Problem: Suppose the federal government (back in 1985?) decided to encourage an efficient amount of cigarette consumption by imposing a per-unit tax of $0.50, on cigarette manufacturers equal to the vertical distance between MPB and MSB at Q1 as shown in the figure given. We can use linear demand and supply curves to calculate the effect of a 50-cent-per-pack tax. First, we must consider the four conditions that must hold:
Qd = 150 - Pb (Demand)
Qs = 60 + 40s (Supply)
Qd = Qs (Supply must equal demand)
Pb - Ps = 0.50 (Government must receive 50 cents/pack)
Note: Pb and Ps is the price the buyers pay and the price the sellers receive, respectively, after the tax is imposed. These are shown as P1 and P2, respectively, in the figure from our notes.
Question 1: Calculate the equilibrium price and quantity (million packs/year) before the tax is imposed. In the figure from our notes, this is where MSC = MPB.
Question 2: Using the conditions above, calculate Pb and Ps after the tax is imposed. What portion of the 0.50 tax are consumers paying? What portion of the tax are producers paying?
Question 3: Using either Demand or Supply from above, determine the total quantity (packs of cigarettes) produced and consumed after the tax is imposed.
Question 4: Using the arc elasticity formula, calculate the price elasticity of demand over this part of the demand curve (i.e. P0 and P1 in the figure).
Question 5: What is the amount of tax revenue per year raised by government from the imposition of the per-unit tax?
Question 6: The cost to consumers and producers, however, will be more than the taxes paid for cigarette production and consumption. That is, even though government has decided that before the tax there was overconsumption, after the tax both producers and consumers lose out on producer and consumer surplus, respectively. What is the deadweight loss from the tax?
Question 7: How would society (all individuals) know that this tax is beneficial? Explain.