Originally Posted by vgcea
I believe Jason's point is pointing at a way to encourage the customer to buy not necessarily more cake but just enough cake that we maximize the input that goes into the cake.
Actually it is a way to encourage the customer to buy more cake, since the more servings you can make in a baking session, the more efficient you are. This is pretty straightforward when selling single tier cakes with flat costs (e.g. "you can get a 10" instead of an 8" for only $10 more"), but it also works for per-serving prices if your formula takes into account the pricing curve leveling off slightly. Obviously if someone wants 100 servings I'm not going to try to sell them 200, but if you have an excellent product your customers (and their guests) will appreciate leftovers.
The price drop is less than the cost savings in order to maintain increasing margins as you scale up.
As cakes get larger, your cost per serving drops due to process efficiencies and fixed overhead. If your price per serving drops at the same rate, the entire benefit of this is realized 100% by the customer, but if you don't drop your price per serving at all there will be no incentive to for customers to increase the size of orders so you won't recognize the cost savings at all.
For example, let's say a 50-serving cake (your smallest and least efficient cake) costs you $3/serving and a 100-serving cake costs you $2.50/serving. If your profit margin is 20%, you could price the 50-serving cake at $3.60. But if you price the 100-serving cake the same way ($3) you would probably be underpricing the market (assuming your 50-serving price is on target). What you can do is gradually lower the price between 50 and 100 servings, but not by as much as your cost savings, so your 100 serving price might be, say, $3.30. So with a 50-serving cake you might try to upsell another 10 servings for an additional $30 (50 * $3.60 = $180, 60 * $3.50 = $210)...the customer might think "wow, only $3/serving!" but in reality the price has only been lowered by 10 cents to $3.50/serving. The difference between the cost savings and the lowered price is pure profit.
In practice, you could either manually price out tiers (e.g. 50-60 servings is X, 60-80 is X*0.9, 80-120 is X*0.8, etc.), or you could plot your servings vs. desired price based on the share of profitability you want to keep and use Excel to fit a trend line to the results. For my example above, an approximate fit for the price per serving would be 5.9 divided by the eighth root of the number of servings. In Excel, this would be =5.9/(<servings>^( 1/8 )).
Once you have this formula, you can plug any number of servings into Excel and you'll instantly have a price with as much decimal precision as you want, although you'll probably want to quote the final price rounded to the nearest dollar instead of telling the customer their cake costs $3.536577 per serving.
From a microeconomics perspective this matches the left side of the long run average total cost curve. If you expand enough you will eventually hit diminishing returns, but most custom cake shops won't reach that kind of volume, and by the time you reach that point you'll probably be able to afford to hire your own full-time financial analyst.