Relative supply shocks, Unobtainium, Walras' Law, and the Coronavirus

Here's the basic idea:

A temporary 100% output cut in 50% of the sectors (what the Coronavirus does) is very different from a 50% output cut in 100% of the sectors (what our intuitions might expect from supply shocks in aggregate macro models).

The former can easily lead to deficient demand in the unaffected sectors; the latter leads to excess demand in all sectors.

Here's the intuition:

(As they say: "Shit just got real". And one of my daft old thought-experiments just got very real.)

As you know, unobtainium is a very desirable good. Everyone wants to buy it. But nobody produces it. It doesn't exist.

You could say there's an excess demand for unobtainium, because people want to buy some of it, at any price. Maybe they want to spend half their income on unobtainium. But supply is zero. And if you do say there's an excess demand for unobtainium, and if you also believe in Walras' Law, you get into one helluva mess theoretically, because the excess demand for unobtainium must (by Walras' Law) be matched by an excess supply of other things. So even thinking about unobtainium creates a general glut -- a recession. Which is silly. Because Walras' Law is wrong. Because, as Clower said long ago, it's constrained not notional demands that matter. As I explained in my old post.

But now imagine that someone actually invents a way to produce unobtainium. They can't produce it just yet, but everyone knows they will produce it, and sell it at an affordable price, a few months from now.

What happens when they hear the news? Everybody (or everybody except borrowing-constrained Hand To Mouth agents) suddenly wants to save up to half their income, so they can spend it on unobtainium in a couple of months time. Their money will be worth more in a couple of months than it is now, because they will be able to buy unobtainium with it, and not just all the stuff they can already buy now. We get a general glut (deficient demand) now.

And that is pretty much what's happening with the Coronavirus, in the real world. Half the goods we used to buy are temporarily unobtainium. But we expect to buy them in a couple of months.

It would be very different if unobtainium were a perfect substitute for existing goods, so its invention is exactly like increasing the supply of existing goods in a couple of months. Then we would want to dissave now, like in standard aggregate macro models, because the Marginal Utility of Consumption is high when consumption is low, so we want to prepone consumption from the future to the present. But unobtainium isn't a perfect substitute for existing goods. High intertemporal substitution can beat low cross-section substitution.

(Sure, unlike in my thought-experiment, we used to be able to buy unobtainium in the past. But that's irrelevant; bygones are bygones. It's only the present and the expected future that matter.)

That's why we need temporarily looser monetary and fiscal policy. (Plus, we also need fiscal policy to redistribute between people differentially affected by the Coronavirus, but that's another story.)

Think that's (basically) right.

OK, I've oversimplified (of course). Much of the stuff that's still obtainable is the more essential stuff, like food. But not all. And, at the margin, we still face intertemporal vs cross section substitutibility.

Comments

[Abby]

Who knew unobtanium = toilet paper!

[JohnL]

What if we look at unobtainium a little differantly.
What if we always had unlimited access to unobtainium in the past. We had so much of it we never gave it much thought, like toilet paper. Now the environment has changed and unobtainium suddenly becomes hard to come by, it's difficult to attain. One would truly think the value would raise. ....right?

But in my thought experiment I call unobtainium.......credit, now the story ends differently, doesn't it?

[Frances Woolley]

Nick, interesting post.

What if we went the other way, and assumed that there was little to no possibility for intertermporal substitution of unobtainium? Personally I think that's more realistic than assuming a high degree of intertemporal substitutability. I can't make up for the latte I didn't consume yesterday by consuming two lattes tomorrow, because the marginal utility of a latte diminishes sharply after one/day. Same for the Ottawa '67s game I didn't go to a couple of weeks ago - that's gone, it won't be made up.

How would your thinking change then? I would have thought that we'd want to wait to step on the gas, from a monetary point of view, until the unobtainium sector was back on-line. And keep those fiscal transfers flowing so that people can pay their rent and don't go hungry.

