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The math of marketing
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Mister Death RJ: McFlono McFloninoo Post Rating: 8 + / - Total Posts: 266 Karma: 300 Joined: Feb 6, 2012 |
Posted on Apr 17, 2012 Summary: The optimal steady-state marketing level for a store isL = (MP/1.2)^(4/3), where L = marketing level, and MP = baseline marginal profit of store (in cents/tick). As a f'rinstance, my 100m^2 supermarket would have been making about 5 million cents/tick in profit yesterday ($50,000) with a 0% marketing bonus, so its optimal marketing level is 670M - much higher than I'd figured! Due to store size generating its own marketing, there is in fact a store size that would generate its own optimal marketing, and above which you'd prefer to spend negative marketing dollars. This value is S = sqrt(0.03)B^2, where B is baseline profit (at 0% marketing) in cents/tick/m^2. With the above figure, my store's B is about 50,000, so I'd need a store in the hundreds of millions of square metres. In practice, base profit decreases with store size due to maintenance and salaries, so the self-marketing store won't be nearly that large. Formulae for the nerds (assuming steady-state, so all derivatives = 0): L = marketing level X = marketing expense (cents/tick) P = profit (cents/tick) B = baseline profit (cents/tick/m^2) S = store size (m^2) dL/dt = X - 0.003L + S^2/10 = 0 X = 0.003L - S^2/10 P = SB(1+(L^0.25)/100) - X P = SB(1+(L^0.25)/100) + S^2/10 - 0.003L dP/dL = SB(L^-0.75)/400 - 0.003 = 0 Solving this last equation gives the formula at the top of the post. |
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Nwabudike Morgan RJ: CEO Nwabudike Morgan CO: CEO Nwabudike Morgan Post Rating: 0 + / - Total Posts: 108 Karma: 344 Joined: Apr 4, 2012 |
Posted on Apr 17, 2012 I crunched these numbers today as well, and was similarly surprised at how powerful marketing is. Most fully-stocked stores of any reasonable size should have billions or tens of billions of marketing power!
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Tony Wooster RJ: Johnny Appleseed Post Rating: 0 + / - Total Posts: 41 Karma: 51 Joined: Apr 4, 2012 |
Posted on Apr 17, 2012 Crikey. Is there any easy way to determine MP for a given store? Seems like I'd have to toss my other stores into construction to figure it out.
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Mister Death RJ: McFlono McFloninoo Post Rating: 0 + / - Total Posts: 266 Karma: 300 Joined: Feb 6, 2012 |
Posted on Apr 17, 2012 (Last edited on Apr 18, 2012) (marginal baseline revenue) = MR = (daily sales in cents) / (1+L^0.25/100) / 96; MP = MR * k. k will depend on, among other things, the profit margins on your products; maintenance and salaries; and a portion of your taxes and dividends. (You didn't think accountants got rich for no reason did you?)If you have multiple stores, you can probably estimate one store's revenues/profits by looking at the 3-day sales reports of sample products and multiplying by a sufficient amount. If you're using the "2*cost" rule of thumb for your retail prices, and I strongly recommend you do, your k should be a little less than 0.5 for a starting business that's buying most its goods from the B2B or importers. This will go down as your store size goes up, and go up as you make your own product. |
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