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,

Q P=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 $3.80 a bottle. Bubbles PLC produces 140,000 bottles per year, paying $56,000 in bottle tax. CarbonCorp produces 80,000 bottles and pays $32,000. It is estimated that it costs Bubbles PLC $2.00 per bottle of soft drink produced, while producing a bottle of soft drink cost CarbonCorp $2.60. The fixed costs of production can be neglected in this analysis.

Question:

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.

Step 2: Using the cost functions from step 1, derive a profit function for each firm