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. Step 1: Using the information provided in the scenario, derive a total cost function foreach soft drink producer for the case in which the government levies a tax of $1.00 perbottle. Use QBto denote the quantity produced by Bubbles PLC, and QCto denote thequantity produced by CarbonCorp. Note that a firm's marginal cost will be the sum of itscost of producing a bottle, and the tax that it must pay to the government on each bottlesold. (5 marks)