Tag Archives: Black

Zero Marginal Utility Goods

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Standard consumer theory says that rational consumers will select their consumption of goods A and B such that \frac{MU_A}{P_A} = \frac{MU_B}{P_B}, with of course the tiny disclaimer that for some pairs of goods, there will be a corner solution; that is, for some goods A and B, some consumers will optimize not according to the preceding expression, but by consuming zero of either good A or good B.

Now, is that really a tiny disclaimer? Don’t we each get zero marginal utility from most goods? I made this point on Twitter yesterday and got this reply from Alex Tabarrok.

Now, it’s true that in a world of discrete goods, when price is high, that will result in a corner solution. But sometimes marginal utility is just really low, zero, or even negative due to storage and disposal costs. There are some things that even most billionaires do not buy.


I pointed Alex to a squirrel yard statue, which I found by searching “knick knacks” on Amazon.com (it was the fourth item). He yielded.

This resulted in a fun game of finding weird, zero-marginal-utility stuff online. Among other good items, Adam Ozimek found Vanna Speaks, Adam Gurri the Misty Mate Pet Misting System, and Jim Ulbright a life-size Anubis statue.

What can we learn from this exercise? I think there are a few things. First, while it’s fun to have a laugh at some of the weird products on the market, somebody is buying at least some of this stuff at least some of the time. I was memorably reminded of this because when Daniel Lin nominated gold lamé MC Hammer Parachute Pants as a ZMU good, Adam Ozimek vociferously disagreed. He ended up buying a pair for himself.

It’s tempting to think of the economy as supplying goods we all want to everyone (in uneven proportions of course), but it’s important to remember that the economy also supplies goods that most of us would not want to the few people who want them, including ourselves. This is not a trivial problem and it may not be solved smoothly through time. Fischer Black built his theory of the business cycle around the idea that it is difficult to match today’s production to tomorrow’s tastes, but it is also difficult to find the right buyers for today’s products.

Second, there is a direct analogy from the goods market to the labor market. Once you concede that most goods provide zero marginal utility to most consumers, you almost must concede that most workers provide zero marginal product to most firms. The math is the same. The ZMP hypothesis, therefore, is not some extraordinary claim that defies common sense.

Just as matching weird goods to weird people is hard, matching some workers to the right firm is hard. Nominal shocks can make this harder even in the absence of sticky wages and prices. People who have nominal debt change their consumption patterns when a nominal shock hits, and both people and firms can misinterpret nominal shocks in the short run per the Lucas Islands model. In the face of changing consumption and production patterns, Black’s Noise plays a role, and when the consumer-product matching problem is hard, the firm-worker matching problem is that much harder. Again, this is true even if wages and prices are totally flexible, and even if you support NGDP targeting (I do).

Oddly since these ideas owe much to Hayek, some Hayekians are slow to accept the ZMP hypothesis. Don Boudreaux at Cafe Hayek tells a comparative advantage story to rebut ZMP that is completely devoid of firms and therefore employment, in which all parties have perfect information and do not need to discover patterns of production. But ZMP is on the march; Karl Smith, a diehard New Keynesian, is starting to make some pro-ZMP noises.

So when you start to think that ZMP is a weird claim, just remember ZMU goods. I myself am not expecting to have much difficulty remembering ZMU goods. One is on its way to me. Tweeter @fbaseggio has bought for me the squirrel yard statue.

I’m looking forward to installing it in Alex’s office when he isn’t there.

The Economics of Cryptocurrency

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Is there a word for serendipitous Wikipedia browsing? Yesterday I started out seeking information on punk music and I ended up discovering Bitcoin, an open source peer-to-peer digital currency. Bitcoin uses strong cryptography and decentralized computing to produce scarcity in the money supply, which grows at a predefined rate that is clearly visible in the source code. Tamper with that growth rate and your software becomes incompatible with the rest of the cloud, and your Bitcoin holdings become valueless. Double-spending is impossible unless at least half the computing power of the cloud is in on the attack against the currency. You can read all the technical details here.

The total supply of Bitcoins is scheduled to grow geometrically and will asymptotically approach 21 million. This means that if the currency becomes successful and its velocity does not accelerate proportionally to its use, we should expect long-run deflation in Bitcoin-denominated prices. Bitcoins are technically divisible to 8 decimal places to accommodate this. Notably, if I am reading the data correctly, Bitcoins have appreciated by a factor of 300 against the dollar in the last year. One Bitcoin is worth around 88 cents as of this writing.

