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A Tech-Econ Mashup with a Libertarian Flavor

Guest Post: Markets in Everything

Today’s post is courtesy of my friend and former colleague, Jon Arfa, a student at Washington University, St. Louis:

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I’d like to thank Libby for letting me share my thoughts here.
Think of this as “markets in everything.”

There’s this bar in St. Louis that, every Thursday night, is packed full of WashU students. Starting at 10PM they run this deal for $2 pitchers (small-ish pitchers, ~48oz) of absolutely delicious beer that they brew on the premises. This might sound too good to be true. That’s because it is.
The supply of pitchers is very limited. Many people, like my friends and I, try to show up by 10:30 in order to make sure that we get our hands on one. Often, we’ll end up getting 1 pitcher per person in our group because they end up being quite valuable. Other people are not so lucky, and are faced with two options in order to take advantage of the deal. Most commonly, people “steal” pitchers from other tables when the previous “owners” aren’t looking (obviously, none of the patrons truly own the pitchers, but it’s still a tiny bit unethical.) More rare is something I saw the last time I went: a friend of mine sold his pitcher for $4. That is the only time I’ve seen it happen, but I bet that it would be pretty easy to conduct a brisk trade in pitchers if one was so inclined, and not too hammered.

What I’m wondering is how the bar could maximize their profits and take advantage of this market. I’m assuming that they have purposefully limited the number of pitchers. Perhaps the price could be raised: after all, the majority of WashU students come from well-off families and could easily afford to pay $3 or $4 per filled pitcher (in other words, I think the demand is somewhat inelastic at that margin.) A friend of mine proposed that the bar rent out the actual plastic pitchers. I don’t think this would work, it would probably be such a pain in the ass for the bar patrons that they simply wouldn’t buy pitchers, or even show up.

Any thoughts?

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Filed under: Economics

4 Responses

  1. Jon says:

    One thing I could’ve made clearer is that there are 2 markets: the market for a pitcher-full of beer and the somewhat underground market for the plastic pitchers. Any change in the bar’s pricing needs to take into effect the effect on both of those markets.

  2. Andy J. says:

    Optimally maximized pitcher price would be determined as a dynamical function of variable consumption (forecasted demand) versus the retailer’s mean fixed inventory (real supply) for any given day.

    The “demand” half of the equation requires surveying local bars to first learn the average standard price for a pitcher; in a more generalized equation, we can potentially set this maximal value to ~infinity. The minimal potential value for the discounted beer pricing would be zero, meaning that the retailer is giving it away for free. The optimum profitable pitcher price then obviously falls somewhere between these extremes in the final graphed function. As the discounted price (DP) approaches too near the standard price found at neighbourhood bars, it will impact the customer’s perceived sense of value, causing a reduction in attendance or consumption, thus negatively impacting on sales; contrarywise, as the DP approaches too near the retailer’s actual brewing cost, the profit margin becomes minimized and may not prove cost-effective to the business.

    The intersecting “supply” component of the graph will necessarily be a fixed volume for each night. This amount can be anticipated by taking maximum occupancy of the bar multiplied by an estimated maximum consumption per seat (including cheap pitchers) in a given night. It wouldn’t particularly matter if we assume a high turnover rate of customers at the door — leaving after a few hours — because even if they’re replaced by thirsty new arrivals, all comers will be restricted in the estimated maximum consumption rate as a fixture of time (ie., the bar’s operating hours and projected drunkard metabolism — need more data on progressive drinking pace to be sure).

    Plot these values on your standard economics price-to-cost x/y-axis graph, dropping down a plumb line to determine the ideal pricing where the two tangents intersect (…or something like that — I don’t study economics).

    However, applying such a linear estimate is not optimized. Because there are overhead expenses involved in holding inventory, stock levels should be kept as low as possible. Yet failure to deliver on demand may force customers to seek out alternate suppliers [just like sex, haha]. For this reason, penalty costs are assessed for accumulating a backlog of unfulfilled orders (ie., failing to meet demand). Each stock manager must therefore attempt to keep his inventory at the lowest possible level while at the same time avoid being sold out.

    The supply-demand chain in a beer distribution hierarchy is non-linearly connected with time delays (acquisition lag) involved in brewing or (more typically) in communicating orders to an off-site brewery, a consequence of which is an amplification phenomenon (a la accelerator effect) characterized in the “Beer Game” (check wiki/google), a simplified stock management simulation which uses 27 state variables representing quantities such as expected demands, inventory levels, and order rates for dealers.
    …Without getting into a longwinded explanation of chaotic attractors and Lyapunov exponents (see wiki again, if mathematically inclined), in order to stabilize the distribution chain it pays to adopt an inventory policy where stock discrepancies are adjusted slowly while the information exchange rate in the supply line is moderately high but not “1” (excessive, increasing operating costs), otherwise the system will stabilize into an unwanted state with negative inventories. In observed play of the game, ordering decisions turn out to be far from optimal, regularly exceeding this theoretical inventory minimum by over 400 percent.

