Consider the U.S. market for cigarettes. Suppose an econometric analysis estimates that the equation of the market demand curve is P=98−9Q (where P is measured in dollars per pack, and Q is measured in billions of packs per year), and at first the equation of the market supply curve is P=−2+Q. a. Solve the supply and demand equations simultaneously to find the initial market equilibrium quantity (Q*) and price (P*). Show your work. b. Now suppose the government imposes a tax of $ t on each pack of cigarettes produced. - After the per-unit tax of $t is imposed, what is the new equation of the market supply curve? - Solve the new supply equation and the demand equation simultaneously to find equations for the new market equilibrium quantity (Q*tax) and price (P*tax) as functions of t. Show your work.
c. The government's revenue from the cigarette tax is equal to tQ. - Using your equation for Q*tax from the last part, write down an equation for the government's tax revenue as a function of the size of the tax, t. - If the government wants to earn $19.6 (billions) from the cigarette tax, how high should it set the tax per pack? Show your work. d. Suppose the government sets the cigarette tax at t=$1 per pack. - Using your results above, calculate the new market equilibrium quantity and price after the tax (Q*tax and P*tax). Show your work.
- In this case, what percentage of the $1 tax is passed on to buyers as a price increase? Show your work.