Risk, Reward, and People See To Believe Then Buy.
Vintage selling is risk and reward. Here’s our fundamental premise about selling: “People only buy what they see.” They have to see it to believe it, and then they buy.
Here’s some questions to introduce everything:
Pick a random item in the store. “How many people on average have to walk into the store until the item is sold? How many people until the item has a \(50 \%\) chance of selling?”
“How many customers per week are entering the store? What’s the value of increasing the foot traffic by 15 percent into the store?”
“Is it better to sell a given item for twenty dollars today, or thirty dollars next month?”
“How many customers have to see an item and say no until the item is purged from inventory or the selling price updated for clearance?”
Formal Model: Time to Sale, Holding Cost, Surplus.
Formally we assume there is a collection \(X\) of clothing items available to the vintage seller. The seller chooses to buy items \(x\) at price \(-\psi(x)\) measured in units of dollars.
The item \(x\) is in inventory for a random period until “time to sale” which we denote by \(\tau=\tau(x)\). The time to sale occurs when some customer eventually purchases \(x\) at sale price \(+ \phi(x)\). The time to sale \(\tau\) is a random variable \(\tau: X \to R_{> 0}\). The law of \(\tau\) is unspecified at this stage.
We assume there is a holding cost \(\alpha: R_{>0} \to R_{> 0}\) representing the cost of holding an item in inventory over a period of time \(t\). We assume the holding cost \(\alpha\) is independant of \(x\) and depends only on time. The inventory cost \(\alpha\) depends on operating hours, rent, basically the expenses of running the business from day to day. Ideally these are fixed costs and \(\alpha\) becomes linear function of \(\tau\).
Definition:(surplus beta) If item \(x\) is sold at future time \(\tau\) and price \(\phi(x)\), the seller’s surplus \(\beta\) on item \(x\) is represented as \[\beta(x) := -\psi(x) -\alpha. \tau(x) + \phi(x).\]
The vintage seller’s goal is to find inventory and customers with prices \(\psi, \phi\) which maximize surplus beta \(\beta\).
Maximizing beta is art and science. The supply of clothing \(X\) is huge, and the seller puts capital at risk when purchasing the item (represented by \(-\psi\)) and commiting capital to future holding costs (represented by the random cost \(-\alpha.\tau\)). The art is finding high beta inventory, where maximizing beta \(\beta\) means optimizing the market conditions where supply of items \(x\) meets customers in timely manner (\(\tau(x)>0\) not too large) and at good price (\(-\psi+\phi\) positive nominal profit).
Beta \(\beta\) represents net gain when \(\beta=\beta(x)\) is positive \(> 0\) for a given item \(x\). On average the seller is profitable if the average of \(\beta(x)\) over the entire supply \(x\in X\) is positive, but ideally we want a positive surplus for every inventory item. This is the simplest way to ensure the average is positive as desired.
Remark: The time to sale \(\tau=\tau(x)\), the holding cost \(\alpha\), and the surplus \(\beta\) are random variables with unknown probability laws at this stage. To statistically sample we need apply a “Rule of Five”. This means taking a random sample of five customers, and noting their transaction and experience in detail. The averages of these five random customers will give useful information.
How Long Until…?
Naively one looks to maximize the price difference \(-\psi(x)+\phi(x)\). But realistically the item \(x\) might never sell at the price \(\phi(x)\). The item will therefore sit in inventory for long time \(T\) and represent a persistent negative cost and liability represented in \(-\alpha.T\). Sellers might consider defining a baseline to purge items from their inventory. This is to avoid the sunken cost fallacy, but also because unsold items can interfere with sale of other items. Unused items lock up inventory, waste the client’s time, and basically the seller has better things to sell. So there’s better use of the space. A rule of thumb for purging, for example, might be “never buy the same item twice” represented by the rule of purging \(x\) after time \(t\) if \(\psi(x) < \alpha(t)\).
Where is the lowest risk return in vintage market?
Wherever there is risk there needs be reward. The vintage sellers have capital at risk, as represented by the costs \(-\phi, \alpha\). So what is their fair reward? The standard economics textbook answer says the interest earned from government bonds, for example, is a risk free return. Therefore every vintage seller could buy bonds instead of clothes, but this is obviously unrealistic. Yet the environment of vintage selling somewhere has it’s own form of risk free return, and this lowest risk return needs be identified. It could be in the form of charitable donations and tax receipts.
[To be continued - JHM]