ECON1056 Price Theory

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 alternatives 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.

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,
• the impact on consumers, and
• the impact on the environment.

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 QB to denote the quantity produced by Bubbles PLC, and QC to 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)