    Your beer pitcher example seems to be a modified version of that problem, having fewer steps in the delivery chain — hop re-supply and brewing time delays. I would assume to construct the optimum pricing policy graph with a third axis (z) which plots the retailer’s attendance or sales stats over a measured span of time, then checking for the biggest correlation spike against the x/y pricing plane. But if I’m just eyeballing a guess, I’d say the discounted pitcher can safely be priced exactly halfway between the retailer’s brewing cost and the mean pitcher price offered at other local bars, thereby maintaining an optimally preferential perceived value at this establishment which is simultaneously profit-maximized insofar as not discouraging patronage.
    […There are some noticed parallels in all of this to chaotic behaviours in stock market prices as collectively determined by individual human buying decisions. And despite my seeming joke above, the same profit/loss interactivity also holds for human choices in romantic transactions. “…Mother told me to pick a boyfriend who is like a rising stock.” haha. ‘Markets in everything’ indeed.]

    The self-brewing retailer may have less concern for acquisition lag in his inventory (more info required here on brewing turnaround times), and need not bother with any of this mathematical jargon if profit “optimization” isn’t his primary interest. He can simply calculate his immediate brewing expenses (materials, time, employee and electricity/heating/rent overheads) and then divide his produced beer volume by pitcher size, pricing accordingly anywhere above operating cost (depending on how generous he cares to be) while still coming out ahead. Reasons to purposely adopt such an suboptimal pricing scheme might be to establish customer loyalty or for word-of-mouth promotion to yield greater gains over the long term [per monogamy, if referencing the romance market again].

    Restricting or elastically modifying the number of available discount pitchers adds another dimension of complexity to the system, introducing inter-consumer [male-male] competition (on top of local retailer [female-female] competition) as an incentive to early patronage [courtship], not unlike the strategy of routine sale “deadlines” seen with many online retailers to instill an artificial sense of urgency. (Hurry!! Offer expires while you wait…. until next week’s sale begins!) In this case I suspect the pitcher restriction is in place to minimize their already realized losses — they may be selling at cost or below — while still dangling a carrot to encourage earlybird crowds, but in doing so they’re risking creating hostility among excluded patrons (ergo the pitcher thefts, stabbings, shootings…)

    Maybe I missed something in your description, but I don’t see why all patrons with pitchers wouldn’t just freely share with others, each paying his own two bucks; or sharing refills (if there are refills?) between pitchers and those with smaller glasses. Or you could set up your own private rental scheme (say $3) traded strictly between patrons, though I imagine the bar might retract their discount offer altogether or numerically tag the pitchers if they caught on to widespread abuse; but even before that happens, I expect the unauthorized renters might encounter difficulty retrieving their “rental equipment” given their fellow drunken clientelle (…ergo the pitcher thefts, stabbings, shootings.)

    Beer is gross and fattening. :p
    I like those Smirnoff Ice fruity vodka coolers, and similar girly drinks.

    wait… why am i yammering on the internet again.
    [hello, blondie. Get back to your desk. ;)]

    …Less talking, more boozing!

  3. Kat says:

    It would be cool if the bar ran something like a $2 deal from 10:30 to 11:30 (or 11…you get the idea), then $6, then $10 or something like that–so people would weed out according to what they’re willing to pay. This would also encourage turnover (you’d have to take back the pitcher and give a fresh one for seconds), because there would be incentive to chug.

    Or the opposite might be awesome: to charge $10 from 10-10:30, then $8 from 10:30 -11 or something like that–so people would get to the bar early and buy when the price is right. There would be less inefficiency that way, bc people wouldn’t want to stand around not drinking, but they’d be more likely to buy in early to avoid the risk of not getting a pitcher at all.

    The last consideration I think is the question of wasted folks at the bar. I don’t know this bar, but from working a long time in a college town I know bars consider how wasted their patrons will be, and look for somewhat quality clientele. Right now the average patron isn’t that drunk, because it’s so hard to buy pitchers. In the first scenario above you’d have good turnover, which would be great, but you’d also have lots of very drunk people who just begin or end their night there, not stay and add quality atmosphere (or whatever). The second scenario would make for a much more fun night, I think. You would have more varied clientele, and the clientele average would be much higher quality–i.e., loyal enough to know the price scheme, sophisticated enough to know when the beer is worth it, and *not* stealing pitchers from other people’s tables!

    Just a thought! 🙂
    Kat

  4. AJ says:

    @ Kat:
    A pricing scheme incrementing with advancing hours would encourage patrons to get there early, fill up on the lowest priced pitchers, then increasingly file out as the price becomes less attractive. It may not help profits, it could offer the self-regulating benefit of shuffling those cheapo binge-drinkers out the door earlier so that drunken crowd control becomes less of an issue. (…I still can’t know what qualifies as a good discount without doing a preliminary price comparison for the neighbourhood bars.)

    The hourly decimating price model seems more problematic. Bar-hopping crowds might show up late (perhaps already drunk and rowdy) to only take advantage of the discount — or not show up at all if they’re comfortably/forgetably drunk elsewhere — but more to the point, sales opportunities during earlier hours would run sluggish as patrons inactively occupy seats waiting all night for the discount to kick in, possibly getting bored/tired/’other’ (wink) and leaving.

    Do college-aged bar-goers tend to immediately cut loose and spend wildly early in the evening, or do their wallets open wider as they get more intoxicated (assuming they haven’t already expired all their cash and appetite for booze by then)?

    To incentivize sales evenly throughout the night and for added entertainment novelty, I would suggest the bar could instead award their discounted (or FREE!) pitchers randomly with refill purchases, and make a real spectacle out of the winning pitchers, with colored lights and noise at the register, as in a slot machine or bingo payout. This system would spread the reward-potential equally among all patrons at all hours, along with creating a celebratory atmosphere of cheering: “Let’s drink to that!!” (Note: this idea may constitute gambling and be prohibited by law in 48 states. :p)

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