Balakrishnan sivaramakrishnan sprinkle 2e for

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Balakrishnan, Sivaramakrishnan, & Sprinkle – 2e FOR INSTRUCTOR USE ONLY 5-46
This simplifies to: Profit = 492.50( Price ) – 9.85( Price ) 2 – 4,250 + 85 P – 3,360. Or, the relation between Jessica’s profit and price is: Profit = 577.50( Price) – 9.85(Price) 2 – 7,610. We can solve for the best P using calculus or Excel’s solver function. The exact answer is P = $29.31 and expected profit is $854.63 e. Taxes affect profit in a relatively straightforward fashion. We can take the profit model developed in part [d] and add the tax variable – doing so yields: Profit after taxes = Profit before taxes – taxes paid. Here, because taxes are proportional to income, taxes paid = (tax rate pre-tax profit). Adding this column yields: Price per cap Demand Expected Profit After-tax profit $20 300 $0.00 $0.00 $25 250 $671.25 $503.44 $28 220 $837.60 $628.02 $30 200 $850.00 $637.50 $32 180 $783.60 $587.70 $34 160 $638.40 $478.80 The optimal price continues to be $30 per cap . Notice that the optimal price does not change – this occurs because (in this example), taxes are a linear function of pre-tax profit. Thus, Jessica still wishes to maximize pre-tax profit which, in turn, will also maximize after-tax profit. This aspect of the problem allows instructors to discuss the relation between pre-tax income and tax rates, including extending the discussion to non-linear relations between pre-tax and after-tax income. Taxes will, of course, reduce the amount of Jessica’s profit. In our example, Jessica will now earn an after-tax monthly profit of: $850 .75 = $637.50. Note (Can skip without loss of continuity): In the calculus approach, incorporating taxes yields Balakrishnan, Sivaramakrishnan, & Sprinkle – 2e FOR INSTRUCTOR USE ONLY 5-47
Profit after taxes = (577.50( Price ) – 9.85( Price ) 2 – 7,610) (1 – tax rate). Since t = .25, we have: Profit after taxes = (577.50( Price ) – 9.85( Price ) 2 – 7,610) (.75). Profit after taxes = 433.125( Price ) – 7.3875( Price ) 2 – 5707.50. Again, we can solve for the best P using calculus or Excel’s solver function. The exact answer is Price = $29.31 (which is exactly what we arrived at earlier). f. While Jessica’s venture has intuitive appeal and our original calculations seemed to indicate that the venture might be a “go” (after all, selling 22 hats a day does not seem like a lot) the numbers simply do not add up. Given the totality of the costs involved and Jessica’s market research, it appears that (at best) Jessica will earn a very modest profit and will be unlikely to maintain a reasonable lifestyle with this business. We can see, though, how modest amounts add up – for example, if Jessica were to “manage” 10 kiosks in various malls around the state, she could earn a reasonable sum of money – this is precisely what franchisers seek to do. 5.66 Rick’s English Hut. a. Currently, Rick’s is generating $60,000 in sales. For alcohol and food, this translates to: Alcohol Sales: $60,000 .55 = $33,000, or $33,000/$4 = 8,250 “alcohol units.” Food Sales: $60,000 .45 = $27,000, or $27,000/$5 = 5,400 “food units.” Monthly profit can then be calculated as: [8,250 ($4 – $2)] + [5,400 ($5 – $4)] – $10,950 = $10,950.

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