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"But if all prices are fixed, the berry producers will not want to sell their land."

Really, I thought we started in equilibrium?

Adam. You lost me there. We started in equilibrium, where the berry producers are holding exactly their desired quantity of land. Then we fix prices. Then we introduce a shock, so peach producers suddenly want to buy more land. But berry producers don't want to sell.

But we fixed prices at the euilibrium prices, we had to. If we didn't fix them at the equilibrium prices then it wouldn't be true that berry producers are holding exactly their desired quantity of land.

At equilibrium prices berry producers are perfectly happy to trade a unit of land for the appropriate number of peaches, at least the first unit.

So why can't the peach producers buy some land?

Adam: OK, at equilibrium the berry producers are indifferent to trading the first unit. But they won't want to trade the second or third units. And the peach producers want to buy thousands of units.

Take the limit of the above as the size of the "unit" goes to zero.

But as soon as they've diverted enough peaches out of the berry market and into the land market to cause quantity rationing in that market then they've also, by construction, diverted enough peaches out of the berry market to cause a glut of berries.

Here' my image: They load lots of peaches onto the wagon, and head off to the land/peaches market. They get there, and find they can't buy land, so turn the wagon around and head off to the berry/peach market.

Here's my image of your image: They load all the peaches onto the wagon, get to the land/peaches market, and find they can't buy land. By this time it's evening, and too late to turn around and head off to the berry/peach market. The peaches rot in the wagon. (And the berries rot in the wagon at the berry/peach market too, because the peaches never show up.)

"They load lots of peaches onto the wagon, and head off to the land/peaches market. They get there, and find they can't buy land, so turn the wagon around and head off to the berry/peach market."

But we just established that they can buy *some* land.

What you seem to have in mind is that they load up the peaches, come to market and try to buy say 100 peaches worth of land. They find that they can only buy 20 peaches worth of land so they leave without transacting.

I say they load up the peaches and go to market trying to buy 100 units of land. They find that they can buy at most 20 peaches worth of land so they do that. They then arrive at the berry market and and buy 40 fewer berries then they otherwise would have (assuming the relative price of 2berries/peach).

So it's not that all the peaches rot and all the berries rot, it's that demand for berries falls, replaced by demand for land, while demand for peaches stays the same (in particular doesn't increase).

Thus aggregate demand has fallen, we get the glut of berries.

Clearly, certain assumptions give rise to Walras' Law, while others do not. Could one empirically test the hypothesis that Walras' Law holds?

Nick @ 6:53

Well, the point was not to have a government sector at all, but to show how expectations failures can cause general gluts in a barter economy.

In my model, there are no separate classes of rentiers/workers. There are households that both work and accumulate consols (say for retirement). You can argue that the retirees are the rentiers if you want, but a representative household will have some accumulated bonds and will also be working, and it's easier to just assume that.

There are two markets: the market for consols in terms of wheat, and the market for labor in terms of wheat. The third market -- consols for labor -- is fixed by the production characteristics, as it requires 1 unit of labor to produce 1 unit of planted land.

What is happening is that the harvesting firms have promised to deliver, say, 1 ton of wheat to households as interest payments. And the household sector also gets, say, 3 tons of wheat as wage payments. The households will consume whatever wheat they want and will turn around and roll over some of their wheat income by purchasing more consols with whatever consumption of wheat they want to defer.

The new consols purchased will correspond to new firms planting land in that period, and that exact amount will correspond to the wages paid to households employed by the new firms that are planting.

Therefore I am sneaking in an endogenous money economy, hopefully with proper accounting, into a barter economy, where consols play the role of money.

When the discount rate falls, households want to consume less wheat in the present, the amount of wheat that a consol buys goes up, and households obtain more of their wheat in the form of wages paid by planting firms as more wheat is used to pay workers making planted land.

When the discount rate rises, then households want to consume more wheat in the present, the amount of wheat that a consol buys goes down, and households earn more of their income working for harvesters, with less employment and investment by planters.

However, the price of a consol in terms of wheat is not determined just by the discount rate, but is also determined by the numerator -- the expected future profits earned by harvesters -- and *only* by harvesters -- that are being discounted.

And in this economy those profits are exactly equal to the amount of total borrowing each period by the new planting firms.

So if, for some reason, there is a belief that expected future profits of harvesters will be higher, you can get excessive investment in terms of more planters today wishing to become harvesters tomorrow. These planters will buy more wheat today from harvesters without creating any wheat themselves, causing wheat prices to rise, and profits to rise in a self-fulfilling prophecy.

If, on the other hand, there is a belief in low future profits, you get a self-fulfilling prophecy of falling investment, meaning less non-wage demand for wheat, meaning that harvester profits fall, and they have no option but to reduce employment (if they can increase MPL by doing so) in order to meet their bond obligations.

The underlying assumption here is that in the sum

NPV consol = P_1/(1+R) + P_2/(1+R)^2 + …

the numerators -- the P's -- are volatile -- whereas the denominator -- the R -- is relatively constant. And in that case, you would get volatile employment and investment even in a barter economy, and without any government fixing of interest rates, or any price fixing at all. I am assuming perfectly flexible prices, but imperfect future knowledge of the P_s.

And in the downturn, this does correspond to a fall in aggregate demand for wheat because there are fewer planters desiring to buy wheat on credit, meaning a glut of wheat matched by an excess demand for consols.

And perhaps the easiest way to think about this is that, even though each individual household wants to defer some consumption of wheat, it is impossible, in aggregate, to defer consumption of wheat that has been harvested.

This is unlike the macro assumption that income is some "goop" that is transmuted into capital or consumption. It's a different accounting.

When household A decides to defer consumption of the wheat income that it receives, it purchases a consol and then household B is provided this wheat as wage payment for working for the firm that sold the consol. So even if 100 tons of wheat are harvested, to say that households succeed in "deferring" the consumption of 50 tons of wheat means that 50 tons of wheat are re-sold in exchange for consols, with wheat aggregate income equal to 150 tons of wheat. It's still the case that 100 tons of wheat were produced and 100 tons of wheat were consumed. But 50 tons of wheat were successfully "saved" only because wheat incomes increased in excess of actual wheat production.

When household savings demands are too high, then they fail to save wheat and wheat incomes decline up until households succeed in saving a portion of their (smaller) wheat income, even if the amount of wheat produced by the production function is unchanged.

This is the exact same paradox of thrift effect that you see in a monetary economy.

The more I think about it, the more it seems the conclusions drawn depend on the model used and how one thinks about it.

In the simple 2 good model with wheat (storeable) and berries (perishable), it's possible that an increased desire to save leads to a price shift that causes the market to clear.

It's also possible that there's a maxium total demand for berry consumption that places an upper bound on berry demand. (Think of this as an individual's demand curve that goes flat below a certain price. This doesn't really show up in economics textbooks, but if you think about it, most of us could only consume a certain amount of berries even if they were free.) Depending on what this upper limit is and the ratio of wheat growers to berry producers, it's possible that this mechanism (or something similar) would limit the demand adjustment.

Er... I think I'm getting bogged down in details. I think the main point is that if anything makes prices sticky, the higher demand for savings/investment causes production of perishable goods to fall. Money isn't required to come up with a story that justifies sticky prices. If the durable goods sector can't absorb the extra labour, you get unemployment. (When production requires land or some sort of capital accumulation, it's possible that the employment in the durable goods sector can't just instantly increase.)

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