ooooo AT&T LTE Tq31t21 L @ 55% E' < is 13434-3741187-Case+Study+3+ Case Study #3 - Profit Maximizing 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 profit) 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. Median Price Median Tax ($ per package) ($ per package) Data on sales of tobacco products from 2001 through 2014 is available on the US Federal Trade Commission's website, in Table 1A and 1B (beginning on page 10, the "units sold" column) of the report: https : //www . ft c . gov/system/f nes/document s/report s/federal- trade- commission- cigarette- report- 2014- federal- trade- commission- smokeless- tobacco- ftc-cigarette-report-2014.pdf (It is easiest if you view this report by clicking on the link from the Project 2 PDF on Canvas or Google "ftc cigarette report" and select the 2014 report issued in 2016). Things you will need: The table provided on this page of the project The data from Table 1A and/or 1B 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. If your discussion section is with... Janelle Currey, use data from 2012 and 2014 Daniel Hothem, use data from 2010 and 2012 Clover May, use data from 2008 and 2010 Joe Webster, use data from 2006 and 2008 Han WVeinschelbaum, use data from 2004 and 2006 Circle the line above that corresponds to the data set you will use. ldocument located at http://www.taxadmin.org/assets/docs/Tobacco/papers/taxburden-2014.pdf 3Median by market share, includes generic brands 3Median by market share, includes state and federal tax Case Study #3 - Profit Maximizing Under Taxation 2. 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.3/6 g. weate a linear demand function q = f(p) for the number of packages (in billions) sold at a pre-tar): median price of p dollars per package. 3. Write an equation for the revenue, R, obtained by cigarette companies as a function of p. 4. Estimates for the cost to produce cigarettes (including materials, manufacture, advertising, etc) vary, so let's say that it costs $0.60 plus the last two digits of your student number (in cents) per package of cigarettes (eg. if the last two numbers of your student number are 34 then the cost would be $0.60 + $034 = $094). Write a formula for the cost to produce q packages of cigarettes. 5. Now use your cost and revenue formulas from the previous two questions to write a formula for the profit, P, as a function of price per package, p. Case Study #3 - Profit Maximizing Under Taxation 6. 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 profit in the exercise above to include the company's requirement to pay these taxes. Your answer should contain both t and p. 7. What value of p maximizes the profit function P in the exercise above? Your answer will contain the constant t.4/6 Case Study #3 - Profit Maximizing Under Taxation 0 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 profit in the exercise above to include the company's requirement to pay these taxes. Your answer should contain both t and p. 7. What value of p maximizes the profit function P in the exercise above? Your answer will contain the constant t. 8. The government decides to be clever. Assuming that the cigarette companies will always price their product so that profit 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 7, which maximizes the businesses' profit) Case Study #3 - Profit Maximizing Under Taxation (b) What tax rate t maximizes the total tax revenue T? (c) Consult the second page of the project and write the median taxes for the two years you studied. Is your answer to 8b close to either of these values?5/6 'o) What tax rate t maximizes the total tax revenue T? (c) Consult the second page of the project and write the median taxes for the two years you studied. Is your answer to 8b close to either of these values? (d) Give two different reasons why the true combined state and federal taxes might be different from what you calculated. Case Study #3 - Profit Maximizing Under Taxation 9. 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 profit? (Hint: you found this formula in Exercise 7) (b) Now assume that the tax rate t you found in Exercise 8b is in effect. Again, use the result from exercise 7 to find the price at which the cigarette company will obtain its maximum profit.6/6 Case Study #3 - Profit Maximizing Under Taxation 9. 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 profit? (Hint: you found this formula in Exercise 7) (b) Now assume that the tax rate t you found in Exercise 8b is in effect. Again, use the result from exercise 7 to find the price at which the cigarette company will obtain its maximum profit. (c) If the cigarette company passed on the entirety of the tax to the customers, then the answer to 9a plus the tax rate t from 8b would equal the answer in 9b. Does it? Again assuming the optimal tax rate from 8b and that the company prices its cigarettes at the value in 9b, how much of the government's tax does the company actually pass on to the consumer? Presentation: Illegible / Quite difficult to read / Several corrections Mostly clear Perfect / Mostly illegible Many corrections Nearly perfect Total