Mini-Project #3 - Prot Maximization Under Taxation When a government agency taxes a company (or a whole industry, as is the case with tobacco), both industries have choices to make: how much to tax, in the case of the government, and how much of that tax to pass onto their customers, in the case of the tobacco companies. Although it may seem optimal to increase the price of the product an amount equal to the tax, it may not actually serve the companies' purpose (maximizing prot) to do so. \"The Tax Burden on Tobacco\"1 has relevant data summarized below regarding the historical pricing of cigarettes. Some selected years are given in the table below. Year Median2 Price ($ per package) Median3 Tax ($ per package) 2004 2006 2008 2010 2012 3.74 3.93 4.35 5.55 5.65 1.17 1.34 1.59 2.46 2.50 1. If your discussion section is with... Doeke Buursma, Claire Dodson, Helen Jenne, Karl Schmidt, Ryan Takahashi, use use use use use data data data data data from from from from from 2004 2006 2008 2004 2006 and and and and and 2008 2008 2012 2006 2010 Circle the line above that corresponds to the data set you will use. 2. Data on sales of tobacco products from 2001 through 2012 is available on the US Federal Trade Commission's website, in Table 1 (beginning on page 9, the \"units sold\" column) of the report: https://www.ftc.gov/system/files/documents/reports/federal-trade-commission-cigarette-report-2012/150327-2012cigaretterpt.pdf (It is easiest if you view this report by clicking on the link from the Project 2 PDF on Canvas). Create a linear demand function q = f (p) for the number of packages (in billions) sold at a pre-tax median price of p dollars per package. Things you will need: The table listed on this page of the project The data from Table 1 of the FTC link provided above That the pretax price is the median price minus the median tax per package That there are 20 cigarettes per package of cigarettes 1 document located at http://www.taxadmin.org/assets/docs/Tobacco/papers/tax_burden_2014.pdf Median by market share, includes generic brands 3 Median by market share, includes state and federal tax 3 2 Mini-Project #3 - Prot Maximization Under Taxation /5 3. Write an equation for the revenue, R, obtained by cigarette companies as a function of p. /2 4. Assume that the net cost to produce (including materials, manufacture, advertising, etc) is $1 per package of cigarettes. Write a formula for the prot, P , as a function of price per package, p. /3 3 Mini-Project #3 - Prot Maximization Under Taxation 5. Now assume that in addition to production costs (which you included in the exercise above), the federal and state governments also tax the sale of cigarettes (which they do). If the net tax rate is t dollars per package, revise your equation for prot in the exercise above to include the company's requirement to pay these taxes. Your answer should contain both t and p. /2 6. What value of p maximizes the prot function P in the exercise above? Your answer will contain the constant t. /4 7. The government decides to be clever. Assuming that the cigarette companies will always price their product so that prot is maximized, the government can choose a value for t that also maximizes the total tax revenue gained from cigarette sales. (a) Write an equation for T , the total tax revenue gained from cigarette sales as a function of the tax rate, t. (Hint: write T in terms of t and p, then use the expression for p from Exercise 6, which maximizes the businesses' prot) /3 4 Mini-Project #3 - Prot Maximization Under Taxation (b) What tax rate t maximizes the total tax revenue T ? /3 (c) Consult the rst page of the project and write the median taxes for the two years you studied. Is your answer to 7b close to either of these values? /2 (d) Give two dierent reasons why the true combined state and federal taxes might be dierent from what you calculated. /2 5 Mini-Project #3 - Prot Maximization Under Taxation 8. The government has now determined how much it wants to tax the sale of cigarettes. What remains to be seen is how much the cigarette companies will increase the price of their product as a result. (a) If there were no tax, what would the cigarette company charge for a package of cigarettes in order to maximize its prot? (Hint: you found this formula in Exercise 6) /2 (b) Now assume that the tax rate t you found in Exercise 7b is in eect. Again, use the result from exercise 6 to nd the price at which the cigarette company will obtain its maximum prot. /2 (c) If the cigarette company passed on the entirety of the tax to the customers, then the answer to 8a plus the tax rate t from 7b would equal the answer in 8b. Does it? Again assuming the optimal tax rate from 7b and that the company prices its cigarettes at the value in 8b, how much of the government's tax does the company actually pass on to the consumer? /2 Presentation (out of 5 points): Illegible Mostly illegible 0/5 1/5 Quite di cult to read / Many corrections 2/5 6 Several corrections Mostly clear 3/5 4/5 Perfect / Nearly perfect 5/5