The island nation of Autarka is growing concerned over the amount of rubbish accumulating in the waters off its coastlin

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The island nation of Autarka is growing concerned over the
amount of rubbish accumulating
in the waters off its coastline. This pollution is harming marine
life, damaging fish stocks,
and washing up on tourist beaches. Research by the National
University of Autarka has
determined that a significant component of the solid waste is the
single-use plastic bottles
used by soft-drink manufacturers.
Currently, soft drink manufacturers in Autarka pay a tax of $0.40
on each bottle of
drink they sell. The revenue from the tax is used to fund the
cleaning of roads and public
spaces. The scientific community is lobbying the government to
increase the tax to $1.00 a
bottle. The scientists suggest that any additional revenue could be
used to fund programs
to remove rubbish from the coastal waters.
There are two producers of soft drinks in Autarka: Bubbles PLC and
CarbonCorp.
The two companies do not face competition from imports as the cost
of transporting soft
drinks into Autarka is prohibitively high. Moreover, there are no
cost effective alterna-
tives to single use plastic containers. The two companies have made
submissions to the
government opposing the proposed tax increase, which they claim
will harm consumers.
2.1 Your task
The Minister for the Environment has instructed you to determine
the likely impact of the
proposed tax increase on the market for soft drinks, and to
recommend whether or not the
government should implement the proposed tax increase. Your
recommendation should
take into account
• the impact on government revenues from the bottle tax,
• the impact on consumers, and
• the impact on the environment.
Note that competition policy prevents the government from imposing
any other form of
market regulation, including price controls.
2.2 Industry structure
Research into the soft drink market indicates that the two firms
compete by selecting
quantities (Cournot competition). Soft drinks are regarded as a
homogeneous good by
consumers, and inverse demand in the market is estimated to
be,
P = 3.6 −Q
100,000 ,
where P represents the price of a bottle of soft drink, and Q is
the total number of bottles
sold per year.
At present soft drinks sell for $2.95 a bottle. Bubbles PLC
produces 40,000 bottles per
year, paying $16,000 in bottle tax. CarbonCorp produces 25,000
bottles and pays $10,000.
It is estimated that it costs Bubbles PLC $2.15 per bottle of soft
drink produced, while
producing a bottle of soft drink cost CarbonCorp $2.30. The fixed
costs of production
can be neglected in this analysis.
2
3 Industry analysis
For your Industry Analysis you must complete each of the steps
detailed below. When
completing the steps you must:
• Type all equations using the ‘Insert Equation’ function (or
equivalent).
• Show all of your working.
• Include sufficient written description for the reader to follow
your process.
• Use appropriate notation and economic terminology.
Your audience for the industry analysis is other expert economists
who may be required to
review your work. There is no page limit for the Industry
Analysis.
3.1 Required steps
When completing the industry analysis you should assume that firms
are engaged in
Cournot Competition.
Step 1: Using the information provided in the scenario, derive a
total cost function for
each soft drink producer for the case in which the government
levies a tax of $1.00 per
bottle. Use QBto denote the quantity produced by Bubbles PLC, and
QCto denote the
quantity produced by CarbonCorp. Note that a firm’s marginal cost
will be the sum of its
cost of producing a bottle, and the tax that it must pay to the
government on each bottle
sold. (5 marks)
Step 2: Using the cost functions from step 1, derive a profit
function for each firm. (10
marks)
Step 3: Derive each firm’s best-response function. (15 marks)
Step 4: Solve the best-response functions simultaneously to find
the equilibrium quantities
for each firm. (10 marks)
Step 5: Find the equilibrium price and tax revenue. (10 marks)