So, I posted this over on the EoS forums, but I thought I'd ask the bright folks here, as well.
First, here are the equations and varibles in question, provided by Scott, the developer.
$n_sold = $price_eq * $store_prod_eq * demand_eq
$price_eq = ( max(0.3, (1 + 0.02 * ($quality - $quality_avg)) ) / $price )^2
$store_prod_eq = ( (0.3 * $price_avg + 2 * $price_base) * $category_price_multiplier )^2 * $store_size / $selltime;
$demand_eq = (3/(1 + 2*$demand_met))^2
$price - Your product's listing price (in cents)
$quality - Your product's quality
$store_size - Your store size
$price_avg - World average price for this product (in cents)
$quality_avg - World average quality for this product
$price_base - This product's Wholesale Value as listed in the Pedia pages (in cents)
$selltime - A custom variable I can adjust to balance sales between very small and very large products, as of now it is at $price_base ^ 0.65 / 20, can also be changed manually for each product.
$category_price_multiplier - A category variable I can use to affect all products in a category (world events)
$n_sold - Number sold per tick. Partially sold units (< 1) will be carried over to the next tick(s).
I've been looking at these equations, and pondering the math, and I wanted someone else to check me on this.
Postulates:
1) You are selling goods with a set quality and infinite supply (i.e. the import market)
2) Your effects on average price, demand met, and average quality are negligible (i.e. you are a small retailer)
3) You are selling a product that is not > 35 points below the average world quality (this isn't strictly necessary, but let's me remove the MAX function to make my point clearer.
Theory:
The most profitable (per tick) price to set a good at, given those postulates, is twice its cost.
Math:
If you go over the variables in the equations Scott provided above, the vast majority of them are, from the perspective of the retailer, constants. This is obvious in the case of
$selltime or $price_base; but with the postulates I give above, we can treat values like $price_avg and $quality_avg as constants, as well.
If we do that, we can describe the equation above in this way:
The number of units of a good sold is inversely proportional to the square of the price at which they are sold. Thus, doubling your sale price means you sell 1/4 of what you did before; halving it means you sell four times as many. (For the econ junkies out there, this means EoS currently has uniform price elasticity across all goods.)
Now, for any given good, calculating the per-tick profit is pretty easy:
profit = (sale_price - cost)*quantity_sold. (If we wanted to be more sophisticated, we might want to divide out the labor and building costs of our retail stores, but it won't affect the overall point much.)
Now, above, we saw that the quantity sold was inversely proportional to the square of the sale price. This means that, to maximize our profit, there are only two independent variables: sales price and cost. So, given the cost, if we want to maximize profit, we can figure out the right sales price to do so.
If anyone is interested in the calculus, I can write it out, but, basically, when you take the basic equations
quantity = C/price^2
profit = (price - cost)*quantity
substitute the first for quantity in the second, find the maximum by setting the first derivative equal to 0, and solving for price, you end up with:
price = 2 * cost
Given the postulates I started with, does anybody see a hole in the math? Are any of the postulates particularly unreasonable for a young retail startup? (It seems likely, though I haven't taken the steps to prove it with any rigor, that once one is attempting to sell the goods they produce themselves, the rule likely becomes: profit is maximized by selling at no less than twice the cost to produce the good, and only increasing price from there when one's means of production cannot keep up with the demand provided by that price.)
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Topic: Economies of Scale *Free Browser Game* (Read 323958 times)