
equation should be zero. Hence,
Equation 2 is the best response function of Carbon Corp .
From equat ions 1 and 2 the output of the firms can be determined:
Putting the value of into 2 the value of can be determined:
The total quantity traded in the market is:
The amount of tax revenue is: C B B
B
C B B B B
Q Q Q or
Q Q Q Q
00001.0 00002.0 45.0 ,
00001.0 00001.0 45.0 2
   

    1 ……… ………. ………. 5.0 22500 ,
0 00001.0 00001.0 45.0
C B
C B
Q Q or
Q Q
 
   B C C
C
B C C C C
Q Q Q or
Q Q Q Q
00001.0 00002.0 30.0 ,
00001.0 00001.0 30.0 2
   

    000, 20 ,
25.0 7500 22500 ,
) 5.0 15000(5.0 22500

  
  
B
B B
B B
Q or
Q Q or
Q Q BQ CQ 5000 20000* 25.0 15000   CQ 000, 25 ,
000,5 000, 20 ,

 
 
Q or
Q or
Q Q Q B C 2 ……. ………. ………. 5.0 15000 ,
0 00001.0 00002.0 30.0
B C
B C
Q Q or
Q Q
 
  
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The new market price is:
The reduction in consumers’ welfare/benefit is:
The re duction in the quantity traded is:
The deadweight loss is area:
000, 25$ ,
25000*1$


T or
T bottles P / 35.3$ ) 25000( 00001.0 6.3    $18000 CS or,
$8000 $10000 CS or,
0.40* 25000)- 0.5(65000 25000* $2.95)- ($3.35 CS

 
  bottles Q 000, 40 ) 25000 65000(    000, 20$ 40000*) 35.2 35.3$(*5.0    ASE
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Reference
Besanko, D. and Braeutigam, R., 2020. Microeconomics . John Wiley & Sons.
Pindyck , R.S. and Rubinfeld, D.L., 2020 . Microeconomics . Pearson Education.

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