I have a number of questions. Perhaps my readers know some of the answers, or perhaps some enterprising young monetary economist will address some of these in an academic paper (calling Will Luther).

  1. Currencies are based on trust, and trust in money is accomplished through scarcity. Bitcoin is cryptographically guaranteed to be scarce since its supply will never exceed 21 million. But there is reason to believe that a perfectly fixed supply is not optimal. If people suffer from money illusion, it is better if prices increase gradually over time. If money has real effects, then it is best if the money supply is countercyclical. These two facts are at least part of why Sumner advocates a fixed NGDP trajectory. Is it possible to create a cryptocurrency that targets NGDP instead of the money supply?
  2. If there are competing currencies would we still want any one currency to target NGDP? MV ≡ PT, but notably T only represents transactions denominated in a particular currency. In general, what is the optimal path of the various money supplies when there is more than one currency in use in a given economy? When there are competing currencies, is there less money illusion? Does money continue to have real effects?
  3. What are the monetary implications of the fact that governments will probably have difficulty regulating banking in cryptocurrency? Does cryptocurrency provide a test of the legal restrictions theory developed by Fischer Black, Neil Wallace, and others?
  4. What if prices come to be denominated in Bitcoin (with its fixed supply), but different media of exchange and settlement are used? How does that change any of the above?
  5. In a number of the above scenarios, there may not be much deflation in Bitcoin-denominated prices (since the money supply is not defined, say, under the absence of legal restrictions on financial intermediation). Putting these scenarios aside, if deflation were consistent, then Bitcoins would yield a positive return due to appreciation. Would we see more money hoarding during recessions? Would the world finally see a real liquidity trap? With monetary policy out of the picture, would fiscal policy become necessary? Is crypto-anarchy self-defeating because it requires big government interventions?
  6. Decentralization of the currency means that it cannot be debased, but it also means that it cannot be confiscated at an institutional level. What are the political effects of this change?

I suppose I should add that I am not exposed to Bitcoin and am long USD. And by the way, thinking about Bitcoin reminded me of David Friedman’s Future Imperfect, which you may want to read if you enjoyed this post.

Update 4/4/11 — Bitcoin is the subject of today’s EconTalk.

Hail Fischer Black!

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Twitter engineer Alex Payne made news today by announcing that he is leaving Twitter to co-found a bank, called banksimple. The new bank is supposedly focusing on simplicity and transparency: there are no fees, you can deposit checks by uploading a picture of them, the website is nice and clear, etc. That’s great and all, but I got really excited when I looked into the bank a little more. One of the things they claim on their About page is “No overdraft fees.” Further down the page it says, “We will launch later this year with a simple card with in built checking, savings, rewards and a line of credit.”

If I am interpreting their claims correctly, it seems that every checking account will be linked with a line of credit, and there are no fees for switching between a positive and a negative balance. This is a large step toward making Fischer Black’s famous article, Banking and Interest Rates in a World Without Money, a reality. Black imagines that everyone has a single account at a bank. At the end of each month, if your average balance was positive, they pay you interest. If your average balance was negative, they charge you interest.

The interesting aspect of this world is that if most payments are made by check or electronic transfer, there is no reasonable definition for the quantity of money. Gross deposits are not the quantity of money, because this makes an arbitrary distinction between positive and negative balances. The net value of bank accounts is not the quantity of money, since they will equal (by an accounting identity) the capital of the banking sector. That’s not too useful. If there is no quantity of money, then a lot of what we know about macroeconomics breaks down. There is no quantity theory of money, and there is no liquidity preference theory. “Monetary policy” is powerless. This goes to show how much of monetary macroeconomics is completely dependent on particular institutions and legal restrictions.

I would like to live in a world with the simple kind of Fischer Black-style banking, so I hope that banksimple takes off and works the way I expect it to. Even if it doesn’t, I think that the next few decades are ripe for changes in how we think about money; Black’s influence is likely to grow. If you haven’t yet read Business Cycles and Equilibrium (which contains a reprint of Banking and Interest Rates in a World Without Money), do it soon.