Statistics Solutions

(See Solution) Assume that the demand and supply functions of cigarettes are given by: P=14-2Q^d , P=5+0.25Q^s , where P is the price per pack of cigarettes and

Question: Assume that the demand and supply functions of cigarettes are given by:

\[\begin{aligned} & \text{P}=14-2{{\text{Q}}^{\text{d}}} \\ & \text{P}=5+0.25{{\text{Q}}^{\text{s}}} \\ \end{aligned}\]

where \(\mathrm{P}\) is the price per pack of cigarettes and \(\mathrm{Q}\) is the number of packs per day. Also assume a negative consumption externality of $3 per pack of cigarettes.

  1. What is the equilibrium quantity and price in the market? What are the consumer surplus, producer surplus, and the external costs to the society?
  2. What is the quantity and price under the efficient allocation?
    Suppose that the government wants to impose a tax on consumers so that they internalize the external costs.
  3. What is the optimum tax rate? What are the consumer surplus, producer surplus, tax revenues, and the external costs to the society?
  4. Compare the efficient and private allocations using consumer surplus, producer surplus, tax revenues, and the external costs?

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