There isn’t a convenient way to get from Philadelphia Airport (PHL) to Wilmington DE. I did some traveling this past weekend (which was a welcomed break for me!) and when I landed despite the stormy weather in Philly I had a few options to get home. Between walking 25 miles, calling an Uber for roughly $50, or taking the Septa for $11 I opted for the Septa. even though I needed to first go to center city Philadelphia, which was the opposite direction, to then take the local train back south towards Wilmington. I was fine to do so and take the extra time since I had most of the day on Sunday to sleep after a weekend hanging out with friends.
My choice of travel, train, worked fine for me. It was way cheaper than the quickest option, but way quicker than the cheapest option. If I was in more of a hurry, or the trains weren’t running, I would have opted for the expensive option, but I didn’t. In economist jargon, the “good that was allocated” to me turned out to work pretty well. I even got to feel like a main character watching the rain:
Sometimes economics as a whole is referred to as the science of this allocation scarce resources (Robbin 1932). As such, there is a natural next question of “allocate the scarce resources to who?” And there are whole fields of economics aimed at answering this question.
Who do you allocate the goods to?
It might be tempting to say “the highest bidder” if you’re the seller, or “me!” if you’re the buyer. But the more philosophical approach is allocate these scarce resources so as to “maximize social welfare.” What this means is to allocate the goods in such a way that society as a whole is better off. In order to do this, one needs to have a way to measure the well-being of society, which in classical economic theory shows up as a social welfare function. In reality, we mainly use GDP as a proxy for this. When GDP increases, by definition more goods and services are consumed in the economy. People like goods, and they like services, so this must mean that society is better off! (the author says sarcastically)
Back to the point about allocating resources, if your social welfare function is the average of everyone’s utility, if you distribute resources in such a way that the median voter improves, then you’re at least doing better than before. Your welfare function might instead be the value of the least happy (poorest) person, so you might choose to allocate resources to that person(s). Whatever your social welfare function tells you is how you should allocate goods.
But there becomes a problem when you don’t necessarily know who the median voter, or worst off person in the economy is. Or maybe you don’t care about the wealth of who you’re allocating to, but just that the resource gets allocated to those who value it most- thinking that then from the will of the invisible hand the social value is maximized. This insight isn’t necessarily all that helpful, because we don’t know how people value the good. Or at least it’s costly to find out since there is an incentive for people to exaggerate how much they value the good. If you want to give it to the highest value person, and you simply ask them, they might lie and tell you that they value it an infinite amount!
Enter the auction
Auctions have been historically used as a way to allocate goods without needing to find out ahead of time how people value the good. The classic English style auction accomplishes this, by gathering all the interested parties, starting at a price, and allowing for increasingly priced bids to compete away for the good, given to the highest bidder. And if the ending price falls below your valuation of the good, then you pocket that difference in value.
An improvement on the classical English style auction is called a Vickrey Auction, or a sealed bid second price auction. In this type of auction, instead of calling out bids aloud, the bidders write down their bids and the good is awarded to the highest bidder. However, the price that the winner pays is the second highest bid. This type of auction incentivizes truth telling amongst the bidders and works as follows:
If you’re the highest bidder:
And bid higher than your valuation, you still get the good at the second highest bidder’s price. No change in utility than if you bid your true value.
And bid lower than your valuation, you run the risk of not getting the good if your bid is lower than the second highest bidder: 0 utility. You would still get the good at the second highest price if you were still higher than the second highest bidder, or again no change in utility.
If you’re not the highest bidder:
And you bid higher than your true valuation you might end up as the highest bidder and get the good, and have to pay the second highest price, which is greater than your valuation! So you end up with negative utility
And you bid lower than your true valuation, you still don’t get the good: 0 utility
This is an example of designing a mechanism to incentivize truth telling. This works well when bidders work in isolation, or they can’t communicate. But what if they can? Or if there are different sized bidders? Like if they are two very large bidders in a pool of much smaller bidders? The two large agents might be able to collude and tell each other what they will bid, knowing that they’ll be able to outbid the smaller bidders despite offering a lower bid than what they value. Not so truthful then!
This might be something to be mindful of in a price setting scenario. Larger companies aren’t necessarily pricing at their marginal costs such to make 0 profit in a perfect competition setting. Something similar to collusion in a Vickrey Auction might be happening here, and if you are the consumer who only cares about final price you might not necessarily care. But if you are on the fence between two sellers, and know that for example a large company might not support its workers with fair wages, then maybe knowing this bit of economics might change your purchasing decisions.
*Note* Speaking of allocating scarce goods (time): I’m taking a short break from writing for the next few months. I’ll need to focus on my comprehensive exams coming up, along with some personal travel. I'm looking forward to restarting these weekly-ish posts sometime in July when I can devote the (then less scarce) time that I would like to these posts.