Suppose that you work as an anti-trust economist for the Department of Justice of the U.S. Your research division is investigating an anti-trust case of a major cigarette company. Given the following information:

Price elasticity of demand for cigarettes at current prices is -0.5. Current price of cigarettes is $0.05 per cigarette.

Cigarettes are being purchased at a rate of 10 million per year.

1. (a) Find a linear demand function that fits this information.
2. (b) Using the inverse elasticity pricing rule (IEPR), show that this cigarette market cannot be a monopoly.
3. (c) What do we know about the relationship between price elasticity of demand and total revenue? How can you use that information to explain the economic intuition behind your answer to part (b)?