Assume an economy with 10 individuals with identical preferences: U (C,M) = 0.25log C + 0.75log M , with C-cigarettes and M-apples.

Initially there is no tax on the goods in this economy and the price of a cigarette is 0.5. Suppose that the supply elasticity of cigarettes as well as of apples is 2 and that each individual has a fixed income of 100.

a) The government, having decided to discourage cigarette smoking, imposes a tax of 0.5 per unit consumed. What is the consumer surplus loss resulting from that tax? What is the deadweight loss of tax revenue? What is the relationship between the deadweight loss and tax revenue? What is the relationship between marginal deadweight loss and marginal tax revenue?

b) If the price of apples is 2, what is the optimal tax on apples suggested by Ramsey Rule?

c) Suppose now that there is a negative externality associated with the cigarette smoke of 0.25 per packet and that the supply is perfectly elastic. Recalculate the deadweight loss.