“If the coin be locked up in chests, it is the same thing with regard to prices, as if it were annihilated.” David Hume — Of Money

One more post on Steven Landsburg’s taxation problem. My previous post is here.

As I had stated before, as a matter of simple accounting, you make the math work out fairly easily to where consumption would have to fall a cumulative total of $84 million dollars. But introduce savings vehicles, which you can not assume away. How is this idle money being horded? There are a quite a few options, I’ll detail three:

Money Market Account: What if our idle millionaire holds his money in an MMA, earning (say) the 10yr Treasury rate of interest, which is then reinvested in Treasuries? The IRS takes his money, and the government spends it on goods and services. Does this reduce consumption future consumption while not affecting idle millionaire’s position? Yes-ish, but only to the extent that the risk-free real interest rate rises, and causes a fall in investment. You could get to a wash in this situation, though…if the government is investing the money at a higher ROI (i.e. it takes the money and invests in a project that cures all cancers with a single pill*).

An Index Fund: Now say our idle millionaire has his money in broad index fund, earing the average rate of return (5%), which is then reinvested back into the fund. The IRS takes his $84 million, and spends it. What the IRS has done here is to reduce the long-run stock of capital in the economy by some amount. IF the government can find a higher ROI than the entire basket of companies that idle millionaire held, then in the long run, there is no fall in consumption. However, that is a tall order, and unlikely to happen. Thus, I falls, and over a period C falls by ~G. Giving an answer that could be close to Landsburg’s result. This is because at the margin S ≘ I.

Mattress: Finally, lets say that our idle millionaire stuffs his mattress full of $84 million. His preference for sleeping on mattresses full of money non-withstanding, what our millionaire has done is reduce the stock of currency. This is the assumption that leads to the phrase “money is not wealth”. Indeed, money is not wealth! But the key is that our guy has already reduced long-run consumption by at least $84 million! This is because S ≠ I in this scenario. Hume explains this in the above quote. So, say the IRS steals his money, and simply keeps it in the mattress for IRS agent Joe to sleep on during lunch? The net effect is nothing happens, because consumption has already been reduced. What if the government spends it on stocks of a company which immediately goes bankrupt? Then society has lost. But if the government simply transfers $1 to 84 million people, then consumption will rise by…~$84 million.

However, this is not optimal. The optimal solution, given that the monetary authority is aware of our guy’s mattress, is to increase the money supply by $84 million. As Leigh Caldwell said in a Twitter conversation (the question was “What Would [Scott] Sumner Do?”):

@leighblue: well, I think he’d say that first the Fed should be printing a new $84m if it knows about the mattress; to be withdrawn when the guy takes his money out of the mattress. NGDP futures in theory would make this happen automatically.

In the real world, our millionaire, Mr. Kendrick, probably owns a basket of assets that includes Treasuries, stocks, corporate bonds, real assets, and currency. In the real world, the government may be hard pressed to tax Mr. Kendrick in a way that is welfare enhancing in the aggregate (even at less than full employment). Not saying that it couldn’t, just saying that it would be uphill battle.

P.S. I still firmly stand behind my “club goods” critique of this problem, although I’m assuming that Landsburg would disagree.

P.P.S. You can object that I’m overestimating the investment efficiency of the private sector over the public sector.

P.P.P.S. You’ll notice that I used investment above quite liberally. It is extremely hard to think of situations where the government is strictly consuming income, besides deadweight loss of transfer. It is also very hard to think of situations where individuals are strictly consuming income, which is a technical point that caused Garett Jones a lot of flack recently. Hence, money does not equal wealth.

The FINAL P.S. (I swear!): Paul Krugman posted a rebuttal to Landsburg’s problem that I think is misunderstood by many looking for contradictions (including my favorite blogger). PK’s hypothetical model assumes that government > no government. So if G is at 0, then any other state of affairs is welfare enhancing. Take your stand on the political spectrum on this one (mine is far to the…I guess right?…from Krugman’s, if you were wondering), but this is the model. The idea is that C (and I) in a world without a financed government would be drastically lower than C (and I) in a world where government steals Kendrick’s money, so by taxing Kendrick, the government (as an institution) is providing a higher level of C (and I) and would otherwise prevail under a situation where G = 0.

Extreme, I know. But the point is that government starts from the disadvantage of a priori deadweight loss. More realistically, you could say that government takes $84 million and invests in a technology which is capable of educating children and young adults much more efficiently than our current arrangement. As an aside, in this scenario, the Treasury issuing $84 million in new Treasury notes, and the Fed buying them with $84 million in newly minted currency would make this situation a wash.