[David Andolfatto]

Nick,

"What happens when they hear the news? Everybody (or everybody except borrowing-constrained Hand To Mouth agents) suddenly wants to save up to half their income, so they can spend it on unobtainium in a couple of months time."

This is basically a "good news" shock. There will be more production (and hence, more income) tomorrow. The standard consumption smoothing story is that people will want to dissave or borrow against the higher future income. Generally, if there's a positive wealth effect, the consumption demand for all things will rise.

So not sure if you story hangs together. Or, if it does, you must be making some implicit assumptions that I'm not seeing.

David

[Frances Woolley]

Nick - being a bit slow here - perhaps the point is that we can prepone our consumption of things other than unobtainium and that will help the economy keep moving? Unfortunately pretty much the only things that aren't unobtainium right now are necessities - food, housing, car repairs, that kind of thing. And the demand for necessities is highly inelastic. Home repairs might be one exception here, especially DIY home repairs, and I suspect the hardware stores are doing relatively o.k. out of this. There's also frozen food, toilet paper, etc - but there's a strict limit to how much frozen food people can store, and toilet paper isn't big bucks. But perhaps a monetary kick might get firms to do more preponing - make capital investments, say? Or am I still missing the point?

[jj]

So if we're all saving dollars today, hoping to spend them on goods in the future (which are not actually being produced and stored!), then there should be a great price inflation when all of those future goods come back online. For example: everybody wants to go on that cruise they missed, but there are the same number of cruise berths as before.

Will this lead to monetary tightening, withdrawing the all the extra money being pumped out today?

[Nick Rowe]

Frances and David: let me try this, to see if it makes sense to you:

2 sectors are apples and bananas. Both non-durable. Bananas temporarily become unobtainium.

Consider two extreme cases:

1. Apples and bananas are perfect substitutes. It's basically a one-good economy, on the consumption side. Then we get David's case. Permanent income is almost double current income, so there's an almost double excess demand for apples (at the old prices and interest rates).

2. Apples and bananas are perfect complements. So if you have no bananas today, you don't want any apples either. Demand for apples drops to zero.

The real world can be anywhere between those two extremes. So we can easily get a fall in demand for apples, by assuming it's nearer the second extreme than the first.

And all that is before we consider differences in intertemporal substitutibility.

And if we add in any degree of substitutibility on the supply side (unemployed banana producers switching to producing apples) that would make it more likely we get an excess supply of apples.

(Plus, if they can't switch, unemployed banana producers may be borrowing-constrained, which reduces their demand for apples.)

[Frances Woolley]

Nick, o.k., neither of those two extreme cases are what I had in mind because they don't allow for intertemporal substitutability.

What if the one period utility function is of the form Ut=a*ln(obtaniumt)+b*unobtanium, and the two period utility function is U1+U2. So perfect intertemporal substitutablity of utility, linear utility in unobtanium, diminishing marginal utility in obtanium.

I think this is the closest approximation of how I think about the world. What's the optimal policy response in this case?

[Nick Rowe]

Frances: if I'm getting the math right (big IF), I *think* that utility function gives us an excess supply of obtainium (i.e. apples) if and only if there is *any* supply response from unemployed banana (unobtainium) producers switching to apples.

[Frances Woolley]

Nick, another crucial thing is whether or not the unemployed unobtainium workers can borrow against future consumption and/or receive transfers from the obtainium producers. The way this utility function work is that you spend all of your income on obtainium, until (MU/p)obtanium=(MU/p)unobtanium, and then you spend the rest of your income on unobtanium. So, yes, as long as there's no long-run change in relative prices (your point about there being no supply response), and people can borrow so that they're not at a corner solution, total demand for unobtainium doesn't change.

So I think if you have this utility function, a good policy is to transfer income to unemployed unobtanium workers, and monetary policy won't do much for you.

[Dee]

Question? Can borrowing be considered a catalyst? Wouldn't t be skewed? If majority farmers move to growing apples then wouldn't the end result be a depletion of resources over time because of unknown variables?