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 = 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.

Q1: 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. 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.

Q2: Using the cost functions from step 1, derive a profit function for each firm.

Q3: Derive each firm's best-response function.

Q4: Solve the best-response functions simultaneously to find the equilibrium quantities for each firm.

Q5: Find the equilibrium price and tax revenue.